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- .gitattributes +228 -0
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@@ -4031,3 +4031,231 @@ parse/train/r1te3Fqel/r1te3Fqel_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1te3Fqel/r1te3Fqel_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1te3Fqel/r1te3Fqel_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/wCrH0JBCFNm/wCrH0JBCFNm_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1te3Fqel/r1te3Fqel_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1te3Fqel/r1te3Fqel_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/wCrH0JBCFNm/wCrH0JBCFNm_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/wCrH0JBCFNm/wCrH0JBCFNm_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/wCrH0JBCFNm/wCrH0JBCFNm_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1e5GJBtDr/H1e5GJBtDr_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1e5GJBtDr/H1e5GJBtDr_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/H1e5GJBtDr/H1e5GJBtDr_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HksioDcxl/HksioDcxl_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HksioDcxl/HksioDcxl_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HksioDcxl/HksioDcxl_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/S1jE5L5gl/S1jE5L5gl_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/S1jE5L5gl/S1jE5L5gl_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/S1jE5L5gl/S1jE5L5gl_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/8KokDTctkA8e4/8KokDTctkA8e4_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/8KokDTctkA8e4/8KokDTctkA8e4_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/8KokDTctkA8e4/8KokDTctkA8e4_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/X2K8KVEaAXG/X2K8KVEaAXG_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/X2K8KVEaAXG/X2K8KVEaAXG_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/X2K8KVEaAXG/X2K8KVEaAXG_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BM64dm9HvN/BM64dm9HvN_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BM64dm9HvN/BM64dm9HvN_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BM64dm9HvN/BM64dm9HvN_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/DEsIX_D_vR/DEsIX_D_vR_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/DEsIX_D_vR/DEsIX_D_vR_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/DEsIX_D_vR/DEsIX_D_vR_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ByljMaNKwB/ByljMaNKwB_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ByljMaNKwB/ByljMaNKwB_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ByljMaNKwB/ByljMaNKwB_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BJrFC6ceg/BJrFC6ceg_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BJrFC6ceg/BJrFC6ceg_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BJrFC6ceg/BJrFC6ceg_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HJeYSxHFDS/HJeYSxHFDS_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HJeYSxHFDS/HJeYSxHFDS_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HJeYSxHFDS/HJeYSxHFDS_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SJSVuReCZ/SJSVuReCZ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SJSVuReCZ/SJSVuReCZ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SJSVuReCZ/SJSVuReCZ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1fYuytex/r1fYuytex_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1fYuytex/r1fYuytex_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1fYuytex/r1fYuytex_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1GbfhRqF7/r1GbfhRqF7_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1GbfhRqF7/r1GbfhRqF7_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/r1GbfhRqF7/r1GbfhRqF7_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BkxRRkSKwr/BkxRRkSKwr_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BkxRRkSKwr/BkxRRkSKwr_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/BkxRRkSKwr/BkxRRkSKwr_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ioyq7NsR1KJ/ioyq7NsR1KJ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ioyq7NsR1KJ/ioyq7NsR1KJ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/ioyq7NsR1KJ/ioyq7NsR1KJ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SklD9yrFPS/SklD9yrFPS_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SklD9yrFPS/SklD9yrFPS_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/SklD9yrFPS/SklD9yrFPS_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Xb8xvrtB8Ce/Xb8xvrtB8Ce_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Xb8xvrtB8Ce/Xb8xvrtB8Ce_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/Xb8xvrtB8Ce/Xb8xvrtB8Ce_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/T6AxtOaWydQ/T6AxtOaWydQ_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/T6AxtOaWydQ/T6AxtOaWydQ_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/T6AxtOaWydQ/T6AxtOaWydQ_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/3Aoft6NWFej/3Aoft6NWFej_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/3Aoft6NWFej/3Aoft6NWFej_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/LKUfuWxajHc/LKUfuWxajHc_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/LKUfuWxajHc/LKUfuWxajHc_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/LKUfuWxajHc/LKUfuWxajHc_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/jnRqf0CzBK/jnRqf0CzBK_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/jnRqf0CzBK/jnRqf0CzBK_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/jnRqf0CzBK/jnRqf0CzBK_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/-xEk43f_EO6/-xEk43f_EO6_origin.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/-xEk43f_EO6/-xEk43f_EO6_layout.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/-xEk43f_EO6/-xEk43f_EO6_span.pdf filter=lfs diff=lfs merge=lfs -text
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parse/train/HkxjYoCqKX/HkxjYoCqKX_layout.pdf filter=lfs diff=lfs merge=lfs -text
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| 1 |
+
# Patching open-vocabulary models by interpolating weights
|
| 2 |
+
|
| 3 |
+
Gabriel Ilharco∗1 Mitchell Wortsman∗1 Samir Yitzhak Gadre∗2 Shuran Song2 Hannaneh Hajishirzi1,3 Simon Kornblith4 Ali Farhadi1 Ludwig Schmidt1,3 1University of Washington 2Columbia University 3AI2 4Google Research, Brain Team
|
| 4 |
+
|
| 5 |
+
# Abstract
|
| 6 |
+
|
| 7 |
+
Open-vocabulary models like CLIP achieve high accuracy across many image classification tasks. However, there are still settings where their zero-shot performance is far from optimal. We study model patching, where the goal is to improve accuracy on specific tasks without degrading accuracy on tasks where performance is already adequate. Towards this goal, we introduce PAINT, a patching method that uses interpolations between the weights of a model before fine-tuning and the weights after fine-tuning on a task to be patched. On nine tasks where zeroshot CLIP performs poorly, PAINT increases accuracy by 15 to 60 percentage points while preserving accuracy on ImageNet within one percentage point of the zero-shot model. PAINT also allows a single model to be patched on multiple tasks and improves with model scale. Furthermore, we identify cases of broad transfer, where patching on one task increases accuracy on other tasks even when the tasks have disjoint classes. Finally, we investigate applications beyond common benchmarks such as counting or reducing the impact of typographic attacks on CLIP. Our findings demonstrate that it is possible to expand the set of tasks on which open-vocabulary models achieve high accuracy without re-training them from scratch.
|
| 8 |
+
|
| 9 |
+
# 1 Introduction
|
| 10 |
+
|
| 11 |
+
Open-vocabulary models are characterized by their ability to perform any image classification task based on text descriptions of the classes [56]. Thanks to advances in large-scale pre-training, recent examples of open-vocabulary models such as CLIP and BASIC have reached parity with or surpassed important task-specific baselines, even when the open-vocabulary models are not fine-tuned on task-specific data (i.e., in a zero-shot setting) [57, 31, 56, 88, 1, 86]. For instance, the largest CLIP model from Radford et al. [57] used in a zero-shot setting matches the ImageNet accuracy of a ResNet-50 trained on 1.2 million ImageNet images [14, 24].
|
| 12 |
+
|
| 13 |
+
Nevertheless, current open-vocabulary models still face challenges. The same CLIP model that matches a ResNet-50 on ImageNet has lower MNIST accuracy than simple logistic regression in pixel space [57]. Moreover, even when zero-shot models achieve good performance, they are usually still worse than models trained or fine-tuned on specific downstream tasks.
|
| 14 |
+
|
| 15 |
+
To address these issues, several authors have proposed methods for adapting zero-shot models to a task of interest using labeled data [82, 91, 21, 89, 37, 73]. A common practice is to fine-tune the zero-shot model on the task of interest [82, 56]. However, fine-tuned models can suffer from catastrophic forgetting [48, 76, 20, 33], performing poorly on tasks where the zero-shot model initially performed well [2, 82, 56]. Additionally, fine-tuning typically produces a task-specific classification head, sacrificing the flexible text-based API that makes open-vocabulary models so appealing. Whereas an open-vocabulary model can perform any classification task in a zero-shot fashion, a fine-tuned model with a task-specific head can only process the specific task that it was fine-tuned on. This specialization can prevent knowledge obtained by fine-tuning on one task from transferring to other related tasks with different classes.
|
| 16 |
+
|
| 17 |
+
|
| 18 |
+
Figure 1: Patching open-vocabulary models by linearly interpolating weights. We wish to improve accuracy on tasks where a model performs poorly (patching tasks), without degrading performance on tasks where accuracy is already adequate (supported tasks). When interpolating weights of fine-tuned models and zeroshot (unpatched) models, there are intermediate solutions where accuracy improves on the patching task without reducing accuracy on supported tasks. Results are shown for CLIP models [57], averaged over nine patching tasks (Stanford Cars, DTD, EuroSAT, GTSRB, KITTI distance, MNIST, RESISC45, SUN397 and SVHN [35, 11, 25, 71, 22, 39, 7, 12, 84, 53]) and five supported tasks (ImageNet, CIFAR-10, CIFAR-100, STL-10 and Food101 [14, 36, 12, 5]). We apply PAINT separately on each patching task and average results across experiments. The dashed lines illustrate vertical movement from the unpatched models and horizontal movement from the fine-tuned models.
|
| 19 |
+
|
| 20 |
+
Another approach to adapting zero-shot models would be to add data from the downstream task to the pre-training dataset and train a new open-vocabulary model from scratch. The resulting model could still perform any classification task, and zero-shot performance may improve on related tasks. However, training large image-text models from scratch can require hundreds of thousands of GPU hours [57, 56, 86], which makes this approach practically infeasible in most settings.
|
| 21 |
+
|
| 22 |
+
In this paper, we study patching open-vocabulary models, where the goal is to increase accuracy on new target tasks while maintaining the flexibility of the model and its accuracy on other tasks.1 Patching aims to combine the benefits of fine-tuning and re-training from scratch: improved performance on the task of interest, maintaining the flexibility of an open vocabulary, transfer between tasks, and fast adaptation time. Motivated by these goals, we extend existing fine-tuning techniques [82] to open-vocabulary settings, where the class space is not fixed. We introduce Patching with Interpolation (PAINT), a simple, two-step procedure for patching models: first, fine-tune the model on the patching task without introducing any task-specific parameters; then, linearly interpolate between the weights of the model before and after fine-tuning. Linearly interpolating neural network weights [52, 19, 54] has been previously used to improve accuracy on a single task [28, 81] or robustness to distribution shift [82]. Indeed, averaging network weights has been explored in continual learning contexts, although for closed-vocabulary models [40].
|
| 23 |
+
|
| 24 |
+
With PAINT, accuracy can improve on new tasks without degrading accuracy on unrelated tasks, as illustrated in Figure 1. For instance, applying PAINT to a CLIP ViT-L/14 [57] independently on nine image classification tasks [35, 11, 25, 71, 22, 39, 7, 84, 53] improves accuracy by 15 to 60 percentage points compared to the unpatched model, while accuracy on ImageNet [14] decreases by less than one percentage point. We also observe a promising trend: patching becomes more effective with model scale (Section 4.1).
|
| 25 |
+
|
| 26 |
+
Beyond single tasks, we show that models can be patched on multiple tasks (Section 5). When patching on nine image classification tasks simultaneously, a single CLIP ViT-L/14 model is competitive with using one specialized model for each task—the average accuracy difference is less than 0.5 percentage points.
|
| 27 |
+
|
| 28 |
+
Moreover, PAINT enables broad transfer (Section 6): accuracy on related tasks can increase, even when the class space changes. For instance, we partition EuroSAT [25], a satellite image dataset, into two halves with disjoint labels. Patching a ViT-L/14 model on the first half improves accuracy on the second half by 7.3 percentage points, even though the classes are unseen during patching.
|
| 29 |
+
|
| 30 |
+
Finally, we investigate PAINT on case studies including typographic attacks [23], counting [32], and visual question answering [4] (Section 7). For instance, applying PAINT using synthetic typographic attacks leads to a model that is less susceptible to typographic attacks in the real world, improving its accuracy by 41 percentage points.
|
| 31 |
+
|
| 32 |
+
In summary:
|
| 33 |
+
|
| 34 |
+
• Even the best pre-trained models are not perfect. We introduce PAINT, a method designed to improve accuracy on new tasks without harming accuracy elsewhere.
|
| 35 |
+
• PAINT incurs no extra computational cost compared to standard fine-tuning, neither during fine-tuning itself nor at inference time.
|
| 36 |
+
• PAINT can also be applied with multiple tasks, providing a single model that is competitive with many specialized models.
|
| 37 |
+
• Applying PAINT with one task can improve accuracy on a related task, even when they do not share the same classes.
|
| 38 |
+
• PAINT improves with model scale, indicating a promising trend for future models.
|
| 39 |
+
|
| 40 |
+
# 2 Patching with interpolation (PAINT)
|
| 41 |
+
|
| 42 |
+
This section details our method for patching models on a single and multiple tasks.
|
| 43 |
+
|
| 44 |
+
Patching on a single task. Given an open-vocabulary model with weights $\theta _ { \mathrm { z s } }$ and a patching task $\mathcal { D } _ { \mathrm { p a t c h } }$ , our goal is to produce a new model $\theta _ { \mathrm { p a t c h } }$ which achieves high accuracy on $\mathcal { D } _ { \mathrm { { p a t c h } } }$ without decreasing model performance on tasks where accuracy is already acceptable. We let $\mathcal { D } _ { \mathrm { s u p p } }$ denote a representative supported task where model performance is adequate, and later show that the method is stable under different choices of $\mathcal { D } _ { \mathrm { s u p p } }$ (Section 4.2). The two-step procedure we explore for producing $\theta _ { \mathrm { p a t c h } }$ is given below.
|
| 45 |
+
|
| 46 |
+
Step 1. Fine-tune $\theta _ { \mathrm { z s } }$ on training data from $\mathcal { D } _ { \mathrm { p a t c h } }$ to produce a model with weights $\theta _ { \mathrm { f t } }$ . Step 2. For mixing coefficient $\alpha \in [ 0 , 1 ]$ , linearly interpolate between $\theta _ { \mathrm { z s } }$ and $\theta _ { \mathrm { f t } }$ to produce $\theta _ { \mathrm { p a t c h } } = ( 1 - \alpha ) \cdot \theta _ { \mathrm { z s } } + \alpha \cdot \theta _ { \mathrm { f t } }$ . The mixing coefficient is determined via held-out validation sets for $\mathcal { D } _ { \mathrm { s u p p } }$ and $\mathcal { D } _ { \mathrm { p a t c h } }$ . We refer to the resulting model as $\theta _ { \mathrm { p a t c h } }$ .
|
| 47 |
+
|
| 48 |
+
In our experiments, we do not introduce any additional task-specific parameters when fine-tuning, as discussed in Section 3 and Appendices B and $\textrm { C }$ .
|
| 49 |
+
|
| 50 |
+
Patching on a multiple tasks. In practice, we often want to improve model accuracy on multiple patching tasks D(1)patch $\mathcal { D } _ { \mathrm { p a t c h } } ^ { ( 1 ) } , . . . , \mathcal { D } _ { \mathrm { p a t c h } } ^ { ( k ) }$ D(k)patch, which can be accomplished with straightforward modifications to the procedure above. We explore three alternatives and examine their relative trade-offs in Section 5:
|
| 51 |
+
|
| 52 |
+
• Joint patching, where we merge all the patching tasks $\mathcal { D } _ { \mathtt { p a t c h } } ^ { ( i ) }$ into a single task $\mathcal { D } _ { \mathrm { p a t c h } }$ before running the patching procedure;
|
| 53 |
+
• Sequential patching, where we iteratively repeat the patching procedure above on each new task
|
| 54 |
+
D(i) and let $\theta _ { \mathrm { z s } } \theta _ { \mathrm { p a t c h } }$ after each completed iteration;
|
| 55 |
+
• Parallel patching, where we apply the first step on each task in parallel to produce fine-tuned $\theta _ { \mathrm { f t } } ^ { ( 1 ) } , . . . , \bar { \theta _ { \mathrm { f t } } ^ { ( k ) } }$ e search for mixing coefficients . $\alpha _ { i }$ to produce $\begin{array} { r } { \theta _ { \mathrm { p a t c h } } = \big ( 1 - \sum _ { i = 1 } ^ { k } \alpha _ { i } \big ) \cdot \theta _ { \mathrm { z s } } + \sum _ { i = 1 } ^ { k } \alpha _ { i } \cdot \theta _ { \mathrm { f t } } ^ { ( i ) } } \end{array}$
|
| 56 |
+
|
| 57 |
+
For joint and parallel patching we assume access to held-out validation sets for all tasks, while in sequential patching we only assume access to held-out validation sets from the tasks seen so far. Unless mentioned otherwise, we pick the mixing coefficient $\alpha$ that optimizes average accuracy on the held-out validation sets from the supported and patching tasks.
|
| 58 |
+
|
| 59 |
+
# 3 Experimental setup
|
| 60 |
+
|
| 61 |
+
Tasks. We consider a diverse set of image classification tasks from Radford et al. [57]. In most experiments, we use ImageNet [14] as a representative supported task, although we explore other supported tasks in Section 4.2. We categorize tasks into patching tasks or supported tasks based on the accuracy difference between the zero-shot model and a model specialized to the task. A large accuracy difference indicates that the task is a relevant target for patching because the zero-shot model is still far from optimal. Specifically, we consider a subset tasks from Radford et al. [57], categorizing tasks where the linear probes outperform the zero-shot model by over 10 percentage points as patching tasks: Cars [35], DTD [11], EuroSAT [25], GTSRB [71], KITTI [22], MNIST [39], RESISC45 [7], SUN397 [84], and SVHN [53]. We use the remaining tasks as supported tasks: CIFAR10 [36], CIFAR100 [36], Food101 [5], ImageNet [14], and STL10 [12]. We investigate additional patching tasks as case studies in Section 7 and provide further details in Appendix A.
|
| 62 |
+
|
| 63 |
+
Models. We primarily use CLIP [57] pre-trained vision transformer (ViT) models [15]. Unless otherwise mentioned our experiments are with the ViT-L/14 model, while Section 4.2 studies ResNets [24].
|
| 64 |
+
|
| 65 |
+
Fine-tuning on patching tasks. Unless otherwise mentioned, we fine-tune with a batch size of 128 for 2000 iterations using learning rate 1e-5 with 200 warm-up steps with a cosine annealing learning rate schedule and the AdamW optimizer [43, 55] (weight decay 0.1). When fine-tuning, we use the frozen final classification layer output by CLIP’s text tower so that we do not introduce additional learnable parameters. This design decision keeps the model open-vocabulary and does not harm accuracy, as discussed in in Appendices B and C.
|
| 66 |
+
|
| 67 |
+
Evaluation. We use accuracy as the evaluation metric unless otherwise stated. We refer to the average of the mean accuracy on the patching tasks and the mean accuracy on the supported tasks as combined accuracy.2
|
| 68 |
+
|
| 69 |
+
# 4 Patching models on a single new task
|
| 70 |
+
|
| 71 |
+
As shown in Figure 1, when patching a model on a single task, we interpolate the weights of the zero-shot and fine-tuned model, producing a model that achieves high accuracy on both the patching task and the supported task. On the nine tasks, PAINT improves the accuracy of ViT-L/14 by 15 to 60 percentage points, while accuracy on ImageNet decreases by less than one percentage point. PAINT also allows practitioners to control the accuracy trade-off on the patching and supported tasks without re-training a new model, by varying the mixing coefficient $\alpha$ .
|
| 72 |
+
|
| 73 |
+
# 4.1 The effect of scale
|
| 74 |
+
|
| 75 |
+
We consistently observe that PAINT is more effective for larger models. Our findings are aligned with those of Ramasesh et al. [59], who observed that larger models are less susceptible to catastrophic forgetting. This section formalizes and provides insights for these observations.
|
| 76 |
+
|
| 77 |
+
Measuring the effectiveness of patching. We measure the effectiveness of patching via the accuracy difference between the single patched model and two specialized models with the same architecture and initialization. For both the supported task and patching task, we take specialized models that maximize performance on the task, considering the set of all interpolations between the zero-shot and fine-tuned models. We refer to this measure as accuracy distance to optimal. Formally, accuracy distance to optimal is given by
|
| 78 |
+
|
| 79 |
+
$$
|
| 80 |
+
\frac { 1 } { 2 } \left[ \operatorname* { m a x } _ { \alpha } \mathsf { A c c } ( \theta _ { \alpha } , { \mathcal D } _ { \mathrm { s u p p } } ) + \operatorname* { m a x } _ { \alpha } \mathsf { A c c } ( \theta _ { \alpha } , { \mathcal D } _ { \mathrm { p a t c h } } ) \right] - \frac { 1 } { 2 } \operatorname* { m a x } _ { \alpha } \left[ \mathsf { A c c } ( \theta _ { \alpha } , { \mathcal D } _ { \mathrm { s u p p } } ) + \mathsf { A c c } ( \theta _ { \alpha } , { \mathcal D } _ { \mathrm { p a t c h } } ) \right] ,
|
| 81 |
+
$$
|
| 82 |
+
|
| 83 |
+
where $\operatorname { A c c } ( \theta , { \mathcal { D } } )$ represents the accuracy of model $\theta$ on task $\mathcal { D }$ . In Figure 2 (left), we show that accuracy distance to optimal decreases with scale, indicating that patching becomes more effective for larger models.
|
| 84 |
+
|
| 85 |
+
Model similarity. Fine-tuning modifies overparameterized models less [9], which provides insights on why larger models are easier to patch: less movement is required to fit new data. We demonstrate this by evaluating representational similarity using Centered Kernel Alignment (CKA) [34] (see Appendix $\mathrm { D }$ for details). As shown in Figure 2 (center), the representations of the unpatched and fine-tuned models become more similar as models grow larger, indicated by larger CKA values. Moreover, Figure 2 (right) shows that the cosine similarity between the weights of the unpatched and fine-tuned models, $\mathrm { c o s } \bar { ( \theta _ { \mathrm { z s } } , \theta _ { \mathrm { f t } } ) } = { \langle \theta _ { \mathrm { z s } } , \theta _ { \mathrm { f t } } \rangle } / ( { | | \theta _ { \mathrm { z s } } | } { | | \theta _ { \mathrm { f t } } | } { | | } )$ , increases with scale.
|
| 86 |
+
|
| 87 |
+
|
| 88 |
+
Figure 2: Larger models are easier to patch (left). For larger models, the unpatched and fine-tuned model are more similar with respect to their representations (center) and weights (right). Model scale is measured in Giga Multiply-Accumulate operations (GMACs).
|
| 89 |
+
|
| 90 |
+
|
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Figure 3: The frontier of accuracy trade-offs can be recovered by linearly interpolating weights. Interpolating the unpatched and fine-tuned models recovers the accuracy trade-off of early stopping, regularization towards the initialization, and changes in hyperparameters. Additional details and comparisons can be found in Appendix E.
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# 4.2 Baselines and ablations
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Baselines. There are many alternatives which enable a trade-off between accuracy on the supported and patching tasks. These methods include early stopping during fine-tuning, applying a regularization term which penalizes movement from initialization, or training with different hyperparameters including a smaller learning rate. Unlike interpolation, these methods do not enable navigating the accuracy trade-off without fine-tuning the model again many times. Moreover, Figure 3 demonstrates that the accuracy trade-off frontier for early stopping, regularization, or varying hyperparameters can be recovered by interpolating weights with different mixing coefficients. Appendix $\mathrm { E }$ provides additional baselines and discussion, including EMA [74], EWC [33], LwF [41], re-training a model with data from the patching task, and mixing the pre-training and fine-tuning objectives.
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Additional supported tasks. In Figure 1, we use ImageNet as a representative supported task. This section demonstrates that PAINT is stable under different choices of the supported task. Instead of ImageNet, we use CIFAR10, CIFAR100, Food101 and STL10. Figure 4 displays representative results, where performance is averaged over the nine patching tasks (see Appendix $\mathrm { F }$ for additional results). We observe consistent results across supported tasks, and that the optimal mixing coefficients are stable across different choices of supported tasks (Figure 4, right).
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Additional models. In addition to the CLIP ViTs used in the majority of our experiments, we study four ResNet models [24] from Radford et al. [57] in Appendix G. We find that patching is less effective for ResNets compared to ViTs of similar size, which corroborates the findings of Ramasesh et al. [59] that ResNets are generally more susceptible to catastrophic forgetting. However, similarly to ViTs, we still observe improvements with scale. Finally, we show that patching is also effective for closed-vocabulary models in Appendix H.
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Figure 4: Results are consistent across supported tasks. For multiple supported tasks, we observe similar accuracy improvements on patching tasks, without substantially decreasing supported task accuracy. Additional results for the supported tasks Food101, STL10 and ImageNet are in Appendix F. Moreover, choosing the mixing coefficients using a different supported task does not substantially decrease combined accuracy on patching and supported tasks (right).
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# 5 Patching models on multiple tasks
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This section details experimental results for patching on multiple datasets. Recall from Section 2 that there are various strategies for extending PAINT to multiple datasets, which we briefly revisit. For joint patching we merge all the datasets into a single fine-tuning task and apply our patching procedure as before. For sequential patching we iteratively perform our procedure once per task, using the patched model at each step as the initialization for the next step.3 We also explore parallel patching, for which we have an unpatched model $\theta _ { \mathrm { z s } }$ and independently fine-tune on each of the tasks in parallel. We then search for mixing coefficients to combine the resulting models. For tasks $1 , . . . , k$ , let θ(1)ft , . $\theta _ { \mathrm { f t } } ^ { ( 1 ) } , . . . , \theta _ { \mathrm { f t } } ^ { ( k ) }$ denote the fine-tuned models for each task. Since it is impractical to exhaustively search over each $\alpha _ { i }$ , we instead search over a one-dimensional scalar $\alpha \in [ 0 , 1 ]$ , which interpolates between $\theta _ { \mathrm { z s } }$ and the average of all fine-tuned solutions $\begin{array} { r } { \frac { 1 } { k } \sum _ { i = 1 } ^ { k } \theta _ { \mathrm { f t } } ^ { ( i ) } } \end{array}$ .4 Appendix J provides further experimental details.
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These methods have various trade-offs and may be applicable for different scenarios. Joint patching is only possible when data from all tasks you wish to patch is available. On the other hand, sequential patching is appropriate when the tasks are observed one after another. Finally, parallel patching can leverage distributed hardware.
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Figure 5 displays experimental results when patching on all nine tasks from Section 4. We observe that joint patching is the best-performing method on average. This is perhaps unsurprising since joint patching has simultaneous access to all patching datasets, unlike other patching strategies. Nevertheless, it is still interesting that for ViT-L/14, joint patching yields a single model with only 0.5 percentage points worse combined accuracy than using multiple specialized models.5 Joint patching also achieves a 15.8 percentage points improvement over the unpatched model. Moreover, patching a ViT-B/32 model with the joint strategy achieves a combined accuracy 6.1 percentage points higher than a ViT-L/14 unpatched model, which requires $1 2 \mathbf { x }$ more GMACs.
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The accuracy of sequential patching approaches that of joint patching, especially for larger models. Note that, unlike in joint patching, forgetting can compound since the patching procedure is applied multiple times in sequence. In sequential patching, weight interpolations do not completely eradicate forgetting, but greatly mitigate it. This is most noticeable for smaller models: sequentially fine-tuning a ViT-B/32 without interpolation reduces the combined accuracy by 4.6 percentage points compared to the unpatched model, as shown in Appendix J. This is compared to a combined accuracy increase of 11 percentage points when using sequential patching. Additional results, including experiments on SplitCIFAR [61], can be found in Appendix J.
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Finally, parallel patching underperforms other patching strategies. Like sequential patching, parallel patching is in the challenging setting where data from all patching tasks is not available simultaneously.
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Figure 5: Contrasting various strategies for patching on multiple tasks. On all experiments, ImageNet is used as the supported task while the other nine datasets are used for patching. When data from all patching tasks is available, joint patching yields a single model that is competitive with using ten different specialized models. Weight interpolations greatly mitigate catastrophic forgetting on the sequential case, but do not completely eradicate it. Finally, parallel patching underperforms other patching strategies, but still provides improvements over the unpatched model.
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<table><tr><td></td><td>Cars</td><td>DTD</td><td>EuroSAT</td><td>GTSRB</td><td>KITTI</td><td>MNIST</td><td>RESISC45</td><td>SUN397</td><td>SVHN</td></tr><tr><td>Unpatched accuracy</td><td>86.2</td><td>64.9</td><td>79.9</td><td>51.7</td><td>43.4</td><td>82.6</td><td>73.4</td><td>76.9</td><td>72.8</td></tr><tr><td>Patched accuracy</td><td>87.0 (+0.8)</td><td>66.1 (+1.2)</td><td>87.2 (+7.3)</td><td>71.1 (+19.4)</td><td>60.4 (+17.0)</td><td>91.3 (+8.7)</td><td>74.2 (+0.8)</td><td>79.3 (+2.4)</td><td>88.9 (+16.1)</td></tr></table>
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Table 1: PAINT can generalize to unseen classes. We randomly partition each dataset into tasks $A$ and $B$ with disjoint class spaces of roughly equal size. This table reports how patching on task $A$ affects accuracy on task $B$ for the ViT-L/14 model. In all cases, accuracy on task $B$ improves when patching on task $A$ even though the classes are unseen during patching.
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Moreover, unlike in joint or sequential patching, no model is optimized on data from all patching tasks. Using a black box optimization algorithm for finding the mixing coefficients did not yield large improvements over using the same mixing coefficient for all models. However, it is possible that more sophisticated search methods could yield better results. In Appendix J, we present additional experiments for a subset of the tasks where exhaustively searching the space of mixing coefficients is tractable, finding headroom for improvement in most cases.
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# 6 Broad transfer
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An alternative to our patching approach is to introduce parameters which are specific to each new task. By contrast, PAINT always maintains a single model. This section describes an additional advantage of the single model approach: patching the model on task $A$ can improve accuracy on task $B$ , even when task $A$ and $B$ do not share the same classes. We refer to this phenomenon as broad transfer. Note that we are able to study this phenomenon because the single patched model remains open-vocabulary throughout the patching procedure. This is a key advantage of PAINT compared to maintaining a collection of task-specific models.
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We now describe two experiments to measure the effects on a task $B$ when patching the model on a task $A$ . First, we explore broad transfer by randomly partitioning datasets into disjoint sets with no class overlap. For a dataset $\mathcal { D }$ we partition the class space $\mathcal { V }$ into two disjoint sets of roughly equal size $\mathcal { V } _ { A }$ and $\mathcal { { V } } _ { B }$ . We build task $A$ with the examples $( x , y ) \in \mathcal { D }$ where $y$ belongs to $\mathcal { V } _ { A }$ , and task $B$ with examples $( x , y )$ where $y$ belongs to $\mathcal { { V } } _ { B }$ . Table 1 shows how patching a model on task $A$ affects the accuracy on task $B$ for nine datasets $\mathcal { D }$ . The accuracy improvements on task $B$ range from 0.8 to 19.4 percentage points, even though the classes from task $B$ are not seen during patching.
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To further understand transfer, we consider additional task pairs $A$ and $B$ , which are now different datasets. While some pairs $A$ , $B$ share classes, there are still instances of broad transfer. Concretely,
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Table 2: Patching on task $A$ can improve accuracy on a related task $B$ . For a pair of tasks $A$ and $B$ , we report accuracy of the ViT-L/14 on task $B$ , after patching on task $A$ , finding improvements on seven out of eight cases.
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<table><tr><td>Task A Task B</td><td>MNIST SVHN SVHN</td><td>MNISTRESISC45</td><td>EuroSAT RESISC45</td><td>MNIST EuroSAT FashionMNIST</td><td>FashionMNISTGTSRB MNIST</td><td>MTSD MTSD GTSRB</td></tr><tr><td>Unpatched accuracy</td><td>58.6</td><td>76.4 71.0</td><td>60.2</td><td>67.7</td><td>76.4</td><td>19.3 50.6</td></tr><tr><td>Patched accuracy</td><td>68.9 93.2 (+10.3) ） (+16.8)</td><td>69.7 (-1.3)</td><td>70.4 (+10.2)</td><td>70.8 (+3.1)</td><td>77.5 (+1.1)</td><td>30.8 69.8 (+11.5) (+19.2)</td></tr></table>
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Figure 6: Guarding against real-world typographic attacks by patching on synthetic data. (a) A sample from our real-world typographic attacks test set. A CLIP ViT-L/14 is “tricked” into classifying this image as a dog instead of a cat. (b) Sample of synthetic typographic attack data. (c) Performance on real-world data with unseen classes after patching on only synthetic typographic attacks (curves produced by interpolating between the unpatched and fine-tuned model). (d) Analogous curves for the test set of the synthetic data used for patching.
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Table 2 examines i) MNIST and SVHN, two digit recognition tasks with shared classes; ii) EuroSAT and RESISC45, two satellite imagery recognition tasks where there are unshared classes but some overlap; iii) GTSRB and MTSD [17], two traffic sign recognition datasets where there are unshared classes but some overlap; and iv) MNIST and FashionMNIST [83], which do not share any classes but appear visually similar. In seven out of eight experiments, patching on task $A$ improves accuracy by 1.1 to 19.2 percentage points on task $B$ . The exception is when $A$ is EuroSAT and $B$ is RESISC45, where accuracy decreases by 1.3 percentage points.
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In all experiments, when patching on task $A$ we choose the mixing coefficient $\alpha$ by optimizing the held-out validation accuracy on task $A$ and a supported task (in this experiment we use ImageNet). While it is possible for a method that introduces new parameters for each task to exhibit broad transfer to new data, this also requires knowing which parameters to apply for the new data. This is not necessary in the single model approach.
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# 7 Case studies
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We further examine the performance of PAINT in three additional settings, which highlight weaknesses of the zero-shot CLIP model and showcase broad transfer (Section 6).
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Typographic attacks. Goh et al. [23] find that CLIP models are susceptible to typographic attacks, where text superimposed on an image leads to misclassification. For example, in Figure $6 ( a )$ , the text on the pink note saying “dog” leads a CLIP to misclassify the image of a cat as a dog. To fix this vulnerability, we procedurally generate typographic attack data by adding text with incorrect class names to SUN397 [84], as seen in Figure 6 $( b )$ . We then collect a test set of 110 real world images by placing notes on objects and taking photos.6 After applying PAINT using the synthetic data, we evaluate on the real-world images (Figure 6 (c)) and synthetic test set (Figure 6 (d)). We observe that while larger models are more susceptible to typographic attacks, they are also more amenable to patching. Furthermore, we see an example of broad transfer between the synthetic and real-world data: when patching ViT-L/14 on synthetic data, its accuracy on real-world typographic attacks improves 41 percentage points even though the real-world classes are unseen. The cost is a reduction of less than 1 percentage point on ImageNet. We present details on the task and data collection in Appendix K.
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Counting. Radford et al. [57] find that CLIP models struggle to count the number of objects in CLEVR [32]. Here, the task is to choose an integer between 3 and 10 for each image, corresponding to the number of visible objects. While a straightforward way to patch such a task is to fine-tune on it directly, we investigate if applying PAINT using a subset of the classes allows the patched model to generalize to other numbers. Specifically, we patch on images with 4, 5, 6, 8, or 9 objects. To evaluate broad transfer, we test on images with 3, 7, and 10 objects (7 for understanding interpolation and 3 and 10 for extrapolation). We find that PAINT improves accuracy from $59 \%$ to over $9 9 \%$ o n unseen classes with less than half a percentage point decrease in ImageNet accuracy. For more details see Appendix L.
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Visual question answering. As shown by Shen et al. [68], zero-shot CLIP models perform poorly on visual question answering [4]. Using CLIP for VQA typically involves additional parameters—for instance, Shen et al. [68] trains a transformer [77] on CLIP features. In contrast, our procedure for patching CLIP on VQA does not introduce new parameters. Following Shen et al. [68], we contrast images with a series of text prompts, where each prompt corresponds to an option in multiple-choice VQA, formed by both the question and a candidate answer using the following template: “Question: [question text] Answer: [answer text]”. We evaluate on multiple-choice VQA v1 [4], where each question is associated with 18 candidate answers. Our results, further detailed in Appendix M, show that patching is effective for visual question answering: PAINT improves the accuracy of a ViT-L/14 model by 18 percentage points, while accuracy drops by less than one percentage point on ImageNet.
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# 8 Related work
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Continual learning and catastrophic forgetting. Learning tasks sequentially remains a challenge for neural networks. When a neural network learns a new task, the accuracy on other tasks often decreases, a phenomenon known as catastrophic forgetting [48, 76, 20, 33]. While forgetting in neural networks may actually aid learning [90], researchers have proposed various approaches for alleviating catastrophic forgetting, including: i) Regularization-based approaches such as elastic weight consolidation (EWC) [33] and synaptic intelligence (SI) [87] which penalize the movement of parameters and are related to weight-interpolation by Lubana et al. [44]; ii) Replay methods [61, 69, 42, 6, 64, 50], which incorporate data or gradient information from previous tasks when learning a new task; and iii) Introducing task-specific parameters [65, 85, 46, 8, 78, 80].
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In contrast to these approaches, PAINT requires no modification to the standard fine-tuning process besides the later weight interpolation step. Moreover, unlike regularization or replay based methods, PAINT requires no extra computational cost during training. In contrast to methods with task specific parameters, we maintain a single model. Having a single model is beneficial when there is new data which is similar to one of the tasks which have already been patched. Even without explicitly knowing which task the new data is similar to, we can observe accuracy improvements (see Section 6).
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Similar to our work is that of Mirzadeh et al. [50], who observe high accuracy on task A on the linear path between a model which achieves high accuracy on task A and a model which is fine-tuned jointly on task A and B. Moreover, they observe high accuracy on task B on the linear path between a model fine-tuned on task B, and the jointly fine-tuned model. Therefore, there exists a path between a model which achieves good performance on task A and a model fine-tuned on task B along which accuracy is high on both tasks. However, in Mirzadeh et al. [50] this combined path can be non-linear, leading them to propose a regularization and replay based method. In our work, we find that examining models on a linear path between the unpatched model (which has high accuracy on task A) and the model fine-tuned on task B is often sufficient for obtaining a model which achieves high accuracy on both tasks (Figure 1). We speculate that this is due to scale and model architecture: in contrast to Mirzadeh et al. [50], we initialize with a model pre-trained on a large dataset consisting of 400 million images [57], and primarily use vision transformers [15]. As shown in Section 4.2, our method performs substantially worse with ResNets [24], which are used by Mirzadeh et al. [50].
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Finally, Ramasesh et al. [59] and Mehta et al. [49] also observed that catastrophic forgetting is less problematic for large and pre-trained models. In addition, Ramasesh et al. [59] found—similar to our results—that vision transformers are less susceptible to forgetting than ResNets of the same size.
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Linear mode connectivity and robust fine-tuning. Linearly interpolating neural network weights is a key step in PAINT. Because of the many nonlinear activations in a neural network, it is not clear a priori that linearly interpolating between two sets of weights can result in a high accuracy solution. However, researchers have observed that interpolating neural network weights can achieve high accuracy when training on MNIST from a common initialization [52] or when part of the optimization trajectory is shared [19, 28, 54, 18, 82, 47, 16, 81, 10]. The term linear mode connectivity was coined by Frankle et al. [19]: two networks exhibit linearly mode connectivity if the accuracy does not decrease when using weights on the linear path between them [52, 19]. Weight averaging for continual learning has also been studied by Lee et al. [40] for closed-vocabulary models.
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While Nagarajan and Kolter [52] and Frankle et al. [19] focused on accuracy on a single task, Wortsman et al. [82] use linear mode connectivity to fine-tune models while preserving their robustness to natural distribution shifts. By interpolating the weights of a zero-shot and fine-tuned model, they find a solution which performs well both on the fine-tuning task and under distribution shift. In contrast to Wortsman et al. [82], we do not modify any task-specific parameters when fine-tuning, preserving the open-vocabulary nature of the models we patch. Unlike Wortsman et al. [82], we examine accuracy trade-offs across different tasks with little or no class overlap and adapt a model to multiple tasks.
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In addition, closely related to our work is that of Matena and Raffel [47], who use Fisher-weighted averaging of language models before and after fine-tuning on downstream tasks. Unlike Fisherweighted averaging of Matena and Raffel [47], we do not use different mixing coefficients for each parameter, and thus require no extra compute when patching. Moreover, we explore new strategies for patching on multiple tasks (see Section 5), and focus on open-vocabulary image classifiers.
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Interventions to change the behavior of a trained model. Several authors have studied the problem of updating a model to locally alter its behavior on certain inputs without external disruptions on other inputs [70, 13, 51, 66, 63, 62]. Previous literature uses various terms to refer to this process, including model editing, patching or debugging. A popular use case is to update trained language models to reflect changes in the world (for instance, facts like who is the current president of Brazil) [29, 45, 38, 30]. Moreover, inspired by software engineering practice, previous work explored “debugging” language models through user interaction [63, 62], including providing corrective feedback to the models via natural language [3]. Mitchell et al. [51], De Cao et al. [13] propose training auxiliary networks to perform local edits on pre-trained models. Santurkar et al. [66] introduce a method for rewriting the prediction rules of a classifier, focusing on specific failure modes such as reliance on spurious correlations. In contrast with previous literature, our work explores patching models at the task level, aiming to systemically improve accuracy on a dataset—for instance, enabling a model to recognize dozens of satellite imagery classes with a single patch.
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# 9 Limitations and conclusion
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Limitations. When applying PAINT, accuracy on supported tasks can still decrease, especially for smaller models. This limitation is perhaps best reflected in the case of sequential patching: patched models underperform using multiple specialized models when many tasks are added sequentially. Using larger models and weight interpolations can alleviate this issue, but do not completely resolve it. Finally, better understanding on which datasets patching is more effective is an exciting direction for future research.
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Conclusion. In this work, we explore several techniques for patching open-vocabulary models with the goal of improving accuracy on new tasks without decreasing accuracy elsewhere. PAINT is effective in several scenarios, ranging from classifying digits to defending against typographic attacks. PAINT becomes more effective with scale, and can be applied on multiple tasks sequentially or simultaneously. Our findings demonstrate that in many circumstances it is possible to expand the set of tasks on which models achieve high accuracy, without introducing new parameters, without re-training them from scratch, and without catastrophic forgetting.
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# Acknowledgments
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We thank Akari Asai, Alex Fang, David Fleet, Huy Ha, Ari Holtzman, Pieter-Jan Kindermans, Marco Tulio Ribeiro, Ofir Press, Sarah Pratt, Sewon Min, Thao Nguyen and Tim Dettmers for helpful discussions and feedback, and Hyak at UW for computing support. This work is in part supported by the NSF AI Institute for Foundations of Machine Learning (IFML), Open Philanthropy, NSF IIS 1652052, NSF IIS 17303166, NSF IIS 2044660, NSF IIS 2132519, ONR N00014-18-1-2826, DARPA N66001-19-2-4031, DARPA W911NF-15-1-0543, the Sloan Fellowship and gifts from Allen Institute for AI.
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|
| 1 |
+
[
|
| 2 |
+
{
|
| 3 |
+
"type": "text",
|
| 4 |
+
"text": "Patching open-vocabulary models by interpolating weights ",
|
| 5 |
+
"text_level": 1,
|
| 6 |
+
"bbox": [
|
| 7 |
+
294,
|
| 8 |
+
123,
|
| 9 |
+
702,
|
| 10 |
+
172
|
| 11 |
+
],
|
| 12 |
+
"page_idx": 0
|
| 13 |
+
},
|
| 14 |
+
{
|
| 15 |
+
"type": "text",
|
| 16 |
+
"text": "Gabriel Ilharco∗1 Mitchell Wortsman∗1 Samir Yitzhak Gadre∗2 Shuran Song2 Hannaneh Hajishirzi1,3 Simon Kornblith4 Ali Farhadi1 Ludwig Schmidt1,3 1University of Washington 2Columbia University 3AI2 4Google Research, Brain Team ",
|
| 17 |
+
"bbox": [
|
| 18 |
+
202,
|
| 19 |
+
224,
|
| 20 |
+
795,
|
| 21 |
+
268
|
| 22 |
+
],
|
| 23 |
+
"page_idx": 0
|
| 24 |
+
},
|
| 25 |
+
{
|
| 26 |
+
"type": "text",
|
| 27 |
+
"text": "Abstract ",
|
| 28 |
+
"text_level": 1,
|
| 29 |
+
"bbox": [
|
| 30 |
+
462,
|
| 31 |
+
305,
|
| 32 |
+
535,
|
| 33 |
+
321
|
| 34 |
+
],
|
| 35 |
+
"page_idx": 0
|
| 36 |
+
},
|
| 37 |
+
{
|
| 38 |
+
"type": "text",
|
| 39 |
+
"text": "Open-vocabulary models like CLIP achieve high accuracy across many image classification tasks. However, there are still settings where their zero-shot performance is far from optimal. We study model patching, where the goal is to improve accuracy on specific tasks without degrading accuracy on tasks where performance is already adequate. Towards this goal, we introduce PAINT, a patching method that uses interpolations between the weights of a model before fine-tuning and the weights after fine-tuning on a task to be patched. On nine tasks where zeroshot CLIP performs poorly, PAINT increases accuracy by 15 to 60 percentage points while preserving accuracy on ImageNet within one percentage point of the zero-shot model. PAINT also allows a single model to be patched on multiple tasks and improves with model scale. Furthermore, we identify cases of broad transfer, where patching on one task increases accuracy on other tasks even when the tasks have disjoint classes. Finally, we investigate applications beyond common benchmarks such as counting or reducing the impact of typographic attacks on CLIP. Our findings demonstrate that it is possible to expand the set of tasks on which open-vocabulary models achieve high accuracy without re-training them from scratch. ",
|
| 40 |
+
"bbox": [
|
| 41 |
+
233,
|
| 42 |
+
330,
|
| 43 |
+
766,
|
| 44 |
+
564
|
| 45 |
+
],
|
| 46 |
+
"page_idx": 0
|
| 47 |
+
},
|
| 48 |
+
{
|
| 49 |
+
"type": "text",
|
| 50 |
+
"text": "1 Introduction ",
|
| 51 |
+
"text_level": 1,
|
| 52 |
+
"bbox": [
|
| 53 |
+
174,
|
| 54 |
+
579,
|
| 55 |
+
310,
|
| 56 |
+
595
|
| 57 |
+
],
|
| 58 |
+
"page_idx": 0
|
| 59 |
+
},
|
| 60 |
+
{
|
| 61 |
+
"type": "text",
|
| 62 |
+
"text": "Open-vocabulary models are characterized by their ability to perform any image classification task based on text descriptions of the classes [56]. Thanks to advances in large-scale pre-training, recent examples of open-vocabulary models such as CLIP and BASIC have reached parity with or surpassed important task-specific baselines, even when the open-vocabulary models are not fine-tuned on task-specific data (i.e., in a zero-shot setting) [57, 31, 56, 88, 1, 86]. For instance, the largest CLIP model from Radford et al. [57] used in a zero-shot setting matches the ImageNet accuracy of a ResNet-50 trained on 1.2 million ImageNet images [14, 24]. ",
|
| 63 |
+
"bbox": [
|
| 64 |
+
174,
|
| 65 |
+
603,
|
| 66 |
+
825,
|
| 67 |
+
700
|
| 68 |
+
],
|
| 69 |
+
"page_idx": 0
|
| 70 |
+
},
|
| 71 |
+
{
|
| 72 |
+
"type": "text",
|
| 73 |
+
"text": "Nevertheless, current open-vocabulary models still face challenges. The same CLIP model that matches a ResNet-50 on ImageNet has lower MNIST accuracy than simple logistic regression in pixel space [57]. Moreover, even when zero-shot models achieve good performance, they are usually still worse than models trained or fine-tuned on specific downstream tasks. ",
|
| 74 |
+
"bbox": [
|
| 75 |
+
176,
|
| 76 |
+
707,
|
| 77 |
+
825,
|
| 78 |
+
762
|
| 79 |
+
],
|
| 80 |
+
"page_idx": 0
|
| 81 |
+
},
|
| 82 |
+
{
|
| 83 |
+
"type": "text",
|
| 84 |
+
"text": "To address these issues, several authors have proposed methods for adapting zero-shot models to a task of interest using labeled data [82, 91, 21, 89, 37, 73]. A common practice is to fine-tune the zero-shot model on the task of interest [82, 56]. However, fine-tuned models can suffer from catastrophic forgetting [48, 76, 20, 33], performing poorly on tasks where the zero-shot model initially performed well [2, 82, 56]. Additionally, fine-tuning typically produces a task-specific classification head, sacrificing the flexible text-based API that makes open-vocabulary models so appealing. Whereas an open-vocabulary model can perform any classification task in a zero-shot fashion, a fine-tuned model with a task-specific head can only process the specific task that it was fine-tuned on. This specialization can prevent knowledge obtained by fine-tuning on one task from transferring to other related tasks with different classes. ",
|
| 85 |
+
"bbox": [
|
| 86 |
+
174,
|
| 87 |
+
768,
|
| 88 |
+
825,
|
| 89 |
+
866
|
| 90 |
+
],
|
| 91 |
+
"page_idx": 0
|
| 92 |
+
},
|
| 93 |
+
{
|
| 94 |
+
"type": "image",
|
| 95 |
+
"img_path": "images/27454f67282ad59a0cde948bc9974465c3d8f122323b75d055c62f58685f01e7.jpg",
|
| 96 |
+
"image_caption": [
|
| 97 |
+
"Figure 1: Patching open-vocabulary models by linearly interpolating weights. We wish to improve accuracy on tasks where a model performs poorly (patching tasks), without degrading performance on tasks where accuracy is already adequate (supported tasks). When interpolating weights of fine-tuned models and zeroshot (unpatched) models, there are intermediate solutions where accuracy improves on the patching task without reducing accuracy on supported tasks. Results are shown for CLIP models [57], averaged over nine patching tasks (Stanford Cars, DTD, EuroSAT, GTSRB, KITTI distance, MNIST, RESISC45, SUN397 and SVHN [35, 11, 25, 71, 22, 39, 7, 12, 84, 53]) and five supported tasks (ImageNet, CIFAR-10, CIFAR-100, STL-10 and Food101 [14, 36, 12, 5]). We apply PAINT separately on each patching task and average results across experiments. The dashed lines illustrate vertical movement from the unpatched models and horizontal movement from the fine-tuned models. "
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"text": "Another approach to adapting zero-shot models would be to add data from the downstream task to the pre-training dataset and train a new open-vocabulary model from scratch. The resulting model could still perform any classification task, and zero-shot performance may improve on related tasks. However, training large image-text models from scratch can require hundreds of thousands of GPU hours [57, 56, 86], which makes this approach practically infeasible in most settings. ",
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"type": "text",
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"text": "In this paper, we study patching open-vocabulary models, where the goal is to increase accuracy on new target tasks while maintaining the flexibility of the model and its accuracy on other tasks.1 Patching aims to combine the benefits of fine-tuning and re-training from scratch: improved performance on the task of interest, maintaining the flexibility of an open vocabulary, transfer between tasks, and fast adaptation time. Motivated by these goals, we extend existing fine-tuning techniques [82] to open-vocabulary settings, where the class space is not fixed. We introduce Patching with Interpolation (PAINT), a simple, two-step procedure for patching models: first, fine-tune the model on the patching task without introducing any task-specific parameters; then, linearly interpolate between the weights of the model before and after fine-tuning. Linearly interpolating neural network weights [52, 19, 54] has been previously used to improve accuracy on a single task [28, 81] or robustness to distribution shift [82]. Indeed, averaging network weights has been explored in continual learning contexts, although for closed-vocabulary models [40]. ",
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"type": "text",
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"text": "With PAINT, accuracy can improve on new tasks without degrading accuracy on unrelated tasks, as illustrated in Figure 1. For instance, applying PAINT to a CLIP ViT-L/14 [57] independently on nine image classification tasks [35, 11, 25, 71, 22, 39, 7, 84, 53] improves accuracy by 15 to 60 percentage points compared to the unpatched model, while accuracy on ImageNet [14] decreases by less than one percentage point. We also observe a promising trend: patching becomes more effective with model scale (Section 4.1). ",
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"type": "text",
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"text": "Beyond single tasks, we show that models can be patched on multiple tasks (Section 5). When patching on nine image classification tasks simultaneously, a single CLIP ViT-L/14 model is competitive with using one specialized model for each task—the average accuracy difference is less than 0.5 percentage points. ",
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"text": "Moreover, PAINT enables broad transfer (Section 6): accuracy on related tasks can increase, even when the class space changes. For instance, we partition EuroSAT [25], a satellite image dataset, into two halves with disjoint labels. Patching a ViT-L/14 model on the first half improves accuracy on the second half by 7.3 percentage points, even though the classes are unseen during patching. ",
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"text": "Finally, we investigate PAINT on case studies including typographic attacks [23], counting [32], and visual question answering [4] (Section 7). For instance, applying PAINT using synthetic typographic attacks leads to a model that is less susceptible to typographic attacks in the real world, improving its accuracy by 41 percentage points. ",
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"type": "text",
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"text": "In summary: ",
|
| 188 |
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"type": "text",
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"text": "• Even the best pre-trained models are not perfect. We introduce PAINT, a method designed to improve accuracy on new tasks without harming accuracy elsewhere. \n• PAINT incurs no extra computational cost compared to standard fine-tuning, neither during fine-tuning itself nor at inference time. \n• PAINT can also be applied with multiple tasks, providing a single model that is competitive with many specialized models. \n• Applying PAINT with one task can improve accuracy on a related task, even when they do not share the same classes. \n• PAINT improves with model scale, indicating a promising trend for future models. ",
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"type": "text",
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"text": "2 Patching with interpolation (PAINT) ",
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"text_level": 1,
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"type": "text",
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"text": "This section details our method for patching models on a single and multiple tasks. ",
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"text": "Patching on a single task. Given an open-vocabulary model with weights $\\theta _ { \\mathrm { z s } }$ and a patching task $\\mathcal { D } _ { \\mathrm { p a t c h } }$ , our goal is to produce a new model $\\theta _ { \\mathrm { p a t c h } }$ which achieves high accuracy on $\\mathcal { D } _ { \\mathrm { { p a t c h } } }$ without decreasing model performance on tasks where accuracy is already acceptable. We let $\\mathcal { D } _ { \\mathrm { s u p p } }$ denote a representative supported task where model performance is adequate, and later show that the method is stable under different choices of $\\mathcal { D } _ { \\mathrm { s u p p } }$ (Section 4.2). The two-step procedure we explore for producing $\\theta _ { \\mathrm { p a t c h } }$ is given below. ",
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"type": "text",
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"text": "Step 1. Fine-tune $\\theta _ { \\mathrm { z s } }$ on training data from $\\mathcal { D } _ { \\mathrm { p a t c h } }$ to produce a model with weights $\\theta _ { \\mathrm { f t } }$ . Step 2. For mixing coefficient $\\alpha \\in [ 0 , 1 ]$ , linearly interpolate between $\\theta _ { \\mathrm { z s } }$ and $\\theta _ { \\mathrm { f t } }$ to produce $\\theta _ { \\mathrm { p a t c h } } = ( 1 - \\alpha ) \\cdot \\theta _ { \\mathrm { z s } } + \\alpha \\cdot \\theta _ { \\mathrm { f t } }$ . The mixing coefficient is determined via held-out validation sets for $\\mathcal { D } _ { \\mathrm { s u p p } }$ and $\\mathcal { D } _ { \\mathrm { p a t c h } }$ . We refer to the resulting model as $\\theta _ { \\mathrm { p a t c h } }$ . ",
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"type": "text",
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"text": "In our experiments, we do not introduce any additional task-specific parameters when fine-tuning, as discussed in Section 3 and Appendices B and $\\textrm { C }$ . ",
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"type": "text",
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"text": "Patching on a multiple tasks. In practice, we often want to improve model accuracy on multiple patching tasks D(1)patch $\\mathcal { D } _ { \\mathrm { p a t c h } } ^ { ( 1 ) } , . . . , \\mathcal { D } _ { \\mathrm { p a t c h } } ^ { ( k ) }$ D(k)patch, which can be accomplished with straightforward modifications to the procedure above. We explore three alternatives and examine their relative trade-offs in Section 5: ",
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"type": "text",
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"text": "• Joint patching, where we merge all the patching tasks $\\mathcal { D } _ { \\mathtt { p a t c h } } ^ { ( i ) }$ into a single task $\\mathcal { D } _ { \\mathrm { p a t c h } }$ before running the patching procedure; \n• Sequential patching, where we iteratively repeat the patching procedure above on each new task \nD(i) and let $\\theta _ { \\mathrm { z s } } \\theta _ { \\mathrm { p a t c h } }$ after each completed iteration; \n• Parallel patching, where we apply the first step on each task in parallel to produce fine-tuned $\\theta _ { \\mathrm { f t } } ^ { ( 1 ) } , . . . , \\bar { \\theta _ { \\mathrm { f t } } ^ { ( k ) } }$ e search for mixing coefficients . $\\alpha _ { i }$ to produce $\\begin{array} { r } { \\theta _ { \\mathrm { p a t c h } } = \\big ( 1 - \\sum _ { i = 1 } ^ { k } \\alpha _ { i } \\big ) \\cdot \\theta _ { \\mathrm { z s } } + \\sum _ { i = 1 } ^ { k } \\alpha _ { i } \\cdot \\theta _ { \\mathrm { f t } } ^ { ( i ) } } \\end{array}$ ",
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"text": "For joint and parallel patching we assume access to held-out validation sets for all tasks, while in sequential patching we only assume access to held-out validation sets from the tasks seen so far. Unless mentioned otherwise, we pick the mixing coefficient $\\alpha$ that optimizes average accuracy on the held-out validation sets from the supported and patching tasks. ",
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"type": "text",
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"text": "3 Experimental setup ",
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| 299 |
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"text_level": 1,
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| 300 |
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"type": "text",
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"text": "Tasks. We consider a diverse set of image classification tasks from Radford et al. [57]. In most experiments, we use ImageNet [14] as a representative supported task, although we explore other supported tasks in Section 4.2. We categorize tasks into patching tasks or supported tasks based on the accuracy difference between the zero-shot model and a model specialized to the task. A large accuracy difference indicates that the task is a relevant target for patching because the zero-shot model is still far from optimal. Specifically, we consider a subset tasks from Radford et al. [57], categorizing tasks where the linear probes outperform the zero-shot model by over 10 percentage points as patching tasks: Cars [35], DTD [11], EuroSAT [25], GTSRB [71], KITTI [22], MNIST [39], RESISC45 [7], SUN397 [84], and SVHN [53]. We use the remaining tasks as supported tasks: CIFAR10 [36], CIFAR100 [36], Food101 [5], ImageNet [14], and STL10 [12]. We investigate additional patching tasks as case studies in Section 7 and provide further details in Appendix A. ",
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"text": "",
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| 322 |
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"type": "text",
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"text": "Models. We primarily use CLIP [57] pre-trained vision transformer (ViT) models [15]. Unless otherwise mentioned our experiments are with the ViT-L/14 model, while Section 4.2 studies ResNets [24]. ",
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"type": "text",
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"text": "Fine-tuning on patching tasks. Unless otherwise mentioned, we fine-tune with a batch size of 128 for 2000 iterations using learning rate 1e-5 with 200 warm-up steps with a cosine annealing learning rate schedule and the AdamW optimizer [43, 55] (weight decay 0.1). When fine-tuning, we use the frozen final classification layer output by CLIP’s text tower so that we do not introduce additional learnable parameters. This design decision keeps the model open-vocabulary and does not harm accuracy, as discussed in in Appendices B and C. ",
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"type": "text",
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"text": "Evaluation. We use accuracy as the evaluation metric unless otherwise stated. We refer to the average of the mean accuracy on the patching tasks and the mean accuracy on the supported tasks as combined accuracy.2 ",
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"type": "text",
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"text": "4 Patching models on a single new task ",
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"text_level": 1,
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"type": "text",
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"text": "As shown in Figure 1, when patching a model on a single task, we interpolate the weights of the zero-shot and fine-tuned model, producing a model that achieves high accuracy on both the patching task and the supported task. On the nine tasks, PAINT improves the accuracy of ViT-L/14 by 15 to 60 percentage points, while accuracy on ImageNet decreases by less than one percentage point. PAINT also allows practitioners to control the accuracy trade-off on the patching and supported tasks without re-training a new model, by varying the mixing coefficient $\\alpha$ . ",
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"type": "text",
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"text": "4.1 The effect of scale ",
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"text_level": 1,
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"type": "text",
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"text": "We consistently observe that PAINT is more effective for larger models. Our findings are aligned with those of Ramasesh et al. [59], who observed that larger models are less susceptible to catastrophic forgetting. This section formalizes and provides insights for these observations. ",
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"type": "text",
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"text": "Measuring the effectiveness of patching. We measure the effectiveness of patching via the accuracy difference between the single patched model and two specialized models with the same architecture and initialization. For both the supported task and patching task, we take specialized models that maximize performance on the task, considering the set of all interpolations between the zero-shot and fine-tuned models. We refer to this measure as accuracy distance to optimal. Formally, accuracy distance to optimal is given by ",
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"type": "equation",
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"img_path": "images/8b7c17fc63adfde3b41dd8fdcc1945f8f446229365359c91fe06bd64742dcd34.jpg",
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"text": "$$\n\\frac { 1 } { 2 } \\left[ \\operatorname* { m a x } _ { \\alpha } \\mathsf { A c c } ( \\theta _ { \\alpha } , { \\mathcal D } _ { \\mathrm { s u p p } } ) + \\operatorname* { m a x } _ { \\alpha } \\mathsf { A c c } ( \\theta _ { \\alpha } , { \\mathcal D } _ { \\mathrm { p a t c h } } ) \\right] - \\frac { 1 } { 2 } \\operatorname* { m a x } _ { \\alpha } \\left[ \\mathsf { A c c } ( \\theta _ { \\alpha } , { \\mathcal D } _ { \\mathrm { s u p p } } ) + \\mathsf { A c c } ( \\theta _ { \\alpha } , { \\mathcal D } _ { \\mathrm { p a t c h } } ) \\right] ,\n$$",
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"text": "where $\\operatorname { A c c } ( \\theta , { \\mathcal { D } } )$ represents the accuracy of model $\\theta$ on task $\\mathcal { D }$ . In Figure 2 (left), we show that accuracy distance to optimal decreases with scale, indicating that patching becomes more effective for larger models. ",
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"text": "Model similarity. Fine-tuning modifies overparameterized models less [9], which provides insights on why larger models are easier to patch: less movement is required to fit new data. We demonstrate this by evaluating representational similarity using Centered Kernel Alignment (CKA) [34] (see Appendix $\\mathrm { D }$ for details). As shown in Figure 2 (center), the representations of the unpatched and fine-tuned models become more similar as models grow larger, indicated by larger CKA values. Moreover, Figure 2 (right) shows that the cosine similarity between the weights of the unpatched and fine-tuned models, $\\mathrm { c o s } \\bar { ( \\theta _ { \\mathrm { z s } } , \\theta _ { \\mathrm { f t } } ) } = { \\langle \\theta _ { \\mathrm { z s } } , \\theta _ { \\mathrm { f t } } \\rangle } / ( { | | \\theta _ { \\mathrm { z s } } | } { | | \\theta _ { \\mathrm { f t } } | } { | | } )$ , increases with scale. ",
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"img_path": "images/b72c4fb36424a430ec0f1a0abae638b6b4155247529a5a5b91ced0b946da30bc.jpg",
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"image_caption": [
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"Figure 2: Larger models are easier to patch (left). For larger models, the unpatched and fine-tuned model are more similar with respect to their representations (center) and weights (right). Model scale is measured in Giga Multiply-Accumulate operations (GMACs). "
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"img_path": "images/2443ac9955361eaece32bc9fb65f1d64c8d05723641e59f827424243e6ead873.jpg",
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"image_caption": [
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"Figure 3: The frontier of accuracy trade-offs can be recovered by linearly interpolating weights. Interpolating the unpatched and fine-tuned models recovers the accuracy trade-off of early stopping, regularization towards the initialization, and changes in hyperparameters. Additional details and comparisons can be found in Appendix E. "
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"type": "text",
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"text": "4.2 Baselines and ablations ",
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"text": "Baselines. There are many alternatives which enable a trade-off between accuracy on the supported and patching tasks. These methods include early stopping during fine-tuning, applying a regularization term which penalizes movement from initialization, or training with different hyperparameters including a smaller learning rate. Unlike interpolation, these methods do not enable navigating the accuracy trade-off without fine-tuning the model again many times. Moreover, Figure 3 demonstrates that the accuracy trade-off frontier for early stopping, regularization, or varying hyperparameters can be recovered by interpolating weights with different mixing coefficients. Appendix $\\mathrm { E }$ provides additional baselines and discussion, including EMA [74], EWC [33], LwF [41], re-training a model with data from the patching task, and mixing the pre-training and fine-tuning objectives. ",
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"type": "text",
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"text": "Additional supported tasks. In Figure 1, we use ImageNet as a representative supported task. This section demonstrates that PAINT is stable under different choices of the supported task. Instead of ImageNet, we use CIFAR10, CIFAR100, Food101 and STL10. Figure 4 displays representative results, where performance is averaged over the nine patching tasks (see Appendix $\\mathrm { F }$ for additional results). We observe consistent results across supported tasks, and that the optimal mixing coefficients are stable across different choices of supported tasks (Figure 4, right). ",
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"text": "Additional models. In addition to the CLIP ViTs used in the majority of our experiments, we study four ResNet models [24] from Radford et al. [57] in Appendix G. We find that patching is less effective for ResNets compared to ViTs of similar size, which corroborates the findings of Ramasesh et al. [59] that ResNets are generally more susceptible to catastrophic forgetting. However, similarly to ViTs, we still observe improvements with scale. Finally, we show that patching is also effective for closed-vocabulary models in Appendix H. ",
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"image_caption": [
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"Figure 4: Results are consistent across supported tasks. For multiple supported tasks, we observe similar accuracy improvements on patching tasks, without substantially decreasing supported task accuracy. Additional results for the supported tasks Food101, STL10 and ImageNet are in Appendix F. Moreover, choosing the mixing coefficients using a different supported task does not substantially decrease combined accuracy on patching and supported tasks (right). "
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"type": "text",
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"text": "5 Patching models on multiple tasks ",
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"text": "This section details experimental results for patching on multiple datasets. Recall from Section 2 that there are various strategies for extending PAINT to multiple datasets, which we briefly revisit. For joint patching we merge all the datasets into a single fine-tuning task and apply our patching procedure as before. For sequential patching we iteratively perform our procedure once per task, using the patched model at each step as the initialization for the next step.3 We also explore parallel patching, for which we have an unpatched model $\\theta _ { \\mathrm { z s } }$ and independently fine-tune on each of the tasks in parallel. We then search for mixing coefficients to combine the resulting models. For tasks $1 , . . . , k$ , let θ(1)ft , . $\\theta _ { \\mathrm { f t } } ^ { ( 1 ) } , . . . , \\theta _ { \\mathrm { f t } } ^ { ( k ) }$ denote the fine-tuned models for each task. Since it is impractical to exhaustively search over each $\\alpha _ { i }$ , we instead search over a one-dimensional scalar $\\alpha \\in [ 0 , 1 ]$ , which interpolates between $\\theta _ { \\mathrm { z s } }$ and the average of all fine-tuned solutions $\\begin{array} { r } { \\frac { 1 } { k } \\sum _ { i = 1 } ^ { k } \\theta _ { \\mathrm { f t } } ^ { ( i ) } } \\end{array}$ .4 Appendix J provides further experimental details. ",
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"text": "These methods have various trade-offs and may be applicable for different scenarios. Joint patching is only possible when data from all tasks you wish to patch is available. On the other hand, sequential patching is appropriate when the tasks are observed one after another. Finally, parallel patching can leverage distributed hardware. ",
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"type": "text",
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"text": "Figure 5 displays experimental results when patching on all nine tasks from Section 4. We observe that joint patching is the best-performing method on average. This is perhaps unsurprising since joint patching has simultaneous access to all patching datasets, unlike other patching strategies. Nevertheless, it is still interesting that for ViT-L/14, joint patching yields a single model with only 0.5 percentage points worse combined accuracy than using multiple specialized models.5 Joint patching also achieves a 15.8 percentage points improvement over the unpatched model. Moreover, patching a ViT-B/32 model with the joint strategy achieves a combined accuracy 6.1 percentage points higher than a ViT-L/14 unpatched model, which requires $1 2 \\mathbf { x }$ more GMACs. ",
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"type": "text",
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"text": "The accuracy of sequential patching approaches that of joint patching, especially for larger models. Note that, unlike in joint patching, forgetting can compound since the patching procedure is applied multiple times in sequence. In sequential patching, weight interpolations do not completely eradicate forgetting, but greatly mitigate it. This is most noticeable for smaller models: sequentially fine-tuning a ViT-B/32 without interpolation reduces the combined accuracy by 4.6 percentage points compared to the unpatched model, as shown in Appendix J. This is compared to a combined accuracy increase of 11 percentage points when using sequential patching. Additional results, including experiments on SplitCIFAR [61], can be found in Appendix J. ",
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"text": "Finally, parallel patching underperforms other patching strategies. Like sequential patching, parallel patching is in the challenging setting where data from all patching tasks is not available simultaneously. ",
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"img_path": "images/ab4c4ccd3a90497f1b687f69c948c94f7552f13a00a84ff2feb8d39fe792a1b1.jpg",
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"image_caption": [
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"Figure 5: Contrasting various strategies for patching on multiple tasks. On all experiments, ImageNet is used as the supported task while the other nine datasets are used for patching. When data from all patching tasks is available, joint patching yields a single model that is competitive with using ten different specialized models. Weight interpolations greatly mitigate catastrophic forgetting on the sequential case, but do not completely eradicate it. Finally, parallel patching underperforms other patching strategies, but still provides improvements over the unpatched model. "
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"img_path": "images/b1b7945c0a9dae4162342796b36ab8d9a3bbc2e1486bcf37a2891a6e0877e091.jpg",
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"table_body": "<table><tr><td></td><td>Cars</td><td>DTD</td><td>EuroSAT</td><td>GTSRB</td><td>KITTI</td><td>MNIST</td><td>RESISC45</td><td>SUN397</td><td>SVHN</td></tr><tr><td>Unpatched accuracy</td><td>86.2</td><td>64.9</td><td>79.9</td><td>51.7</td><td>43.4</td><td>82.6</td><td>73.4</td><td>76.9</td><td>72.8</td></tr><tr><td>Patched accuracy</td><td>87.0 (+0.8)</td><td>66.1 (+1.2)</td><td>87.2 (+7.3)</td><td>71.1 (+19.4)</td><td>60.4 (+17.0)</td><td>91.3 (+8.7)</td><td>74.2 (+0.8)</td><td>79.3 (+2.4)</td><td>88.9 (+16.1)</td></tr></table>",
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"text": "Table 1: PAINT can generalize to unseen classes. We randomly partition each dataset into tasks $A$ and $B$ with disjoint class spaces of roughly equal size. This table reports how patching on task $A$ affects accuracy on task $B$ for the ViT-L/14 model. In all cases, accuracy on task $B$ improves when patching on task $A$ even though the classes are unseen during patching. ",
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"text": "Moreover, unlike in joint or sequential patching, no model is optimized on data from all patching tasks. Using a black box optimization algorithm for finding the mixing coefficients did not yield large improvements over using the same mixing coefficient for all models. However, it is possible that more sophisticated search methods could yield better results. In Appendix J, we present additional experiments for a subset of the tasks where exhaustively searching the space of mixing coefficients is tractable, finding headroom for improvement in most cases. ",
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"text": "6 Broad transfer ",
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"text": "An alternative to our patching approach is to introduce parameters which are specific to each new task. By contrast, PAINT always maintains a single model. This section describes an additional advantage of the single model approach: patching the model on task $A$ can improve accuracy on task $B$ , even when task $A$ and $B$ do not share the same classes. We refer to this phenomenon as broad transfer. Note that we are able to study this phenomenon because the single patched model remains open-vocabulary throughout the patching procedure. This is a key advantage of PAINT compared to maintaining a collection of task-specific models. ",
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"text": "We now describe two experiments to measure the effects on a task $B$ when patching the model on a task $A$ . First, we explore broad transfer by randomly partitioning datasets into disjoint sets with no class overlap. For a dataset $\\mathcal { D }$ we partition the class space $\\mathcal { V }$ into two disjoint sets of roughly equal size $\\mathcal { V } _ { A }$ and $\\mathcal { { V } } _ { B }$ . We build task $A$ with the examples $( x , y ) \\in \\mathcal { D }$ where $y$ belongs to $\\mathcal { V } _ { A }$ , and task $B$ with examples $( x , y )$ where $y$ belongs to $\\mathcal { { V } } _ { B }$ . Table 1 shows how patching a model on task $A$ affects the accuracy on task $B$ for nine datasets $\\mathcal { D }$ . The accuracy improvements on task $B$ range from 0.8 to 19.4 percentage points, even though the classes from task $B$ are not seen during patching. ",
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"type": "text",
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"text": "To further understand transfer, we consider additional task pairs $A$ and $B$ , which are now different datasets. While some pairs $A$ , $B$ share classes, there are still instances of broad transfer. Concretely, ",
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"img_path": "images/74e1ef3194d2e86f89d81b7c5d43b6d3ff0d39963db8ec0e8d0836f2286d38c9.jpg",
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"table_caption": [
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| 712 |
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"Table 2: Patching on task $A$ can improve accuracy on a related task $B$ . For a pair of tasks $A$ and $B$ , we report accuracy of the ViT-L/14 on task $B$ , after patching on task $A$ , finding improvements on seven out of eight cases. "
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"table_body": "<table><tr><td>Task A Task B</td><td>MNIST SVHN SVHN</td><td>MNISTRESISC45</td><td>EuroSAT RESISC45</td><td>MNIST EuroSAT FashionMNIST</td><td>FashionMNISTGTSRB MNIST</td><td>MTSD MTSD GTSRB</td></tr><tr><td>Unpatched accuracy</td><td>58.6</td><td>76.4 71.0</td><td>60.2</td><td>67.7</td><td>76.4</td><td>19.3 50.6</td></tr><tr><td>Patched accuracy</td><td>68.9 93.2 (+10.3) ） (+16.8)</td><td>69.7 (-1.3)</td><td>70.4 (+10.2)</td><td>70.8 (+3.1)</td><td>77.5 (+1.1)</td><td>30.8 69.8 (+11.5) (+19.2)</td></tr></table>",
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"type": "image",
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"img_path": "images/6e73f1e55022da3d02d7e4fcdb5448dcc6e048f006e9441361fb77781b3537fd.jpg",
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"image_caption": [
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"Figure 6: Guarding against real-world typographic attacks by patching on synthetic data. (a) A sample from our real-world typographic attacks test set. A CLIP ViT-L/14 is “tricked” into classifying this image as a dog instead of a cat. (b) Sample of synthetic typographic attack data. (c) Performance on real-world data with unseen classes after patching on only synthetic typographic attacks (curves produced by interpolating between the unpatched and fine-tuned model). (d) Analogous curves for the test set of the synthetic data used for patching. "
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"text": "Table 2 examines i) MNIST and SVHN, two digit recognition tasks with shared classes; ii) EuroSAT and RESISC45, two satellite imagery recognition tasks where there are unshared classes but some overlap; iii) GTSRB and MTSD [17], two traffic sign recognition datasets where there are unshared classes but some overlap; and iv) MNIST and FashionMNIST [83], which do not share any classes but appear visually similar. In seven out of eight experiments, patching on task $A$ improves accuracy by 1.1 to 19.2 percentage points on task $B$ . The exception is when $A$ is EuroSAT and $B$ is RESISC45, where accuracy decreases by 1.3 percentage points. ",
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"text": "In all experiments, when patching on task $A$ we choose the mixing coefficient $\\alpha$ by optimizing the held-out validation accuracy on task $A$ and a supported task (in this experiment we use ImageNet). While it is possible for a method that introduces new parameters for each task to exhibit broad transfer to new data, this also requires knowing which parameters to apply for the new data. This is not necessary in the single model approach. ",
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"type": "text",
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"text": "7 Case studies ",
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"text": "We further examine the performance of PAINT in three additional settings, which highlight weaknesses of the zero-shot CLIP model and showcase broad transfer (Section 6). ",
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"text": "Typographic attacks. Goh et al. [23] find that CLIP models are susceptible to typographic attacks, where text superimposed on an image leads to misclassification. For example, in Figure $6 ( a )$ , the text on the pink note saying “dog” leads a CLIP to misclassify the image of a cat as a dog. To fix this vulnerability, we procedurally generate typographic attack data by adding text with incorrect class names to SUN397 [84], as seen in Figure 6 $( b )$ . We then collect a test set of 110 real world images by placing notes on objects and taking photos.6 After applying PAINT using the synthetic data, we evaluate on the real-world images (Figure 6 (c)) and synthetic test set (Figure 6 (d)). We observe that while larger models are more susceptible to typographic attacks, they are also more amenable to patching. Furthermore, we see an example of broad transfer between the synthetic and real-world data: when patching ViT-L/14 on synthetic data, its accuracy on real-world typographic attacks improves 41 percentage points even though the real-world classes are unseen. The cost is a reduction of less than 1 percentage point on ImageNet. We present details on the task and data collection in Appendix K. ",
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"type": "text",
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"text": "Counting. Radford et al. [57] find that CLIP models struggle to count the number of objects in CLEVR [32]. Here, the task is to choose an integer between 3 and 10 for each image, corresponding to the number of visible objects. While a straightforward way to patch such a task is to fine-tune on it directly, we investigate if applying PAINT using a subset of the classes allows the patched model to generalize to other numbers. Specifically, we patch on images with 4, 5, 6, 8, or 9 objects. To evaluate broad transfer, we test on images with 3, 7, and 10 objects (7 for understanding interpolation and 3 and 10 for extrapolation). We find that PAINT improves accuracy from $59 \\%$ to over $9 9 \\%$ o n unseen classes with less than half a percentage point decrease in ImageNet accuracy. For more details see Appendix L. ",
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"text": "Visual question answering. As shown by Shen et al. [68], zero-shot CLIP models perform poorly on visual question answering [4]. Using CLIP for VQA typically involves additional parameters—for instance, Shen et al. [68] trains a transformer [77] on CLIP features. In contrast, our procedure for patching CLIP on VQA does not introduce new parameters. Following Shen et al. [68], we contrast images with a series of text prompts, where each prompt corresponds to an option in multiple-choice VQA, formed by both the question and a candidate answer using the following template: “Question: [question text] Answer: [answer text]”. We evaluate on multiple-choice VQA v1 [4], where each question is associated with 18 candidate answers. Our results, further detailed in Appendix M, show that patching is effective for visual question answering: PAINT improves the accuracy of a ViT-L/14 model by 18 percentage points, while accuracy drops by less than one percentage point on ImageNet. ",
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"type": "text",
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"text": "8 Related work ",
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"text": "Continual learning and catastrophic forgetting. Learning tasks sequentially remains a challenge for neural networks. When a neural network learns a new task, the accuracy on other tasks often decreases, a phenomenon known as catastrophic forgetting [48, 76, 20, 33]. While forgetting in neural networks may actually aid learning [90], researchers have proposed various approaches for alleviating catastrophic forgetting, including: i) Regularization-based approaches such as elastic weight consolidation (EWC) [33] and synaptic intelligence (SI) [87] which penalize the movement of parameters and are related to weight-interpolation by Lubana et al. [44]; ii) Replay methods [61, 69, 42, 6, 64, 50], which incorporate data or gradient information from previous tasks when learning a new task; and iii) Introducing task-specific parameters [65, 85, 46, 8, 78, 80]. ",
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"text": "In contrast to these approaches, PAINT requires no modification to the standard fine-tuning process besides the later weight interpolation step. Moreover, unlike regularization or replay based methods, PAINT requires no extra computational cost during training. In contrast to methods with task specific parameters, we maintain a single model. Having a single model is beneficial when there is new data which is similar to one of the tasks which have already been patched. Even without explicitly knowing which task the new data is similar to, we can observe accuracy improvements (see Section 6). ",
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"text": "Similar to our work is that of Mirzadeh et al. [50], who observe high accuracy on task A on the linear path between a model which achieves high accuracy on task A and a model which is fine-tuned jointly on task A and B. Moreover, they observe high accuracy on task B on the linear path between a model fine-tuned on task B, and the jointly fine-tuned model. Therefore, there exists a path between a model which achieves good performance on task A and a model fine-tuned on task B along which accuracy is high on both tasks. However, in Mirzadeh et al. [50] this combined path can be non-linear, leading them to propose a regularization and replay based method. In our work, we find that examining models on a linear path between the unpatched model (which has high accuracy on task A) and the model fine-tuned on task B is often sufficient for obtaining a model which achieves high accuracy on both tasks (Figure 1). We speculate that this is due to scale and model architecture: in contrast to Mirzadeh et al. [50], we initialize with a model pre-trained on a large dataset consisting of 400 million images [57], and primarily use vision transformers [15]. As shown in Section 4.2, our method performs substantially worse with ResNets [24], which are used by Mirzadeh et al. [50]. ",
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"text": "Finally, Ramasesh et al. [59] and Mehta et al. [49] also observed that catastrophic forgetting is less problematic for large and pre-trained models. In addition, Ramasesh et al. [59] found—similar to our results—that vision transformers are less susceptible to forgetting than ResNets of the same size. ",
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"text": "Linear mode connectivity and robust fine-tuning. Linearly interpolating neural network weights is a key step in PAINT. Because of the many nonlinear activations in a neural network, it is not clear a priori that linearly interpolating between two sets of weights can result in a high accuracy solution. However, researchers have observed that interpolating neural network weights can achieve high accuracy when training on MNIST from a common initialization [52] or when part of the optimization trajectory is shared [19, 28, 54, 18, 82, 47, 16, 81, 10]. The term linear mode connectivity was coined by Frankle et al. [19]: two networks exhibit linearly mode connectivity if the accuracy does not decrease when using weights on the linear path between them [52, 19]. Weight averaging for continual learning has also been studied by Lee et al. [40] for closed-vocabulary models. ",
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"text": "",
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"type": "text",
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"text": "While Nagarajan and Kolter [52] and Frankle et al. [19] focused on accuracy on a single task, Wortsman et al. [82] use linear mode connectivity to fine-tune models while preserving their robustness to natural distribution shifts. By interpolating the weights of a zero-shot and fine-tuned model, they find a solution which performs well both on the fine-tuning task and under distribution shift. In contrast to Wortsman et al. [82], we do not modify any task-specific parameters when fine-tuning, preserving the open-vocabulary nature of the models we patch. Unlike Wortsman et al. [82], we examine accuracy trade-offs across different tasks with little or no class overlap and adapt a model to multiple tasks. ",
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"text": "In addition, closely related to our work is that of Matena and Raffel [47], who use Fisher-weighted averaging of language models before and after fine-tuning on downstream tasks. Unlike Fisherweighted averaging of Matena and Raffel [47], we do not use different mixing coefficients for each parameter, and thus require no extra compute when patching. Moreover, we explore new strategies for patching on multiple tasks (see Section 5), and focus on open-vocabulary image classifiers. ",
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"text": "Interventions to change the behavior of a trained model. Several authors have studied the problem of updating a model to locally alter its behavior on certain inputs without external disruptions on other inputs [70, 13, 51, 66, 63, 62]. Previous literature uses various terms to refer to this process, including model editing, patching or debugging. A popular use case is to update trained language models to reflect changes in the world (for instance, facts like who is the current president of Brazil) [29, 45, 38, 30]. Moreover, inspired by software engineering practice, previous work explored “debugging” language models through user interaction [63, 62], including providing corrective feedback to the models via natural language [3]. Mitchell et al. [51], De Cao et al. [13] propose training auxiliary networks to perform local edits on pre-trained models. Santurkar et al. [66] introduce a method for rewriting the prediction rules of a classifier, focusing on specific failure modes such as reliance on spurious correlations. In contrast with previous literature, our work explores patching models at the task level, aiming to systemically improve accuracy on a dataset—for instance, enabling a model to recognize dozens of satellite imagery classes with a single patch. ",
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"text": "9 Limitations and conclusion ",
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"text": "Limitations. When applying PAINT, accuracy on supported tasks can still decrease, especially for smaller models. This limitation is perhaps best reflected in the case of sequential patching: patched models underperform using multiple specialized models when many tasks are added sequentially. Using larger models and weight interpolations can alleviate this issue, but do not completely resolve it. Finally, better understanding on which datasets patching is more effective is an exciting direction for future research. ",
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"text": "Conclusion. In this work, we explore several techniques for patching open-vocabulary models with the goal of improving accuracy on new tasks without decreasing accuracy elsewhere. PAINT is effective in several scenarios, ranging from classifying digits to defending against typographic attacks. PAINT becomes more effective with scale, and can be applied on multiple tasks sequentially or simultaneously. Our findings demonstrate that in many circumstances it is possible to expand the set of tasks on which models achieve high accuracy, without introducing new parameters, without re-training them from scratch, and without catastrophic forgetting. ",
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"type": "text",
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"text": "Acknowledgments ",
|
| 976 |
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"text_level": 1,
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| 977 |
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"text": "We thank Akari Asai, Alex Fang, David Fleet, Huy Ha, Ari Holtzman, Pieter-Jan Kindermans, Marco Tulio Ribeiro, Ofir Press, Sarah Pratt, Sewon Min, Thao Nguyen and Tim Dettmers for helpful discussions and feedback, and Hyak at UW for computing support. This work is in part supported by the NSF AI Institute for Foundations of Machine Learning (IFML), Open Philanthropy, NSF IIS 1652052, NSF IIS 17303166, NSF IIS 2044660, NSF IIS 2132519, ONR N00014-18-1-2826, DARPA N66001-19-2-4031, DARPA W911NF-15-1-0543, the Sloan Fellowship and gifts from Allen Institute for AI. ",
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]
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| 1 |
+
# LIGHTGCL: SIMPLE YET EFFECTIVE GRAPH CON-TRASTIVE LEARNING FOR RECOMMENDATION
|
| 2 |
+
|
| 3 |
+
Xuheng Cai Chao Huang∗ Lianghao Xia Xubin Ren Department of Computer Science, University of Hong Kong {rickcai, lhaoxia}@hku.hk chaohuang75gmail.com
|
| 4 |
+
|
| 5 |
+
xubinrencs@gmail.com
|
| 6 |
+
|
| 7 |
+
# ABSTRACT
|
| 8 |
+
|
| 9 |
+
Graph neural network (GNN) is a powerful learning approach for graph-based recommender systems. Recently, GNNs integrated with contrastive learning have shown superior performance in recommendation with their data augmentation schemes, aiming at dealing with highly sparse data. Despite their success, most existing graph contrastive learning methods either perform stochastic augmentation (e.g., node/edge perturbation) on the user-item interaction graph, or rely on the heuristic-based augmentation techniques (e.g., user clustering) for generating contrastive views. We argue that these methods cannot well preserve the intrinsic semantic structures and are easily biased by the noise perturbation. In this paper, we propose a simple yet effective graph contrastive learning paradigm LightGCL that mitigates these issues impairing the generality and robustness of CL-based recommenders. Our model exclusively utilizes singular value decomposition for contrastive augmentation, which enables the unconstrained structural refinement with global collaborative relation modeling. Experiments conducted on several benchmark datasets demonstrate the significant improvement in performance of our model over the state-of-the-arts. Further analyses demonstrate the superiority of LightGCL’s robustness against data sparsity and popularity bias. The source code of our model is available at https://github.com/HKUDS/LightGCL.
|
| 10 |
+
|
| 11 |
+
# 1 INTRODUCTION
|
| 12 |
+
|
| 13 |
+
Graph neural networks (GNNs) have shown effectiveness in graph-based recommender systems by extracting local collaborative signals via neighborhood representation aggregation (Wang et al., 2019; Chen et al., 2020b). In general, to learn user and item representations, GNN-based recommenders perform embedding propagation on the user-item interaction graph by stacking multiple message passing layers for exploring high-order connectivity (He et al., 2020; Zhang et al., 2019; Liu et al., 2021a). Most GNN-based collaborative filtering models adhere to the supervised learning paradigm, requiring sufficient quality labelled data for model training. However, many practical recommendation scenarios struggle with the data sparsity issue in learning high-quality user and item representations from limited interaction data (Liu et al., 2021b; Lin et al., 2021). To address the label scarcity issue, the benefits of contrastive learning have been brought into the recommendation for data augmentation (Wu et al., 2021). The main idea of contrastive learning in enhancing the user and item representation is to research the agreement between the generated embedding views by contrasting the defined positive pairs with negative instance counterparts (Xie et al., 2022).
|
| 14 |
+
|
| 15 |
+
While contrastive learning has been shown to be effective in improving the performance of graphbased recommendation methods, the view generators serve as the core part of data augmentation through identifying accurate contrasting samples. Most of current graph contrastive learning (GCL) approaches employ heuristic-based contrastive view generators to maximize the mutual information between the input positive pairs and push apart negative instances(Wu et al., 2021; Yu et al., 2022a; Xia et al., 2022b). To construct perturbed views, SGL (Wu et al., 2021) has been proposed to generate node pairs of positive view by corrupting the structural information of user-item interaction graph using stochastic augmentation strategies, e.g., node dropping and edge perturbation. To improve the graph contrastive learning in recommendation, SimGCL (Yu et al., 2022a) offers embedding augmentation with random noise perturbation. To work on identifying semantic neighbors of nodes (users and items), HCCF (Xia et al., 2022b) and NCL (Lin et al., 2022) are introduced to pursue consistent representations between the structurally adjacent nodes and semantic neighbors. Despite their effectiveness, state-of-the-art contrastive recommender systems suffer from several inherent limitations: i) Graph augmentation with random perturbation may lose useful structural information, which misleads the representation learning. ii) The success of heuristic-guided representation contrasting schemes is largely built upon the view generator, which limits the model generality and is vulnerable to the noisy user behaviors. iii) Most of current GNN-based contrastive recommenders are limited by the over-smoothing issue which leads to indistinguishable representations.
|
| 16 |
+
|
| 17 |
+
In light of the above limitations and challenges, we revisit the graph contrastive learning paradigm for recommendation with a proposed simple yet effective augmentation method LightGCL. In our model, the graph augmentation is guided by singular value decomposition (SVD) to not only distill the useful information of user-item interactions but also inject the global collaborative context into the representation alignment of contrastive learning. Instead of generating two handcrafted augmented views, important semantic of user-item interactions can be well preserved with our robust graph contrastive learning paradigm. This enables our self-augmented representations to be reflective of both user-specific preferences and cross-user global dependencies.
|
| 18 |
+
|
| 19 |
+
Our contributions are highlighted as follows:
|
| 20 |
+
|
| 21 |
+
• In this paper, we enhance the recommender systems by designing a lightweight and robust graph contrastive learning framework to address the identified key challenges pertaining to this task. • We propose an effective and efficient contrastive learning paradigm LightGCL for graph augmentation. With the injection of global collaborative relations, our model can mitigate the issues brought by inaccurate contrastive signals. • Our method exhibits improved training efficiency compared to existing GCL-based approaches. • Extensive experiments on several real-world datasets justify the performance superiority of our LightGCL. In-depth analyzes demonstrate the rationality and robustness of LightGCL.
|
| 22 |
+
|
| 23 |
+
# 2 RELATED WORK
|
| 24 |
+
|
| 25 |
+
Graph Contrastive Learning for Recommendation. A promising line of recent studies has incorporated contrastive learning (CL) into graph-based recommenders, to address the label sparsity issue with self-supervision signals. Particularly, SGL (Wu et al., 2021) and SimGCL (Yu et al., 2022a) perform data augmentation over graph structure and embeddings with random dropout operations. However, such stochastic augmentation may drop important information, which may make the sparsity issue of inactive users even worse. Furthermore, some recent alternative CL-based recommenders, such as HCCF (Xia et al., 2022b) and NCL (Lin et al., 2022), design heuristic-based strategies to construct view for embedding contrasting. Despite their effectiveness, their success heavily relies on their incorporated heuristics (e.g., the number of hyperedges or user clusters) for contrastive view generation, which can hardly be adaptive to different recommendation tasks.
|
| 26 |
+
|
| 27 |
+
Self-Supervised Learning on Graphs. Recently, self-supervised learning (SSL) has advanced the graph learning paradigm by enhancing node representation from unlabeled graph data (Zhu et al., 2021a;b; Velickovic et al., 2019; Hassani & Khasahmadi, 2020; Peng et al., 2020; Zhu et al., 2020; Wu et al., 2022). For example, to improve the predictive SSL paradigm, AutoSSL (Jin et al., 2022) automatically combines multiple pretext tasks for augmentation. Towards the line of contrastive SSL over graph structures, recent efforts focus on designing various graph contrastive learning methods (Yu et al., 2022b; Yin et al., 2022; Zhang et al., 2022; Xia et al., 2022a; Suresh et al., 2021). For instance, SimGRACE Xia et al. (2022a) proposes to generate contrastive views with the GNN encoder perturbations. In AutoGCL Yin et al. (2022), graph view generators are designed to be jointly trained with the graph encoder in an end-to-end way. Additionally, GCA (Zhu et al., 2021b) performs both topology-level and attribute-level data augmentation for contrastive view generation. In this method, important edges and features will be identified for adaptive augmentation. GraphCL (You et al., 2020) generates correlated graph representation views using various augmentation strategies, such as node/edge perturbation and attribute masking.
|
| 28 |
+
|
| 29 |
+
|
| 30 |
+
Figure 1: Overall structure of LightGCL.
|
| 31 |
+
|
| 32 |
+
# 3 METHODOLOGY
|
| 33 |
+
|
| 34 |
+
In this section, we describe our proposed LightGCL framework in detail. LightGCL is a lightweight graph contrastive learning paradigm as illustrated in Fig. 1. Complementary to the GCN backbone (the upper half of the figure) extracting the local graph dependency, the SVD-guided augmentation (the lower half of the figure) empowers the graph contrastive learning with global collaborative relation analysis for learning effective user and item representations.
|
| 35 |
+
|
| 36 |
+
# 3.1 LOCAL GRAPH DEPENDENCY MODELING
|
| 37 |
+
|
| 38 |
+
As a common practice of collaborative filtering, we assign each user $u _ { i }$ and item $v _ { j }$ with an embedding vector $e _ { i } ^ { ( u ) } , e _ { j } ^ { ( v ) } \in \mathbb { R } ^ { d }$ , where $d$ is the embedding size. The collections of all user and item embeddings are defined as $\pmb { { E } } ^ { ( u ) } \in \mathbb { R } ^ { I \times d }$ and $\pmb { { \cal E } } ^ { ( v ) } \in \mathbb { R } ^ { J \times d }$ , where $I$ and $J$ are the number of users and items, respectively. Following Xia et al. (2022b), we adopt a two-layer GCN to aggregate the neighboring information for each node. In layer $l$ , the aggregation process is expressed as follows:
|
| 39 |
+
|
| 40 |
+
$$
|
| 41 |
+
\begin{array} { r } { \boldsymbol { z } _ { i , l } ^ { ( u ) } = \sigma ( p ( \tilde { \boldsymbol { A } } _ { i , : } ) \cdot \boldsymbol { E } _ { l - 1 } ^ { ( v ) } ) , \quad \boldsymbol { z } _ { j , l } ^ { ( v ) } = \sigma ( p ( \tilde { \boldsymbol { A } } _ { : , j } ) \cdot \boldsymbol { E } _ { l - 1 } ^ { ( u ) } ) } \end{array}
|
| 42 |
+
$$
|
| 43 |
+
|
| 44 |
+
where z(u)i,l and z(v)j,l denote the $l$ -th layer aggregated embedding for user $u _ { i }$ and item $v _ { j }$ . $\sigma ( \cdot )$ represents the LeakyReLU with a negative slope of 0.5. $\tilde { \boldsymbol { \mathcal { A } } }$ is the normalized adjacency matrix, on which we perform the edge dropout denoted as $p ( \cdot )$ , to mitigate the overfitting issue. We implement the residual connections in each layer to retain the original information of the nodes as follows:
|
| 45 |
+
|
| 46 |
+
$$
|
| 47 |
+
\pmb { e } _ { i , l } ^ { ( u ) } = \pmb { z } _ { i , l } ^ { ( u ) } + \pmb { e } _ { i , l - 1 } ^ { ( u ) } , \quad \pmb { e } _ { j , l } ^ { ( v ) } = \pmb { z } _ { j , l } ^ { ( v ) } + \pmb { e } _ { j , l - 1 } ^ { ( v ) }
|
| 48 |
+
$$
|
| 49 |
+
|
| 50 |
+
The final embedding for a node is the sum of its embeddings across all layers, and the inner product between the final embedding of a user $u _ { i }$ and an item $v _ { j }$ predicts $u _ { i }$ ’s preference towards $v _ { j }$ :
|
| 51 |
+
|
| 52 |
+
$$
|
| 53 |
+
\pmb { e } _ { i } ^ { ( u ) } = \sum _ { l = 0 } ^ { L } \pmb { e } _ { i , l } ^ { ( u ) } , \quad \pmb { e } _ { j } ^ { ( v ) } = \sum _ { l = 0 } ^ { L } \pmb { e } _ { j , l } ^ { ( v ) } , \quad \hat { y } _ { i , j } = e _ { i } ^ { ( u ) \top } \pmb { e } _ { j } ^ { ( v ) }
|
| 54 |
+
$$
|
| 55 |
+
|
| 56 |
+
# 3.2 EFFICIENT GLOBAL COLLABORATIVE RELATION LEARNING
|
| 57 |
+
|
| 58 |
+
To empower graph contrastive learning for recommendation with global structure learning, we equip our LightGCL with the SVD scheme (Rajwade et al., 2012; Rangarajan, 2001) to efficiently distill important collaborative signals from the global perspective. Specifically, we first perform SVD on the adjacency matrix $\mathcal { A }$ as $\mathbf { \mathcal { A } } = U S V ^ { \top }$ . Here, $U / V$ is an $I \times I / J \times J$ orthonormal matrix with columns being the eigenvectors of $\mathcal { A }$ ’s row-row $/$ column-column correlation matrix. $_ { s }$ is an $I \times J$ diagonal matrix storing the singular values of $\mathcal { A }$ . The largest singular values are usually associated with the principal components of the matrix. Thus, we truncate the list of singular values to keep the largest q values, and reconstruct the adjacency matrix with the truncated matrices as $\hat { \ b { A } } = \ b { U } _ { q } \ b { S } _ { q } \ b { V } _ { q } ^ { \top }$ , where $U _ { q } \in \mathbb { R } ^ { I \times q }$ and $V _ { q } \in \mathbb { R } ^ { J \times q }$ contain the first $q$ columns of $U$ and $V$ respectively. $S _ { q } \in \mathbb { R } ^ { q \times q }$ is the diagonal matrix of the $q$ largest singular values.
|
| 59 |
+
|
| 60 |
+
The reconstructed matrix $\hat { A }$ is a low-rank approximation of the adjacency matrix $\mathcal { A }$ , for it holds that $r a n k ( { \hat { A } } ) = q$ . The advantages of SVD-based graph structure learning are two-folds. Firstly, it emphasizes the principal components of the graph by identifying the user-item interactions that are important and reliable to user preference representations. Secondly, the generated new graph structures preserve the global collaborative signals by considering each user-item pair. Given the $\hat { A }$ , we perform message propagation on the reconstructed user-item relation graph in each layer:
|
| 61 |
+
|
| 62 |
+
$$
|
| 63 |
+
\pmb { g } _ { i , l } ^ { ( u ) } = \sigma ( \hat { \mathcal { A } } _ { i , : } \cdot \pmb { E } _ { l - 1 } ^ { ( v ) } ) , \quad \pmb { g } _ { j , l } ^ { ( v ) } = \sigma ( \hat { \mathcal { A } } _ { : , j } \cdot \pmb { E } _ { l - 1 } ^ { ( u ) } )
|
| 64 |
+
$$
|
| 65 |
+
|
| 66 |
+
However, performing the exact SVD on large matrices is highly expensive, making it impractical for handling large-scale user-item matrix. Therefore, we adopt the randomized SVD algorithm proposed by Halko et al. (2011), whose key idea is to first approximate the range of the input matrix with a low-rank orthonormal matrix, and then perform SVD on this smaller matrix.
|
| 67 |
+
|
| 68 |
+
$$
|
| 69 |
+
\hat { U } _ { q } , \hat { S } _ { q } , \hat { V } _ { q } ^ { \top } = \mathrm { A p p r o x } { \mathrm { S V D } } ( { \cal A } , q ) , \quad \hat { A } _ { S V D } = \hat { U } _ { q } \hat { S } _ { q } \hat { V } _ { q } ^ { \top }
|
| 70 |
+
$$
|
| 71 |
+
|
| 72 |
+
where $q$ is the required rank for the decomposed matrices, and $\hat { { \cal U } } _ { q } \in \mathbb { R } ^ { I \times q } , \hat { { \cal S } } _ { q } \in \mathbb { R } ^ { q \times q } , \hat { { \cal V } } _ { q } \in \mathbb { R } ^ { J \times q }$ are the approximated versions of $U _ { q }$ , $S _ { q }$ , $V _ { q }$ . Thus, we rewrite the message propagation rules in Eq. 4 with the approximated matrices and the collective representations of the embeddings as follows:
|
| 73 |
+
|
| 74 |
+
$$
|
| 75 |
+
\pmb { G } _ { l } ^ { ( u ) } = \sigma ( \hat { A } _ { S V D } \pmb { E } _ { l - 1 } ^ { ( v ) } ) = \sigma ( \hat { U } _ { q } \hat { S } _ { q } \hat { V } _ { q } ^ { \top } \pmb { E } _ { l - 1 } ^ { ( v ) } ) ; \quad \pmb { G } _ { l } ^ { ( v ) } = \sigma ( \hat { A } _ { S V D } ^ { \top } \pmb { E } _ { l - 1 } ^ { ( u ) } ) = \sigma ( \hat { V } _ { q } \hat { S } _ { q } \hat { U } _ { q } ^ { \top } \pmb { E } _ { l - 1 } ^ { ( u ) } )
|
| 76 |
+
$$
|
| 77 |
+
|
| 78 |
+
where $G _ { l } ^ { ( u ) }$ and $G _ { l } ^ { ( v ) }$ are the collections of user and item embeddings encoded from the new generated graph structure view. Note that we do not need to compute and store the large dense matrix $\hat { \boldsymbol { \mathcal { A } } } _ { S V D }$ . Instead, we can store $\hat { U } _ { q } , \hat { S } _ { q }$ and $\hat { V } _ { q }$ , which are of low dimensions. By pre-calculating $( \hat { U } _ { q } \hat { S } _ { q } )$ and $( \hat { V } _ { q } \hat { S } _ { q } )$ during the preprocessing stage with SVD, the model efficiency is improved.
|
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+
|
| 80 |
+
# 3.3 SIMPLIFIED LOCAL-GLOBAL CONTRASTIVE LEARNING
|
| 81 |
+
|
| 82 |
+
The conventional GCL methods such as SGL and SimGCL contrast node embeddings by constructing two extra views, while the embeddings generated from the original graph (the main-view) are not directly involved in the InfoNCE loss. The reason for adopting such a cumbersome three-view paradigm may be that the random perturbation used to augment the graph may provide misleading signals to the main-view embeddings. In our proposed method, however, the augmented graph view is created with global collaborative relations, which can enhance the main-view representations. Therefore, we simplify the CL framework by directly contrasting the SVD-augmented view embeddings g(u)i,l with the main-view embeddings $\boldsymbol { z } _ { i , l } ^ { ( u ) }$ in the InfoNCE loss (Oord et al., 2018):
|
| 83 |
+
|
| 84 |
+
$$
|
| 85 |
+
\mathcal { L } _ { s } ^ { ( u ) } = \sum _ { i = 0 } ^ { I } \sum _ { l = 0 } ^ { L } - \log \frac { \exp ( s ( z _ { i , l } ^ { ( u ) } , \pmb { g } _ { i , l } ^ { ( u ) } / \tau ) ) } { \sum _ { i ^ { \prime } = 0 } ^ { I } \exp ( s ( z _ { i , l } ^ { ( u ) } , \pmb { g } _ { i ^ { \prime } , l } ^ { ( u ) } ) / \tau ) }
|
| 86 |
+
$$
|
| 87 |
+
|
| 88 |
+
where $s ( \cdot )$ and $\tau$ stand for the cosine similarity and the temperature respectively. The InfoNCE loss $\mathcal { L } _ { s } ^ { ( v ) }$ for the items are defined in the same way. To prevent overfitting, we implement a random node dropout in each batch to exclude some nodes from participating in the contrastive learning. As shown in Eq. 8, the contrastive loss is jointly optimized with our main objective function for the recommendation task (where $\hat { y } _ { i , p _ { s } }$ and $\hat { y } _ { i , n _ { s } }$ denote the predicted scores for a pair of positive and negative items of user $\romannumeral 1$ ):
|
| 89 |
+
|
| 90 |
+
$$
|
| 91 |
+
\mathcal { L } = \mathcal { L } _ { r } + \lambda _ { 1 } \cdot ( \mathcal { L } _ { s } ^ { ( u ) } + \mathcal { L } _ { s } ^ { ( v ) } ) + \lambda _ { 2 } \cdot \Vert \Theta \Vert _ { 2 } ^ { 2 } ; \quad \mathcal { L } _ { r } = \sum _ { i = 0 } ^ { I } \sum _ { s = 1 } ^ { S } \operatorname* { m a x } ( 0 , 1 - \hat { y } _ { i , p _ { s } } + \hat { y } _ { i , n _ { s } } )
|
| 92 |
+
$$
|
| 93 |
+
|
| 94 |
+
# 4 EVALUATION
|
| 95 |
+
|
| 96 |
+
To verify the superiority and effectiveness of the proposed LightGCL method, we perform extensive experiments to answer the following research questions:
|
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+
|
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+
• RQ1: How does LightGCL perform on different datasets compared to various SOTA baselines? • RQ2: How does the lightweight graph contrastive learning improve the model efficiency? • RQ3: How does our model perform against data sparsity, popularity bias and over-smoothing? • RQ4: How does the local-global contrastive learning contribute to the performance of our model? • RQ5: How do different parameter settings affect our model performance?
|
| 99 |
+
|
| 100 |
+
# 4.1 EXPERIMENTAL SETTINGS
|
| 101 |
+
|
| 102 |
+
# 4.1.1 DATASETS AND EVALUATION PROTOCOLS
|
| 103 |
+
|
| 104 |
+
We evaluate our model and the baselines on five real-world datasets: Yelp (29,601 users, 24,734 items, 1,517,326 interactions): a dataset collected from the rating interactions on Yelp platform; Gowalla (50,821 users, 57,440 items, 1,172,425 interactions): a dataset containing users’ check-in records collected from Gowalla platform; ML-10M (69,878 users, 10,195 items, 9,988,816 interactions): a well-known movie-rating dataset for collaborative filtering; Amazon-book (78,578 users, 77,801 items, 2,240,156 interactions): a dataset composed of users’ ratings on books collected from Amazon; and Tmall (47,939 users, 41,390 items, 2,357,450 interactions): a E-commerce dataset containing users’ purchase records on different products in Tmall platform.
|
| 105 |
+
|
| 106 |
+
In accordance with He et al. (2020) and Wu et al. (2021), we split the datasets into training, validation and testing sets with a ratio of 7:2:1. We adopt the Recall $@ \mathbf { N }$ and Normalized Discounted Cumulative Gain $( \mathrm { N D C G } ) @ \mathrm { N }$ , where $\Nu = \{ 2 0 , 4 0 \}$ , as the evaluation metrics.
|
| 107 |
+
|
| 108 |
+
# 4.1.2 BASELINE METHODS
|
| 109 |
+
|
| 110 |
+
We compare our model against 16 state-of-the-art baselines with different learning paradigms:
|
| 111 |
+
|
| 112 |
+
• MLP-enhanced Collaborative Filtering: NCF (He et al., 2017).
|
| 113 |
+
• GNN-based Collaborative Filtering: GCCF (Chen et al., 2020c), LightGCN (He et al., 2020).
|
| 114 |
+
• Disentangled Graph Collaborative Filtering: DGCF (Wang et al., 2020b).
|
| 115 |
+
• Hypergraph-based Collaborative Filtering: HyRec (Wang et al., 2020a).
|
| 116 |
+
• Self-Supervised Learning Recommender Systems: GraphCL (You et al., 2020), GRACE (Zhu et al., 2020), GCA (Zhu et al., 2021b), MHCN (Yu et al., 2021), SAIL (Yu et al., 2022b), AutoGCL (Yin et al., 2022), SimGRACE (Xia et al., 2022a), SGL (Wu et al., 2021), HCCF (Xia et al., 2022b), SHT (Xia et al., 2022c), SimGCL (Yu et al., 2022a).
|
| 117 |
+
|
| 118 |
+
Due to space limit, the detailed descriptions of baselines are presented in Appendix A.
|
| 119 |
+
|
| 120 |
+
# 4.1.3 HYPERPARAMETER SETTINGS
|
| 121 |
+
|
| 122 |
+
To ensure a fair comparison, we tune the hyperparameters of all the baselines within the ranges suggested in the original papers, except the following fixed settings for all the models: the embedding size is set as 32; the batch size is 256; two convolutional layers are used for GCN models.
|
| 123 |
+
|
| 124 |
+
For our LightGCL, the regularization weights $\lambda _ { 1 }$ and $\lambda _ { 2 }$ are tuned from $\{ 1 \mathrm { e } { - } 5 , 1 \mathrm { e } { - } 6 , 1 \mathrm { e } { - } 7 \}$ and {1e4, 1e- $\{ 5 \}$ , respectively. The temperature $\tau$ is searched from $\{ 0 . 3 , 0 . 5 , 1 , \dot { 3 } , 1 0 \}$ . The dropout rate is chosen from $\{ 0 , 0 . 2 5 \}$ . The rank (i.e., $\grave { q } ,$ ) for SVD, is set as 5. We use the Adam optimizer with a learning rate of 0.001 decaying at the rate of 0.98 until the rate reaches 0.0005.\*
|
| 125 |
+
|
| 126 |
+
# 4.2 PERFORMANCE VALIDATION (RQ1)
|
| 127 |
+
|
| 128 |
+
We summarize the experimental result in Table $1 ^ { \dagger }$ , with the following observations and conclusions:
|
| 129 |
+
|
| 130 |
+
Table 1: Performance comparison with baselines on five datasets.
|
| 131 |
+
|
| 132 |
+
<table><tr><td>Data</td><td>Metric</td><td>DGCF</td><td>HyRec</td><td>LightGCN</td><td>MHCN</td><td>SGL</td><td>SimGRACE</td><td>GCA</td><td>HCCF</td><td>SHT</td><td>SimGCL</td><td>LightGCL</td><td>p-val.</td><td>impr.</td></tr><tr><td rowspan="4">o</td><td>R@20</td><td>0.0466</td><td>0.0472</td><td>0.0482</td><td>0.0503</td><td>0.0526</td><td>0.0603</td><td>0.0621</td><td>0.0626</td><td>0.0651</td><td>0.0718</td><td>0.0793</td><td>7e-9</td><td>10%</td></tr><tr><td>N@20</td><td>0.0395</td><td>0.0395</td><td>0.0409</td><td>0.0424</td><td>0.0444</td><td>0.0435</td><td>0.0530</td><td>0.0527</td><td>0.0546</td><td>0.0615</td><td>0.0668</td><td>8e-9</td><td>8%</td></tr><tr><td>R@40</td><td>0.0774</td><td>0.0791</td><td>0.0803</td><td>0.0826</td><td>0.0869</td><td>0.0989</td><td>0.1021</td><td>0.1040</td><td>0.1091</td><td>0.1166</td><td>0.1292</td><td>2e-9</td><td>10%</td></tr><tr><td>N@40</td><td>0.0511</td><td>0.0522</td><td>0.0527</td><td>0.0544</td><td>0.0571</td><td>0.0656</td><td>0.0677</td><td>0.0681</td><td>0.0709</td><td>0.0778</td><td>0.0852</td><td>2e-9</td><td>9%</td></tr><tr><td rowspan="5">Goeaal</td><td>R@20</td><td>0.0944</td><td>0.0901</td><td>0.0985</td><td>0.0955</td><td>0.1030</td><td>0.0869</td><td>0.0896</td><td>0.1070</td><td>0.1232</td><td>0.1357</td><td>0.1578</td><td>1e-6</td><td>16%</td></tr><tr><td>N@20</td><td>0.0522</td><td>0.0498</td><td>0.0593</td><td>0.0574</td><td>0.0623</td><td>0.0528</td><td>0.0537</td><td>0.0644</td><td>0.0731</td><td>0.0818</td><td>0.0935</td><td>2e-6</td><td>14%</td></tr><tr><td>R@40</td><td>0.1401</td><td>0.1356</td><td>0.1431</td><td>0.1393</td><td>0.1500</td><td>0.1276</td><td>0.1322</td><td>0.1535</td><td>0.1804</td><td>0.1956</td><td>0.2245</td><td>3e-6</td><td>14%</td></tr><tr><td>N@40</td><td>0.0671</td><td>0.0660</td><td>0.0710</td><td>0.0689</td><td>0.0746</td><td>0.0637</td><td>0.0651</td><td>0.0767</td><td>0.0881</td><td>0.0975</td><td>0.1108</td><td>3e-6</td><td>13%</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="4">WOI-TN</td><td>R@20</td><td>0.1763</td><td>0.1801</td><td>0.1789</td><td>0.1497</td><td>0.1833</td><td>0.2254</td><td>0.2145</td><td>0.2219</td><td>0.2173</td><td>0.2265</td><td>0.2613</td><td>1e-9</td><td>15%</td></tr><tr><td>N@20</td><td>0.2101</td><td>0.2178</td><td>0.2128</td><td>0.1814</td><td>0.2205</td><td>0.2686</td><td>0.2613</td><td>0.2629</td><td>0.2573</td><td>0.2613</td><td>0.3106</td><td>3e-9</td><td>18%</td></tr><tr><td>R@40</td><td>0.2681</td><td>0.2685</td><td>0.2650</td><td>0.2250</td><td>0.2768</td><td>0.3295</td><td>0.3231</td><td>0.3265</td><td>0.3211</td><td>0.3345</td><td>0.3799</td><td>7e-10</td><td>13%</td></tr><tr><td>N@40</td><td>0.2340</td><td>0.2340</td><td>0.2322</td><td>0.1962</td><td>0.2426</td><td>0.2939</td><td>0.2871</td><td>0.2880</td><td>0.3318</td><td>0.2880</td><td>0.3387</td><td>1e-9</td><td>17%</td></tr><tr><td rowspan="4">VAzaao</td><td>R@20</td><td>0.0211</td><td>0.0302</td><td>0.0319</td><td>0.0296</td><td>0.0327</td><td>0.0381</td><td>0.0309</td><td>0.0322</td><td>0.0441</td><td>0.0474</td><td>0.0585</td><td>2e-7</td><td>23%</td></tr><tr><td>N@20</td><td>0.0154</td><td>0.0225</td><td>0.0236</td><td>0.0219</td><td>0.0249</td><td>0.0291</td><td>0.0238</td><td>0.0247</td><td>0.0328</td><td>0.0360</td><td>0.0436</td><td>2e-6</td><td>21%</td></tr><tr><td>R@40</td><td>0.0351</td><td>0.0432</td><td>0.0499</td><td>0.0489</td><td>0.0531</td><td>0.0621</td><td>0.0498</td><td>0.0525</td><td>0.0719</td><td>0.0750</td><td>0.0933</td><td>1e-7</td><td>24%</td></tr><tr><td>N@40</td><td>0.0201</td><td>0.0246</td><td>0.0290</td><td>0.0284</td><td>0.0312</td><td>0.0371</td><td>0.0301</td><td>0.0314</td><td>0.0420</td><td>0.0451</td><td>0.0551</td><td>9e-7</td><td>22%</td></tr><tr><td rowspan="4">[ig</td><td>R@20</td><td>0.0235</td><td>0.0233</td><td>0.0225</td><td>0.0203</td><td>0.0268</td><td>0.0222</td><td>0.0373</td><td>0.0314</td><td>0.0387</td><td>0.0473</td><td>0.0528</td><td>3e-5</td><td>11%</td></tr><tr><td>N@20</td><td>0.0163</td><td>0.0160</td><td>0.0154</td><td>0.0139</td><td>0.0183</td><td>0.0152</td><td>0.0252</td><td>0.0213</td><td>0.0262</td><td>0.0328</td><td>0.0361</td><td>1e-4</td><td>10%</td></tr><tr><td>R@40</td><td>0.0394</td><td>0.0350</td><td>0.0378</td><td>0.0340</td><td>0.0446</td><td>0.0367</td><td>0.0616</td><td>0.0519</td><td>0.0645</td><td>0.0766</td><td>0.0852</td><td>1e-5</td><td>11%</td></tr><tr><td>N@40</td><td>0.0218</td><td>0.0199</td><td>0.0208</td><td>0.0188</td><td>0.0246</td><td>0.0203</td><td>0.0337</td><td>0.0284</td><td>0.0352</td><td>0.0429</td><td>0.0473</td><td>7e-5</td><td>10%</td></tr></table>
|
| 133 |
+
|
| 134 |
+
• Contrastive Learning Dominates. As can be seen from the table, recent methods implementing contrastive learning (SGL, HCCF, SimGCL) exhibit consistent superiority as compared to traditional graph-based (GCCF, LightGCN) or hypergraph-based (HyRec) models. They also perform better than some of other self-supervised learning approaches (MHCN). This could be attributed to the effectiveness of CL to learn evenly distributed embeddings (Yu et al., 2022a).
|
| 135 |
+
|
| 136 |
+
• Contrastive Learning Enhancement. Our method consistently outperforms all the contrastive learning baselines. We attribute such performance improvement to the effective augmentation of graph contrastive learning via injecting global collaborative contextual signals. Other compared contrastive learning-based recommenders (e.g., SGL, SimGCL, and HCCF) are easily biased by noisy interaction information and generate misleading self-supervised signals.
|
| 137 |
+
|
| 138 |
+
# 4.3 EFFICIENCY STUDY (RQ2)
|
| 139 |
+
|
| 140 |
+
GCL models often suffer from a high computational cost due to the construction of extra views and the convolution operations performed on them during training. However, the low-rank nature of the SVD-reconstructed graph and the simplified CL structure enable the training of our LightGCL to be highly efficient. We analyze the pre-processing and per-batch training complexity of our model in comparison to three competitive baselines, as summarized in Table 2.‡
|
| 141 |
+
|
| 142 |
+
Table 2: Comparisons of computational complexity against baselines.
|
| 143 |
+
|
| 144 |
+
<table><tr><td>Stage</td><td>Computation</td><td>LightGCN</td><td>SGL</td><td>SimGCL</td><td>LightGCL</td></tr><tr><td>Pre-processing</td><td>Normalization SVD</td><td>O(E)</td><td>O(E)</td><td>O(E)</td><td>O(E) O(qE)</td></tr><tr><td>Training</td><td>Augmentation Graph Convolution BPRLoss InfoNCE Loss</td><td>O(2ELd) O(2Bd) 1</td><td>O(2pE) O(2ELd+4pELd) O(2Bd) O(Bd+BMd)</td><td>O(6ELd) O(2Bd) O(Bd+BMd)</td><td>O[2ELd+ 2q(I+ J)Ld] O(2Bd) O[(Bd+BMd)L]</td></tr></table>
|
| 145 |
+
|
| 146 |
+
• Although our model requires performing the SVD in the pre-processing stage which takes $O ( q E )$ , the computational cost is negligible compared to the training stage since it only needs to be performed once. In fact, by moving the construction of contrastive view to the pre-processing stage, we avoid the repetitive graph augmentation during training, which improves model efficiency.
|
| 147 |
+
|
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• Traditional GCN methods (e.g., LightGCN) only perform convolution on one graph, inducing a complexity of $O ( 2 E L d )$ per batch. For most GCL-based methods, three contrastive views are computed per batch, leading to a complexity of roughly three times of LightGCN. In our model, instead, only two contrastive views are involved. Additionally, due to the low-rank property of SVD-based graph structure learning, our graph encoder takes only $O [ 2 q ( I + J ) L d ]$ time. For most datasets, including the five we use, $\bar { 2 q } ( \bar { I } + J ) < E$ . Therefore, the training complexity of our model is less than half of that of the SOTA efficient model SimGCL.
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# 4.4 RESISTANCE AGAINST DATA SPARSITY AND POPULARITY BIAS (RQ3)
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To evaluate the robustness of our model in alleviating data sparsity, we group the sparse users by their interaction degrees and calculate the Recall $@ 2 0$ of each group on $Y e l p$ and Gowalla datasets. As can be seen from the figures, the performance of HCCF and SimGCL varies across datasets, but our LightGCL consistently outperforms them in all cases. In particular, our model performs notably well on the extremely sparse user group $< 1 5$ interactions), as the Recall $@ 2 0$ of these users is not much lower (and is even higher on Gowalla) than that of the whole dataset.
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Figure 2: Performance on users of different sparsity degrees, in terms of Recall (histograms) and relative Recall w.r.t overall performances (charts).
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Figure 3: LightGCL’s ability to alleviate popularity bias in comparison to SOTA CLbased methods HCCF and SimGCL.
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Additionally, we illustrate our model’s ability to mitigate popularity bias compared to HCCF and SimGCL. Similar to Section 4.4, we group the long-tail items by their degree of interactions. Following Wu et al. (2021), we adopt the decomposed Recall@20 defined as Recall(g) = |(Vurec)(g)∩Vutest||Vu | where $\mathbb { V } _ { t e s t } ^ { u }$ refers to the set of test items for the user $u$ , and $( \mathbb { V } _ { r e c } ^ { u } ) ^ { ( g ) }$ is the set of Top-K recommended items for $u$ that belong to group $g$ . The results are shown in Fig. 3. Similar to the results on sparse users, HCCF and SimGCL’s performance fluctuates a lot with the influence of popularity bias. Our model performs better in most cases, which shows its resistance against popularity bias. Note that since the extremely sparse group ( $< 1 5$ interactions) is significantly larger than the other groups in Gowalla, they contribute to a large fraction of the Recall $@ 2 0$ , resulting in a different trend from that of Yelp in the figure.
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# 4.5 BALANCING BETWEEN OVER-SMOOTHING AND OVER-UNIFORMITY (RQ3)
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In this section, we illustrate the effectiveness of our model in learning a moderately dispersed embedding distribution, by preserving user unique preference pattern and inter-user collaborative dependencies. We randomly sample 2,000 nodes from Yelp and Gowalla and map their embeddings to the 2-D space with t-SNE (Van der Maaten & Hinton, 2008). The visualizations of these embeddings are presented in Fig. 4. We also calculate the Mean Average Distance (MAD) (Chen et al., 2020a) of the embeddings, summarized in Table 3.
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Table 3: Mean Average Distance (MAD) of the embeddings learned by different methods.
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<table><tr><td>Dataset</td><td>MHCN</td><td>LightGCN</td><td>LightGCL</td><td>SGL</td><td>SimGCL</td></tr><tr><td>Yelp</td><td>0.8806</td><td>0.9469</td><td>0.9657</td><td>0.9962</td><td>0.9956</td></tr><tr><td>Gowalla</td><td>0.9247</td><td>0.9568</td><td>0.9721</td><td>0.9859</td><td>0.9897</td></tr></table>
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Figure 4: Embedding distributions on Yelp and Gowalla visualized with t-SNE.
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As can be seen from Fig. 4, the embedding distributions of non-CL methods (i.e., LightGCN, MHCN) exhibit indistinguishable clusters in the embedding space, which indicates the limitation of addressing the over-smoothing issue. On the contrary, the existing CL-based methods tend to learn i) over-uniform distributions, e.g., SGL on $Y e l p$ learns a huge cloud of evenly-distanced embeddings with no clear community structure to well capture the collaborative relations between users; ii) highly dispersed small clusters with severe over-smoothing issue inside the clusters, e.g., the embeddings of SimGCL on Gowalla appear to be scattered grained clusters inside which embeddings are highly similar. Compared with them, clear community structures could be identified by our method to capture collaborative effects, while the embeddings inside each community are reasonably dispersed to be reflective of user-specific preference. The MAD of our model’s learned features is also in between of the two types of baselines as shown in Table 3.
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# 4.6 ABLATION STUDY (RQ4)
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To investigate the effectiveness of our SVD-based graph augmentation scheme, we perform the ablation study to answer the question of whether we could provide guidance to the contrastive learning with a different approach of matrix decomposition. To this end, we implement two variants of our model, replacing the approximated SVD algorithm with other matrix decomposition methods: $C L .$ - $M F$ adopts the view generated by a pre-trained MF (Koren et al., 2009); $C L { \cdot } S V D { + } +$ utilizes the $\mathrm { S V D + + }$ (Koren, 2008) which takes implicit user feedback into consideration. As shown in Table 4, with the information distilled from MF or $\mathrm { S V D + + }$ , the model is able to achieve satisfactory results, indicating the effectiveness of using matrix decomposition to empower CL and the flexibility of our proposed framework. However, adopting a pre-trained CL component is not only tedious and timeconsuming but also inferior to utilizing the approximate SVD algorithm in terms of performance.
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Table 4: Ablation study on LightGCL.
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<table><tr><td rowspan="2">Variant</td><td colspan="2">Yelp</td><td colspan="2">Gowalla</td></tr><tr><td>Recall@20</td><td>NDCG@20</td><td>Recall@20</td><td>NDCG@20</td></tr><tr><td>CL-MF</td><td>0.0781</td><td>0.0659</td><td>0.1561</td><td>0.0929</td></tr><tr><td>CL-SVD++</td><td>0.0788</td><td>0.0666</td><td>0.1568</td><td>0.0932</td></tr><tr><td>LightGCL</td><td>0.0793</td><td>0.0668</td><td>0.1578</td><td>0.0935</td></tr></table>
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Figure 5: Recall change w.r.t. $q$
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# 4.7 HYPERPARAMETER ANALYSIS (RQ5)
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In this section, we investigate our model’s sensitivity in relation to several key hyperparameters: the regularization weight for InfoNCE loss $\lambda _ { 1 }$ , the temperature $\tau$ , and the required rank of SVD $q$ .
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• The impact of $\lambda _ { 1 }$ . As illustrated in Fig. 6, for the three datasets Yelp, Gowalla and ML-10M, the model’s performance reaches the peak when $\lambda _ { 1 } = 1 0 ^ { - 7 }$ . It can be noticed that $\lambda _ { 1 }$ with the range of $[ 1 0 ^ { - 6 } , 1 0 ^ { - 8 } ]$ can often lead to performance improvement.
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Figure 6: Impact of $\lambda _ { 1 }$ .
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Figure 7: Impact of $\tau$
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• The impact of $\tau$ . Fig. 7 indicates that the model’s performance is relatively stable across different selections of $\tau$ from 0.1 to 10, while the best configuration of $\tau$ value varies by datasets.
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• The selection of $q$ . $q$ determines the rank of SVD in our model. Experiments have shown that satisfactory results can be achieved with a small $q$ . Specifically, as in Fig. 5, we observe that $q = 5$ is sufficient to preserve important structures of the user-item interaction graph.
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# 4.8 CASE STUDY (RQ4)
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In this section, we present a case study to intuitively show the effectiveness of our model to identify useful knowledge from noisy user-item interactions and make accurate recommendations accordingly. In Fig. 8, we can see that the venues visited by user $\# 2 6$ in Yelp mainly fall into two communities: Cleveland (where the user probably lives) and Arizona (where the user may have travelled to). In the reconstructed graph, these venues are assigned a new weight according to their potential importance. Note that item $\# 2 5 8 3$ , a car rental agency in Arizona, has been assigned a negative weight, which conforms to our common sense that people generally would not visit multiple car rental agencies in one trip. The SVD-augmented view also provides predictions on invisible links by assigning a large weight§ to potential venues of interest, such as #2647 and #658. Note that when exploiting the graph, the augmented view does not overlook the smaller Arizona community, which enables the model to predict items of minor interests that are usually overshadowed by the majority.
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Figure 8: Case study on user $\# 2 6$ in Yelp dataset.
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# 5 CONCLUSION
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In this paper, we propose a simple and effective augmentation method to the graph contrastive learning framework for recommendation. Specifically, we explore the key idea of making the singular value decomposition powerful enough to augment user-item interaction graph structures. Our key findings indicate that our graph augmentation scheme exhibits strong ability in resisting data sparsity and popularity bias. Extensive experiments show that our model achieves new state-of-the-art results on several public evaluation datasets. In future work, we plan to explore the potential of incorporating casual analysis into our lightweight graph contrastive learning model to enhance the recommender system with mitigating confounding effects for data augmentation.
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Lei Chen, Le Wu, Richang Hong, Kun Zhang, and Meng Wang. Revisiting graph based collaborative filtering: A linear residual graph convolutional network approach. In AAAI conference on artificial intelligence, volume 34, pp. 27–34, 2020b.
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Lei Chen, Le Wu, Richang Hong, Kun Zhang, and Meng Wang. Revisiting graph based collaborative filtering: A linear residual graph convolutional network approach. In Proceedings of the AAAI conference on artificial intelligence, volume 34, pp. 27–34, 2020c.
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Yanqiao Zhu, Yichen Xu, Feng Yu, Qiang Liu, Shu Wu, and Liang Wang. Deep graph contrastive representation learning. arXiv preprint arXiv:2006.04131, 2020.
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Yanqiao Zhu, Yichen Xu, Qiang Liu, and Shu Wu. An empirical study of graph contrastive learning. arXiv preprint arXiv:2109.01116, 2021a.
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# A DETAILS OF THE BASELINES
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MLP-enhanced Collaborative Filtering:
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• NCF (He et al., 2017) is a collaborative filtering model that leverages neural network to exploit non-linearity. Two hidden layers are used in our evaluation.
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GNN-based Collaborative Filtering:
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• GCCF (Chen et al., 2020c) strengthens the GNN-based collaborative filtering by implementing a residual network and reducing the non-linear transformation.
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• LightGCN (He et al., 2020) adopts a simplified GCN structure without embedding weight matrices and non-linear projection.
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Disentangled Graph Collaborative Filtering:
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• DGCF (Wang et al., 2020b) learns a more sophisticated representation by segmenting the embedding vectors to represent multiple latent intentions.
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Hypergraph-based Collaborative Filtering:
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• HyRec (Wang et al., 2020a) makes use of hypergraph to encode multi-order information between users and items.
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Self-Supervised Learning Recommender Systems:
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• GraphCL (You et al., 2020) utilizes random node dropping and edge masking to generate two contrastive views, which were aligned by optimizing the SSL loss function.
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• GRACE (Zhu et al., 2020) proposes to corrupt the graph structure by both random edge dropout and random node feature dropping, and uses the corrupted graphs as the contrastive views.
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• GCA (Zhu et al., 2021b) adaptively dropout the nodes and edges by their importance calculated with node centrality.
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• MHCN (Yu et al., 2021) creates self-supervised signals for the graph representation learning by graph infomax network.
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• SAIL (Yu et al., 2022b) maximizes the neighborhood predicting probability between GNNgenerated high-level features and input node features.
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• AutoGCL (Yin et al., 2022) uses GNN to learn to mask nodes and edges in the augmented graph. It minimizes the similarity between the augmented and the original graph, while maximizing the similarity of the embeddings generated through them, so as to uncover the most important information in the graph.
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• SimGRACE (Xia et al., 2022a) creates augmented view by randomly perturbing the parameters of the GNN network.
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• SGL (Wu et al., 2021) adopts random walk sampling and probabilistic edge/node dropout to create augmented views for contrastive learning. In our experiments, we adopt the SGL-ED variant, which implements random edge dropout and exhibits the strongest performance according to the original paper.
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• HCCF (Xia et al., 2022b) encodes global graph information with hypergraph and contrasts it against the local information encoded with GCN. In our experiments, the number of hyper-edges are set as 128 following the original paper.
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• SHT (Xia et al., 2022c) adopts a hypergraph transformer framework to exploit global collaborative relationships and distills the global information to generate the cross-view self-supervised signals. In our experiments, the number of hyper-edges are set as 128 following the original paper.
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• SimGCL (Yu et al., 2022a) propose to simplify the graph augmentation process of contrastive learning by directly injecting random noises into the feature representation.
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# B PERFORMANCE COMPARISON WITH BASELINES (CONTINUED)
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In this appendix, we show the performance of NCF, GCCF, GraphCL, SAIL, GRACE, and AutoGCL, which are not shown in Table 1 due to space limit. The results are summarized in Table 5. As can be seen from the table, our model outperforms these baselines consistently.
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Table 5: Performance comparison with baselines on five datasets (continued).
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| 344 |
+
<table><tr><td rowspan=1 colspan=1>Data</td><td rowspan=1 colspan=1>Metric</td><td rowspan=1 colspan=1>NCF</td><td rowspan=1 colspan=1>GCCF</td><td rowspan=1 colspan=1>GraphCL</td><td rowspan=1 colspan=1>SAIL</td><td rowspan=1 colspan=1>GRACE</td><td rowspan=1 colspan=1>AutoGCL</td><td rowspan=1 colspan=1>LightGCL</td></tr><tr><td rowspan=2 colspan=1>Yelp</td><td rowspan=1 colspan=1>R@20N@20</td><td rowspan=1 colspan=1>0.02520.0202</td><td rowspan=1 colspan=1>0.04620.0398</td><td rowspan=1 colspan=1>0.04620.0401</td><td rowspan=1 colspan=1>0.04710.0405</td><td rowspan=1 colspan=1>0.05500.0470</td><td rowspan=1 colspan=1>0.05930.0494</td><td rowspan=1 colspan=1>0.07930.0668</td></tr><tr><td rowspan=1 colspan=1>R@40N@40</td><td rowspan=1 colspan=1>0.04870.0289</td><td rowspan=1 colspan=1>0.07600.0508</td><td rowspan=1 colspan=1>0.07640.0511</td><td rowspan=1 colspan=1>0.07730.0516</td><td rowspan=1 colspan=1>0.09170.0605</td><td rowspan=1 colspan=1>0.10090.0650</td><td rowspan=1 colspan=1>0.12920.0852</td></tr><tr><td rowspan=2 colspan=1>Gowalla</td><td rowspan=1 colspan=1>R@20N@20</td><td rowspan=1 colspan=1>0.01710.0106</td><td rowspan=1 colspan=1>0.09510.0535</td><td rowspan=1 colspan=1>0.09970.0603</td><td rowspan=1 colspan=1>0.09990.0602</td><td rowspan=1 colspan=1>0.07440.0452</td><td rowspan=1 colspan=1>0.08320.0484</td><td rowspan=1 colspan=1>0.15780.0935</td></tr><tr><td rowspan=1 colspan=1>R@40N@40</td><td rowspan=1 colspan=1>0.02160.0118</td><td rowspan=1 colspan=1>0.13920.0684</td><td rowspan=1 colspan=1>0.14730.0727</td><td rowspan=1 colspan=1>0.14720.0725</td><td rowspan=1 colspan=1>0.10710.0539</td><td rowspan=1 colspan=1>0.12910.0605</td><td rowspan=1 colspan=1>0.22450.1108</td></tr><tr><td rowspan=2 colspan=1>ML-10M</td><td rowspan=1 colspan=1>R@20N@20</td><td rowspan=1 colspan=1>0.10970.1297</td><td rowspan=1 colspan=1>0.17420.2109</td><td rowspan=1 colspan=1>0.16590.2038</td><td rowspan=1 colspan=1>0.17280.2118</td><td rowspan=1 colspan=1>0.21070.2476</td><td rowspan=1 colspan=1>0.23250.2755</td><td rowspan=1 colspan=1>0.26130.3106</td></tr><tr><td rowspan=1 colspan=1>R@40N@40</td><td rowspan=1 colspan=1>0.16340.1427</td><td rowspan=1 colspan=1>0.26060.2331</td><td rowspan=1 colspan=1>0.25600.2250</td><td rowspan=1 colspan=1>0.26390.2332</td><td rowspan=1 colspan=1>0.30750.2711</td><td rowspan=1 colspan=1>0.34150.3023</td><td rowspan=1 colspan=1>0.37990.3387</td></tr><tr><td rowspan=2 colspan=1>Amazon</td><td rowspan=1 colspan=1>R@20N@20</td><td rowspan=1 colspan=1>0.01420.0085</td><td rowspan=1 colspan=1>0.03170.0243</td><td rowspan=1 colspan=1>0.03600.0266</td><td rowspan=1 colspan=1>0.03570.0264</td><td rowspan=1 colspan=1>0.03600.0271</td><td rowspan=1 colspan=1>0.03250.0241</td><td rowspan=1 colspan=1>0.05850.0436</td></tr><tr><td rowspan=1 colspan=1>R@40N@40</td><td rowspan=1 colspan=1>0.02230.0133</td><td rowspan=1 colspan=1>0.04830.0285</td><td rowspan=1 colspan=1>0.05850.0340</td><td rowspan=1 colspan=1>0.05810.0338</td><td rowspan=1 colspan=1>0.05830.0345</td><td rowspan=1 colspan=1>0.05530.0318</td><td rowspan=1 colspan=1>0.09330.0551</td></tr><tr><td rowspan=2 colspan=1>Tmall</td><td rowspan=1 colspan=1>R@20N@20</td><td rowspan=1 colspan=1>0.00820.0059</td><td rowspan=1 colspan=1>0.02090.0141</td><td rowspan=1 colspan=1>0.02510.0175</td><td rowspan=1 colspan=1>0.02540.0177</td><td rowspan=1 colspan=1>0.03030.0210</td><td rowspan=1 colspan=1>0.03120.0204</td><td rowspan=1 colspan=1>0.05280.0361</td></tr><tr><td rowspan=1 colspan=1>R@40N@40</td><td rowspan=1 colspan=1>0.01400.0079</td><td rowspan=1 colspan=1>0.03560.0196</td><td rowspan=1 colspan=1>0.04160.0233</td><td rowspan=1 colspan=1>0.04240.0236</td><td rowspan=1 colspan=1>0.05050.0281</td><td rowspan=1 colspan=1>0.05240.0278</td><td rowspan=1 colspan=1>0.08520.0473</td></tr></table>
|
| 345 |
+
|
| 346 |
+
# C THEORETICAL ANALYSIS
|
| 347 |
+
|
| 348 |
+
We conduct theoretical analyses to show that our local-global CL (Eq. 7) is augmented to maximize the similarity between embeddings of potentially related nodes, based on the SVD-based global relation learning. Specifically, for a node $v _ { j } ~ \in { \mathcal { U } }$ , where $\mathcal { U } = \{ u _ { i ^ { \prime } } | \mathcal { A } _ { i , i ^ { \prime } } = 0 , \hat { \mathcal { A } } _ { i , i ^ { \prime } } \neq 0 \}$ , the embeddings are not updated by $s ( z _ { i , l } , g _ { i , l } )$ in the vanilla InfoNCE loss, as $v _ { j }$ is not adjacent to $u _ { i }$ . Instead, our local-global contrastive assigns the following gradients to the embeddings of $v _ { j }$ :
|
| 349 |
+
|
| 350 |
+
$$
|
| 351 |
+
\begin{array} { l } { \displaystyle \partial s ( z _ { i , l } , g _ { i , l } ) / \partial g _ { i , l - 1 } = \partial s \left( z _ { i , l } , \sigma ( \displaystyle \sum _ { j \in \mathcal { U } } \alpha _ { i , j } g _ { j , l - 1 } + \displaystyle \sum _ { A _ { i , j ^ { \prime } } \neq 0 } \alpha _ { i , j ^ { \prime } } g _ { j ^ { \prime } , l - 1 } ) \right) / \partial g _ { j , l - 1 } } \\ { = \frac { z _ { i , l } } { \| z _ { i , l } \| \| g _ { i , l } \| } \cdot \boldsymbol { \sigma } ^ { \prime } ( \cdot ) \cdot \boldsymbol { \alpha } _ { i , j } } \end{array}
|
| 352 |
+
$$
|
| 353 |
+
|
| 354 |
+
where $\alpha _ { i , j }$ denotes the normalization weight for node $u _ { i }$ and $v _ { j }$ . In this way, the embeddings of nodes in $\mathcal { U }$ are also pulled close to $s _ { i , l }$ , which injects relatedness information learned by the SVD into the local-global CL optimization.
|
| 355 |
+
|
| 356 |
+
# D CALCULATION OF COMPLEXITY
|
| 357 |
+
|
| 358 |
+
# D.1 ADJACENCY MATRIX NORMALIZATION
|
| 359 |
+
|
| 360 |
+
For a sparse user-item matrix stored in the Coordinate Format (COO), it requires visiting every nonzero elements in the matrix to perform normalization. Thus, the computational complexity is in the order of the number of edges ${ \bf \bar { \boldsymbol { O } } } ( E )$ . Note that for the baseline SGL, it requires normalizing the two augmented graph structures during the training phase, each of which contains $\rho E$ edges, so it induces a complexity of $O ( 2 \rho E )$ per batch.
|
| 361 |
+
|
| 362 |
+
# D.2 APPROXIMATE SVD ALGORITHM
|
| 363 |
+
|
| 364 |
+
We refer the readers to Halko et al. (2011) in which the complexity of the approximate SVD algorithm is explained in detail.
|
| 365 |
+
|
| 366 |
+
# D.3 GRAPH CONVOLUTION
|
| 367 |
+
|
| 368 |
+
Given a sparse COO matrix $\mathcal { A }$ with $E$ edges and a dense matrix $\pmb { \cal E }$ with dimensions $I ( J ) \times d$ , it takes $O ( E d )$ time to calculate $\mathcal { A } E$ . To perform graph convolution on a graph, we need to multiply the sparse adjacency matrix with $\pmb { { E } } _ { l - 1 } ^ { ( v ) } \in \mathbb { R } ^ { J \times d }$ and its transpose with $E _ { l - 1 } ^ { ( u ) } \in \mathbb { R } ^ { I \times d }$ , which takes $O ( E d )$ each, and $O ( 2 E d )$ in total. For $L$ layers, $O ( 2 E L d )$ is required. For traditional CL-based methods such as SGL and $\mathrm { S i m C G L }$ , a three-view structure is adopted, resulting in a complexity of $O ( 1 2 E L d )$ (for SGL it again varies a bit depending on $\rho$ ).
|
| 369 |
+
|
| 370 |
+
For the SVD-view of our model, $\hat { V } _ { q } ^ { \top } E _ { l - 1 } ^ { ( v ) }$ takes $O ( q J d )$ , and multiplying the result with the precalculated $( \hat { U } _ { q } \hat { S } _ { q } )$ takes $O ( q I d )$ ; $\hat { U } _ { q } ^ { \top } E _ { l - 1 } ^ { ( v ) }$ takes $O ( q I d )$ , and multiplying the result with the precalculated $( \hat { V } _ { q } \hat { S } _ { q } )$ takes $O ( q J d )$ . So in total it takes $O ( 2 q ( I + J ) d )$ .
|
| 371 |
+
|
| 372 |
+
# D.4 BPR LOSS
|
| 373 |
+
|
| 374 |
+
In each batch with $B$ users, calculating the scores for positive and negative items both take $O ( B d )$ , so in total it takes $O ( 2 B d )$ .
|
| 375 |
+
|
| 376 |
+
# D.5 CL LOSS
|
| 377 |
+
|
| 378 |
+
In each batch with $B$ users, calculating the numerator of InfoNCE loss takes $O ( B d )$ , and calculating the denominator takes $O ( B M d )$ where $M$ denotes the total number of nodes in the batch. Since our model adopts a per layer InfoNCE loss, a factor of $L$ is appended.
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parse/dev/MAMOi89bOL/MAMOi89bOL.md
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|
| 1 |
+
# Masked Autoencoders that Listen
|
| 2 |
+
|
| 3 |
+
Po-Yao Huang1 Hu Xu1 Juncheng Li2 Alexei Baevski1 Michael Auli1 Wojciech Galuba1 Florian Metze1 Christoph Feichtenhofer1
|
| 4 |
+
|
| 5 |
+
1Meta AI 2Carnegie Mellon University
|
| 6 |
+
|
| 7 |
+
# Abstract
|
| 8 |
+
|
| 9 |
+
This paper studies a simple extension of image-based Masked Autoencoders (MAE) [1] to self-supervised representation learning from audio spectrograms. Following the Transformer encoder-decoder design in MAE, our Audio-MAE first encodes audio spectrogram patches with a high masking ratio, feeding only the non-masked tokens through encoder layers. The decoder then re-orders and decodes the encoded context padded with mask tokens, in order to reconstruct the input spectrogram. We find it beneficial to incorporate local window attention in the decoder, as audio spectrograms are highly correlated in local time and frequency bands. We then fine-tune the encoder with a lower masking ratio on target datasets. Empirically, Audio-MAE sets new state-of-the-art performance on six audio and speech classification tasks, outperforming other recent models that use external supervised pre-training. Our code and models is available at https://github.com/facebookresearch/AudioMAE.
|
| 10 |
+
|
| 11 |
+
# 1 Introduction
|
| 12 |
+
|
| 13 |
+
Transformers [2] and self-supervised learning [3, 4, 5, 6, 7, 1] are dominating computer vision (CV) and natural language processing (NLP) research. The revolution firstly started in NLP with the invention of the Transformer architecture and self-attention [8]. Masked autoencoding with BERT [3] set a new state-of-the-art on various NLP tasks by self-supervised pre-training on large-scale language corpus. Similarly in the CV community, Vision Transformers (ViT) [9] have become popular for CV tasks, and, for self-supervised image representation learning, Masked Autoencoders (MAE) [1] have brought the CV community closer to the success of BERT in NLP. In addition to the existing masked autoencoders that can read (BERT) or see (MAE), in this work we study those that can listen.
|
| 14 |
+
|
| 15 |
+
Transformer-based models have recently refreshed leaderboards for audio understanding tasks. For example, AST [10] and MBT [11] improved the audio classification performance on the AudioSet [12], Event Sound Classification [13], etc. The key technique behind this is initialization of audio model weights with ImageNet pre-trained supervised models (e.g., DeiT [14]) by deflating patch embeddings and interpolating positional embeddings for encoding audio spectrograms. However, exploiting ImageNet pre-trained models could be sub-optimal. Unlike initializing video models with weights from image models (e.g., the initial weights of I3D [15] or 3D-ResNets [16] are inflated from ImageNet pre-trained image models), there are clear and notable discrepancies between spectrograms representing audio content and natural images. It remains unclear why such heterogeneous image-toaudio transfer is useful beyond arguably similar low-level semantics such as shapes of spectrograms and shapes of visual objects. Further, any label bias would inevitably be transferred to audio models.
|
| 16 |
+
|
| 17 |
+
Addressing these concerns, self-supervised audio representation learning has recently attracted much research attention. Based on BEiT [17] that learns to reconstruct image patches or learnt patch tokens, SS-AST [18] extends to the audio domain and exploits spectrograms (akin to 1-channel 2D images) and use both contrastive and reconstruction objective as self-supervision. Without using any labels, the key enabler to effective self-supervised representation learning is large-scale pre-training data. In this work we use AudioSet [12] for pre-training, a common dataset containing ${ \sim } 2$ million audio recordings. Performing large-scale training with Transformer architectures is challenging as self-attention in Transformers has quadratic complexity w.r.t. the length of input sequence.
|
| 18 |
+
|
| 19 |
+
|
| 20 |
+
Figure 1: Audio-MAE for audio self-supervised learning. An audio recording is first transformed into a spectrogram and split into patches. We embed patches and mask out a large subset $( 8 0 \% )$ . An encoder then operates on the visible $( 2 0 \% )$ patch embeddings. Finally, a decoder processes the order-restored embeddings and mask tokens to reconstruct the input. Audio-MAE is minimizing the mean square error (MSE) on the masked portion of the reconstruction and the input spectrogram.
|
| 21 |
+
|
| 22 |
+
This computational burden has been addressed in different ways. A popular approach is to reduce the sequence length in self-attention. Various ViT-based architectures have been developed to alleviate such issues for image and video understanding. For example, Swin-Transformer [19] only performs local attention within windows that shift across layers. MViT [20] employs pooling attention to construct a hierarchy of Transformers where sequence lengths are downsampled. For self-supervised learning, MAE [1] efficiently encodes only a small portion $( 2 5 \% )$ of visual patches while the majority of patches is discarded. The simplicity and scalability in MAE make it a promising framework for large-scale self-supervised learning.
|
| 23 |
+
|
| 24 |
+
In this work, we study MAE for sound recognition and the unique challenges of the audio domain. We present Audio-MAE (Fig. 1) as unified and scalable framework for learning self-supervised audio representations. Similar to MAE, it is composed of a pair of a Transformer encoder and decoder. Sound is first transformed and embedded into spectrogram patches. Before feeding them into the Transformer encoder, we mask and discard the majority and only feed a small number of non-masked embeddings into the encoder for efficient encoding. After padding encoded patches with learnable embeddings to represent masked patches, it then restores the order of these patches in frequency and time and propagates them through a Transformer decoder to reconstruct the audio spectrogram.
|
| 25 |
+
|
| 26 |
+
Different from image patches, spectrogram patches are comparably local-correlated. For example, formants, the vocal tract resonances, are typically grouped and continuous locally in the spectrogram. The location in frequency and time embeds essential information that determines the semantics of a spectrogram patch and how it sounds like. To this end, we further investigate using localized attention and a hybrid architecture in the Transformer decoder to properly decode for reconstruction. This simple-yet-effective upgrade leads to improved performance for Audio-MAE.
|
| 27 |
+
|
| 28 |
+
Similar to MAE for images, we minimize the patch-normalized mean square error. At the fine-tuning stage, we discard the decoder and fine-tune the encoder with patch-masking. Empirically, AudioMAE sets a new state-of-the-art performance on six audio and speech classification tasks. It is the first audio-only self-supervised model that achieves state-of-the-art mAP on AudioSet-2M, outperforming other recent models with external supervision. We further provide the visualization and audible examples to qualitatively demonstrate the effectiveness of the Audio-MAE decoder.
|
| 29 |
+
|
| 30 |
+
# 2 Related Work
|
| 31 |
+
|
| 32 |
+
Visual masked pre-training. Masked/Denoising autoencoders [21, 22, 3] are a general representation learning methodology by reconstructing source from masked or corrupted inputs. In CV, visual masked pre-training has made recent progress [23, 24, 1, 20]. Based on ViT [9] that applies Transformers to image patches, BEiT [17] and MAE [1] present masked image modeling frameworks. BEiT [17] learns to predict discrete visual tokens generated by VAE [25] in masked patches. MAE [1] reduces sequence length by masking a large portion of image patches randomly and encoding only non-masked ones for reconstruction of pixel color information. MaskFeat [20] studies features for masked pre-training and finds that Histograms of Oriented Gradients (HoG) [26], which are in turn related to spectrogram features, perform strongly for image and video classification models. Our work extends the MAE framework for representation learning with audio spectrograms.
|
| 33 |
+
|
| 34 |
+
Out-of-domain pre-training for audio. Transferring ImageNet supervised pre-trained ViT [9] or ResNet [27] has become a popular practice for audio models [10, 28, 11, 29, 30, 31]. After pre-training, these models operate over audio spectrograms by deflating from 3-channels (RGB) into 1-channel (spectrogram) in the pre-trained patch embedding in ViT and employing the rest of the transformer blocks on top. For example, HTS-AT [29] encodes spectrograms with hierarchical Transformer initialized from the Swin Transformer [19]. MBT [11] uses ImageNet-21K pre-trained ViT; AST [10] and PaSST [28] employ DeiT [14] as the Transformer backbone. Without using out-of-domain (non-audio) data, the proposed Audio-MAE focuses on audio-only self-supervised pre-training from scratch.
|
| 35 |
+
|
| 36 |
+
In-domain pre-training for audio. Existing in-domain (i.e., audio-only) self-supervised methods can be broadly categorized by the input signal type (e.g., raw waveform [32, 33, 34], frame-level features [35, 36, 37], or spectrogram patches [18, 38]); and the objective used for self-supervision (e.g., contrastive [39, 33, 40, 41, 35] or prediction/reconstruction [18, 34, 37, 36]). For example, wav2vec 2.0 [33] takes raw waveform as inputs and exploits contrastive learning to discriminate contextualized representations in different time segments. Mockingjay [42] proposed a masked acoustic model pretext task to reconstruct frame-level Mel-features of masked time frames. SSAST [18] is the closest work to Audio-MAE and is our main benchmark. Inspired by the success of BERT [3], SS-AST proposed a self-supervised learning method which operates over spectrogram patches and employs joint contrastive and reconstructive objectives on masked patches. These previous methods generate audio representations by encoding full-view of both masked and nonmasked time or spectrogram segments for self-supervised pre-training. In contrast, Audio-MAE encodes only the non-masked spectrogram patches.
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Our work is done independently and concurrently with [38, 43, 44] related methods. We also compare our model to these concurrent works in the experiments and showcase the superiority of Audio-MAE.
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# 3 Audio Masked Autoencoders (Audio-MAE)
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Audio-MAE is a conceptually simple extension of MAE to learn self-supervised representations from audio spectrograms. Fig. 1 depicts an overview. The details of each component are as follows.
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Spectrogram Patch Embeddings. Following [10, 18], we transform audio recordings into Melspectrograms and divide them into non-overlapped regular grid patches. These patches are then flattened and embedded by a linear projection. Similar to MAE [1], we add fixed sinusoidal positional embeddings to the embedded patches.
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Figure 2: Audio-MAE’s masking strategies on Mel-spectrograms.
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Masking Strategies. Audio-MAE masks out a large subset of spectrogram patches. As a spectrogram can be viewed as a 2D representation of time and frequency components of a sound, it is reasonable to explore treating time and frequency differently during masking. In this work, we investigate both the unstructured (i.e., random masking without any prior) and structured (i.e., randomly masking a portion of time, frequency, or time $^ +$ frequency of a spectrogram) in the pre-training and fine-tuning phase. Illustrative examples are shown in Fig. 2. We show masked regions with dark overlay.
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The masking mechanism, as introduced in MAE [1], is the key ingredient for efficient self-supervised learning. For a input patch sequence, this can be regarded as a Bernoulli process where each patch is masked/dropped with probability $p$ (masking ratio). Masking reduces input patch sequence length and encourages learning global, contextualized representations from limited “visible” patches. We observe that akin to images, a large masking rate ( $80 \%$ in our experiments for spectrogram patches, which is similar to $7 5 \%$ in MAE for images) is feasible for learning self-supervised audio representations. Unlike BERT [3] that uses $15 \%$ masking rate for self-supervised learning in NLP, most of the tokens/patches can be discarded for spectrograms as well as images due to high redundancy in these modalities. Beyond self-supervised pre-training, we further explore the effectiveness of masking in the supervised fine-tuning stage. Empirically, we found unstructured (random) masking at a higher ratio for pre-training and structured (time+frequency masking) at a lower ratio for fine-tuning provide best accuracy (ablations are in $\ S \_ 4 )$ ).
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Encoder. Audio-MAE uses a stack of standard Transformers [2] as its encoder. The encoder only processes $( 2 0 \% )$ non-masked patches to reduce computation overhead which is quadratic to the input sequence length. We use the 12-layer ViT-Base (ViT-B) [9] Transformer as our default.
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Decoder with Local Attention. The decoder is also composed of standard Transformer blocks. The encoded patches from the encoder are padded with trainable masked tokens. After restoring the original time-frequency order in the audio spectrogram, we add the decoder’s (fixed sinusoidal) positional embeddings and feed the restored sequence into the decoder. At the top of the decoder stack, we add a linear head to predict and reconstruct the input spectrogram.
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To address the unique characteristics of audio spectrograms, our work investigates an enhancement to the vanilla MAE decoder. Image-based MAE uses global self-attention in the Transformer decoder which is appropriate for visual context, because visual objects are typically invariant under translation or scaling, and their exact position may not affect the semantics of an image. In contrast, the position, scale, and translation of spectrogram features however directly affects the sound or semantics of an audio recording. Consequently, global self-attention is sub-optimal for spectrograms if the timefrequency components is predominantly local. For instance, we would have better success to use the harmonics (e.g., Fig. 2a) in lower bands of a vowel to predict the spectrogram patch vertically in a higher frequency band rather than horizontally in the time domain. Similarly, a frictional sound of a consonant likely only correlates to other part of the consonant, and is without dependency to other silence segments in the audio recording. Compared to images, the spectrogram patches are more similar to speech or text tokens where its order and position is more relevant.
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To address the nature of audio spectrograms, in addition to using Transformers with global self-attention as in vanilla MAE, we incorporate the local attention mechanism which groups and separates the spectrogram patches in to local windows in self-attention for decoding. We investigate two types of local attention: (1) Shifted window location: Inspired by the shifted-window in Swin Transformers [19], we shift window attention by $50 \%$ between consecutive Transformer decoder layers. For padding the margin when shifting, we cyclically shift the spectrogram to the top-left direction. Fig. 3 illustrates the localized decoder attention by shifted windows. (2) Hybrid window attention (global+local attention): Inspired by [45], to add better cross-window connections, we design a simple hybrid (global+local) attention that computes local attention within a window in all but the last few top layers. In this way, the input feature maps for the final reconstruction layer also contain global information. For simplicity, we use $_ { n o }$ pooling or hierarchical structure. Decoders with different attention types are compared in $\ S \ O = 4$ .
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Figure 3: Decoder’s local attention and shifted window (right).
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Objective. The Audio-MAE decoder learns to reconstruct the input spectrogram by predicting the values in the spectrogram patches or their per-patch normalized ones. The objective is the mean squared error (MSE) between the prediction and the input spectrogram, averaged over unknown patches. Empirically we found employing the reconstruction loss alone is sufficient while including additional contrastive objectives (e.g., InfoNCE loss [46]) does not improve Audio-MAE.
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Fine-tuning for Downstream Tasks. In the fine-tuning stage, we only keep and fine-tune the AudioMAE encoder and discard the decoder. Different from the original MAE, and inspired by [47, 28], we also explore to employ masking in the fine-tuning stage to remove a portion of patches to further regularize learning from a limited view of spectrogram inputs, which, as a side effect, also reduces computation during fine-tuning. Compared to SpecAug [48] which takes full-length input with the masked portion set to zero as data augmentation, Audio-MAE sees only a subset of real-valued input patches without the nullified ones. Audio-MAE then encodes these non-masked patches and applies an average pooling layer followed by a linear layer on top for fine-tuning in classification tasks.
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# 4 Experiments
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We perform an extensive evaluation on six tasks, including audio classification on AudioSet (AS-2M, AS-20K) and Environmental Sound Classification (ESC-50), and speech classification on Speech Commands (SPC-1 and SPC-2) and VoxCeleb (SID). We use AudioSet for ablation studies.
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# 4.1 Datasets and Tasks
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AudioSet [12] (AS-2M, AS-20K) contains ${ \sim } 2$ million 10-second YouTube clips for audio classification. 527 types of audio events are weakly annotated [49, 50, 51] for each clip. There could be multiple events in a clip. The full training set has 2 subsets: A class-wise balanced (22,176 clips) and an unbalanced (2,042,985 clips) set. The eval set has 20,383 clips. We downloaded and processed around 1.96M unbalanced training, 21K balanced training, and 19K evaluation clips.
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For the AS-2M experiments, we use the union of unbalanced and balanced training audio for pretraining and fine-tuning. For the AS-20K experiments, we use AS-2M for pre-training and the 20K balanced set for fine-tuning. We report the testing mAP on the 19K eval set used by AST [10].
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Environmental Sound Classification (ESC-50) [13] is an audio classification dataset consists of 2,000 5-second environmental sound recordings. There are 50 classes in ESC. We report accuracy under 5-fold cross-validation with the same split used by [10].
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Speech Commands (SPC-2, SPC-1) [52] are two keyword spotting tasks. In SPC-2, there are 35 speech commands. The training/validation/testing set has 84,843/9,981/11,005 1-second recordings, respectively. In SPC-1, there are 10 classes of keywords, 1 silence class, and 1 unknown class that includes all the other 20 common speech commands. We use the data and split provided in the SUPERB [53] benchmark to report the testing accuracy.
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VoxCeleb (SID) [54] contains 150K utterances from 1,251 speakers. The speaker identification task (SID) is to classify the utterances to identify its original speaker. We use the V1 standard train (138,361), validation (6,904), testing (8,251) sets and report the testing accuracy.
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# 4.2 Implementation Details
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We use a vanilla 12-layer ViT-B by default as the Transformer encoder. For the decoder, we use a 16-layer Transformer with shifted local attention. We investigate the vanilla (global attention) and hybrid (global+local attention) decoder variants (see Table. 1c).
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Following [10, 11], we transform raw waveform (pre-processed as mono channel under 16,000 sampling rate) into 128 Kaldi [55]-compatible Mel-frequency bands with a $2 5 \mathrm { m s }$ Hanning window that shifts every $1 0 ~ \mathrm { m s }$ . For a 10-second recording in AudioSet, the resulting spectrogram is of $1 \times 1 0 2 4 \times 1 2 8$ dimension.
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For patch embedding, we use convolutional kernels with (16, 16) size and stride in time and frequency (thus, patches are non-overlapping) to avoid short-cuts via overlap in self-supervision (though, at high masking ratios such short-cuts are less severe). By default, we use a masking ratio of 0.8 with (unstructured) random masking for pre-training. During fine-tuning, we employ a lower masking ratio (0.3 in time and 0.3 in frequency). Ablations on these design choices are given in $\ S \ O = 4$ .
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# 4.3 Pre-training and Fine-tuning
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We use AudioSet-2M for pre-training and randomly iterate over all audio recordings. We train for 32 epochs with a batch size of 512 and a 0.0002 learning rate. We distribute the training load over 64 V100 GPUs and the total training time is ${ \sim } 3 6$ hours. For each audio, we randomly sample the starting time, cyclically extract 10-second audio, and randomly jitter its magnitude by up to $\pm 6 \mathrm { d B }$ . We use only natural audio spectrograms and apply no augmentations (e.g., [48, 56, 57]) as we do not find these strong augmentations helpful in the pre-training phase.
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In the fine-tuning phase, we remove the decoder and only fine-tune the encoder. For the supervised fine-tuning on AudioSet-2M, since the size of training samples are uneven across classes (unbalanced), we follow the common practice of using a weighted sampling to balance the classes during training. In each epoch, we sample 200K instances ( $\mathord { \sim } 1 0 \%$ of AudioSet-2M) without replacement. We fine-tune for 100 epochs, which aggregate to ${ \sim } 1 0$ full epochs of AudioSet-2M. The probability of sampling an instance is inversely proportional to the dataset-wise occurrences of its classes. Fine-tuning on 64 GPUs takes ${ \sim } 1 2$ hours. For the smaller balanced AudioSet-20K, we fine-tune on 4 GPUs for 60 epochs without weighted sampling. Please see Supplementary for the details on other datasets.
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Figure 4: Masking strategy. For pre-training, a higher ratio and unstructured masking (random) is preferred. For fine-tuning, a lower ratio and structured masking (time $^ +$ frequency) is better. The y-axes are mAP on AS-2M and the $\mathbf { X }$ -axes are masking ratio. This ablation format follows [1].
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# 4.4 Ablations and Model Properties
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Masking Strategies in Pre-training and Fine-tuning. In Fig. 4, we compare different pre-training and fine-tuning masking strategies for Audio-MAE. First, in Fig. 4a we explore the pre-training masking ratio. We observe, similar as in MAE for images [1], that a high pre-training masking ratio $80 \%$ in our case) is optimal for audio spectrograms. This is due to the fact that both audio spectrograms and images are continuous signals with significant redundancy. Further, we find the unstructured random masking works the best for self-supervised pre-training over more structured masking (e.g., time+frequency).
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Unlike MAE for images, there are clear performance differences among masking strategies when pre-training with audio spectrograms. Comparing Audio-MAE reconstructions between Fig. 6a to 6e and 6d to 6h, under the same masking ratio, we observe the unstructured random masking is comparably easier than structured masking (i.e., time and/or frequency) as the model can guess the missing component by extrapolating nearby context (e.g., formants in vowels and frictional sounds in consonants around). We also observe that for higher masking ratios, the structured masking alternatives drop in performance, presumably because the task becomes too difficult while random masking improves steadily up to $80 \%$ . This result show that designing a pretext task with proper hardness is important for effective self-supervised learning of audio representations. We therefore use random masking with ratio of $80 \%$ as our default for pre-training.
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Fig. 4b studies the effect of masking during the fine-tuning phase. We see that in this case, it is more beneficial to use structured masking: time+frequency performs better than time- or frequency-based masking, and these perform better than unstructured masking. Overall, we see that the optimal masking ratios are lower than for pre-training and we use 0.3 as our default in the fine-tuning phase.
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In general, we observe that for task-agnostic pre-training, unstructured masking with a higher ratio is preferred. While in task-specific fine-tuning, structured masking with lower ratios performs better.
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Impact of Patch Size and Stride. We compare the performance of Audio-MAE trained with different patch sizes and strides in Table 1a. A non-zero overlap (i.e., stride $<$ patch size) between patches will increase the number of patches and quadratically increase computation in floating point operations (FLOPs), as reported in the table. Most prior works follow AST [10] to use overlapped patches (patch $= 1 6$ and stride $= 1 0$ ) to boost end task performance. As shown in Table 1a, we do not observe a performance improvement using overlapped patches for Audio-MAE (both $4 7 . 3 \mathrm { m A P }$ ), presumably because due to overlap, the patch embedding can leak information into the masked patches. The non-overlapped $1 6 \times 1 6$ patches achieve a good balance between computation and performance. By default, we use this setup in our experiments.
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Encoder. We investigate the design choices of encoder and decoder architectures in Audio-MAE. Table 1b shows the trade-off between encoder model size and performance. As expected, larger models achieve better performance, at a cost of computation and memory. The accuracy gain of ViT-L over ViT-B/S is more significant on the smaller and balanced AS-20K. For ViT-S, the performance
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<table><tr><td>(16,16), (16,16)</td><td>64×8</td><td>48.647.3</td><td></td></tr><tr><td>(16,16), (10,10)</td><td>101×12</td><td>130.5</td><td>47.3</td></tr><tr><td>(32,16), (16,16)</td><td>63×8</td><td>47.8</td><td>46.6</td></tr><tr><td>(16,32), (16,16)</td><td>64×7</td><td>42.1</td><td>46.8</td></tr></table>
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<table><tr><td>ViT-S</td><td>22M</td><td>32.1</td><td>45.0</td></tr><tr><td>ViT-B</td><td>86M</td><td>37.1</td><td>47.3</td></tr><tr><td>ViT-L</td><td>304M</td><td>37.6</td><td>47.4</td></tr></table>
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scenario IN-SSL IN-SL AS-SSL AS-20K AS-2M
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<table><tr><td>Attention type</td><td>AS-20K AS-2M ESC-50 SID</td></tr><tr><td>Global(8) (vanilla)</td><td>36.6 46.8</td></tr><tr><td>93.6 94.1 47.3 94.1</td><td>Local(16) (shifted) 37.1</td></tr><tr><td>Hwin (local(8)+ global(4) 36.8</td><td>94.8 47.3 93.8 95.0</td></tr></table>
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(h) External ImageNet (IN) pre-training. SSL: w/ selfsupervised MAE. SL: w/ supervised (fine-tuned) MAE.
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Table 1: Ablation studies on AS-2M. The gray entries are the default Audio-MAE setup (ViT-B encoder, decoder with shifted local attention, pre-trained for 32 epochs). Table format follows [1].
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gap to ViT-B can be significantly closed $\mathrm { 5 . 0 \to 2 . 3 \ m A P }$ ) when fine-tuning with more in-domain data $( \mathrm { A S } - 2 0 \mathrm { K } \mathrm { A S } - 2 \mathrm { M } )$ ).
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Decoder. Table 1c compares decoder attention types in Audio-MAE. Note that decoders are discarded after pretraining and only the equal-sized ViT-B encoders are fine-tuned for the end task. Our results show that local attention with shifted window achieves the best performance. Combining local and global attention (i.e., hybrid attention, Hwin) also improves vanilla global self-attention. Fig. 5 shows the qualitative reconstruction comparison. In the spectrogram of vowels, the decoder with local attention reconstructs better harmonics and recovers more context in the spectrogram. Similar phenomena are observed in the frictional sound in the middle consonant.
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Figure 5: Decoder reconstruction comparison.
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Table 1d ablates the impact of decoder depth on mAP. A deeper 16-layer decoder achieves better performance against its shallower variants. Note that our decoder uses local window attention by default where only a fraction of tokens $4 { \times } 4$ local windows vs. $6 4 \times 8$ with global attention) are attended. For global attention we find 8-layer decoders to perform better than 16-layer. Table 1e compares decoder width (embedding dimension). A 512-dimension decoder achieves a good trade-off between computation and performance as a wider one is not better.
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Pre-training Data and Setup. Table 1f summarizes the impact of pre-training dataset size. Overall the model performance is monotonically increasing when using more data for pre-training. Comparing the performance of using $1 \%$ well-annotated AS-20K balanced data to using randomly sampled 20K unbalanced data for pre-training, the similar mAPs (39.4 vs 39.6) suggest that the distribution of data classes (balanced vs. unbalanced) is less important for pre-training. Meanwhile, as shown in Table $1 \mathrm { g }$ , training for longer is beneficial yet the performance saturates after the 24-th epoch.
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Out-of-domain Pre-training on ImageNet. Initializing audio models from ImageNet pre-trained weights has become popular for audio classification. However, as there are significant discrepancies between image and audio modalities, it is questionable if out-of-domain pre-training benefits audio representation learning. In Table 1h we design 3 scenarios to investigate this for Audio-MAE: (1)
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Table 2: Comparison with other state-of-the-art models on audio and speech classification tasks. Metrics are mAP for AS and accuracy $( \% )$ for ESC/SPC/SID. For pre-training (PT) dataset, AS:AudioSet, LS:LibriSpeech, and IN:ImageNet. †: Fine-tuning results with additional supervised training on AS-2M. We gray-out models pre-trained with external non-audio datasets (e.g., ImageNet). Best single models in AS-2M are compared (no ensembles). \*: linear evaluation results from [53].
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<table><tr><td>Moder</td><td>Backbone</td><td></td><td>P1-DataAS-20K</td><td>AS-ZMI</td><td>ESC-30</td><td>SPC-2</td><td>SPC-1</td><td>SID</td></tr><tr><td>No pre-training</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ERANN [58]</td><td>CNN</td><td></td><td></td><td>45.0</td><td>89.2</td><td></td><td></td><td></td></tr><tr><td>PANN [59]</td><td>CNN</td><td></td><td>27.8</td><td>43.1</td><td>83.3</td><td>61.8</td><td></td><td></td></tr><tr><td colspan="9">In-domain self-supervised pre-training</td></tr><tr><td>wav2vec 2.0 [33]</td><td>Transformer</td><td>LS</td><td></td><td></td><td></td><td></td><td>96.2*</td><td>75.2*</td></tr><tr><td>HuBERT[35]</td><td>Transformer</td><td>LS</td><td></td><td></td><td></td><td></td><td>96.3*</td><td>81.4*</td></tr><tr><td>Conformer [37]</td><td>Conformer</td><td>AS</td><td>=</td><td>41.1</td><td>88.0</td><td>=</td><td>-</td><td>-</td></tr><tr><td>SS-AST[18]</td><td>ViT-B</td><td>AS+LS</td><td>31.0</td><td>1</td><td>88.8</td><td>98.0</td><td>96.0</td><td>64.3</td></tr><tr><td colspan="9">Concurrent MAE-based works</td></tr><tr><td>MaskSpec [43]</td><td>ViT-B</td><td>AS</td><td>32.3</td><td>47.1</td><td>89.6</td><td>97.7</td><td>=</td><td></td></tr><tr><td>MAE-AST[38]</td><td>ViT-B</td><td>AS+LS</td><td>30.6</td><td>-</td><td>90.0</td><td>97.9</td><td>95.8</td><td>63.3</td></tr><tr><td>Audio-MAE (global)</td><td>ViT-B</td><td>AS</td><td>36.6±.11</td><td>46.8±.06</td><td>93.6±.11</td><td>98.3±.06</td><td>97.6±.06</td><td>94.1±.06</td></tr><tr><td>Audio-MAE (local)</td><td>ViT-B</td><td>AS</td><td>37.0±.11</td><td>47.3±.11</td><td>94.1±.10</td><td>98.3±.06</td><td>96.9±.00</td><td>94.8± .11</td></tr><tr><td colspan="9">Out-of-domain supervised pre-training</td></tr><tr><td>PSLA [30]</td><td>EffNet [60]</td><td>IN</td><td>31.9</td><td>44.4</td><td>=</td><td>96.3</td><td>=</td><td></td></tr><tr><td>AST[10]</td><td>DeiT-B</td><td>IN</td><td>34.7</td><td>45.9</td><td>88.7</td><td>98.1</td><td>95.5</td><td>41.1</td></tr><tr><td>MBT[11]</td><td>ViT-B</td><td>IN-21K</td><td>31.3</td><td>44.3</td><td>1</td><td>-</td><td>=</td><td></td></tr><tr><td>HTS-AT [29]</td><td>Swin-B</td><td>IN</td><td>=</td><td>47.1</td><td>97.0t</td><td>98.0</td><td></td><td></td></tr><tr><td>PaSST[28]</td><td>DeiT-B</td><td>IN</td><td></td><td>47.1</td><td>96.8†</td><td>-</td><td></td><td></td></tr></table>
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Audio-only pre-training (AS-SSL) from scratch. We consider this the ideal schema for learning audio representations as it is a simple and clean setup that prevents uncontrollable bias transfer from other modalities. (2) Directly using self-supervised ImageNet MAE models (IN-SSL) and its fine-tuned variant (IN-SL). (3) Audio-MAE self-supervised pre-training on top of these ImageNet weights.
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The results show that (1) from-scratch audio-only pre-training is the best. For scenarios (2) and (3), we observe that ImageNet pre-training alone (2) is not sufficient (especially when the downstream data is smaller, AS-20K), and, in self-supervised pre-training on AudioSet, ImageNet initialization (3) does not help but degrades accuracy. Also in (3), supervised ImageNet pre-training (IN-SL) seems harmful. Consequently, the result suggests that out-of-domain pre-training (i.e., ImageNet) is not helpful for Audio-MAE, possibly due to domain shift.
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# 4.5 Comparison with the State-of-the-art
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Table 2 compares Audio-MAE (with 3-run error bars) to prior state-of-the-art. We categorize the comparison into 3 groups. For fair comparison, our main benchmark is the models in the middle group with self-supervised pre-training on in-domain (audio) datasets (AudioSet and LibriSpeech). For reference we also list other models without pre-training (the top group) and other models with supervised pre-training on out-of-domain ImageNet (the bottom group), where the latter contains previous best systems on the datasets.
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Pre-trained on AudioSet, Audio-MAE achieves the best performance across all tasks compared to other models with in-domain self-supervised pre-training. On AudioSet-20K, its $3 7 . 1 \ \mathrm { m A P }$ significantly outperforms all other approaches including concurrent works and other models with outof-domain pre-training. On AudioSet-2M and ESC-50, our method also outperforms Conformer [37] and SS-AST [18]. Notably, unlike SS-AST and concurrent MAE-AST [38], which trained with additional 1,000 hours of speech in Librispeech, we use only AudioSet for pre-training.
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| 154 |
+
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| 155 |
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In the bottom group of Table 2, Audio-MAE also outperforms previous state-of-the-art models with ImageNet supervised pre-training. Note that the proposed Audio-MAE does not rely on any out-ofdomain data and labels, nor using knowledge distillation (e.g., DeiT) from additional CNN-based models. Also, compared to HTS-AT [29] and PaSST [28], Audio-MAE is trained with audio under 16K sampling rate. As experimented in [59], there could be up to 0.4 potential mAP improvement for Audio-MAE if audio with 32K sampling rate are available.
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Figure 6: Spectrogram reconstruction visualizations on the AudioSet eval set. Column-wise type: speech, music, event, others. Masking type: (a-d) unstructured (random); (e-h) structured (time $^ +$ frequency). Masking Ratio: $70 \%$ . In each group, we show the original spectrogram (1, top), masked input (2, middle), and MAE output (3, bottom). The spectrogram size is $1 0 2 4 \times 1 2 8$ ; patch size is $1 6 \times 1 6$ . Each sample has $6 4 \times 8 = 5 1 2$ patches with 154 ( $70 \%$ masked) patches being visible to Audio-MAE. Please click (1 2 3) for audible .wavs. More audible examples are in Supplementary.
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For the speech tasks (SPC-1, SPC-2, and SID), Audio-MAE outperforms other models without pre-training (ERANN [58], PANN [59]), supervised (AST) and self-supervised models (SS-AST, MAE-AST). We further list other works (marked with \*) to include the latest results introduced in the SUPERB [53] benchmark. But note that these results are not strictly comparable since SUPERB employs linear evaluation where the underlying pre-trained models are not end-to-end fine-tuned.
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| 161 |
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| 162 |
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In summary, with audio-only from-scratch pre-training on AudioSet, our Audio-MAE performs well for both the audio and speech classification tasks.
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# 4.6 Visualization and Audible Examples by Audio-MAE Decoder
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For better visualization, we follow MAE [1] to use MSE over non-normalized spectrograms as the selfsupervised objective. We use ViT-L as the Audio-MAE encoder for visualization. Fig. 6 illustrates the reconstruction results sampled from the AudioSet-2M eval set. We further reconstruct .wavs using the Griffin-Lim [61] algorithm, audible under the anonymous links (accessible in respective 1 2 3).
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As can be seen and heard, for various masking strategies and different sounds, our Audio-MAE generates reasonable reconstruction. It works well for noisy event sounds (e.g., the reconstructed siren in Fig. 6c-3), as well as speech and music (e.g., the reconstructed singing in Fig. 6b-3). Notably, unlike visual contents that are typically scale/translation/position invariant [19], absolute positions and arrangement of spectrogram components are critical for humans to understand sound [62]. For example, shifting a pitch will make an audio sounds completely different. Also, phoneme sequences in time are important cues for speech understanding. Consequently, unstructured masking produces better aligned outputs that are closer to the ground-truth (top row in each subfigure) as the model can make better predictions based on nearby spectrogram patches; while structured masking is harder (less accurate or with words missing), especially when masking is performed over the time axis. A failure example (missing words) is the reconstructed speech in Fig. 6e-3.
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# 5 Conclusion
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We have explored a simple extension of MAE [1] to audio data. Our Audio-MAE learns to reconstruct masked spectrogram patches from audio recordings and achieves state-of-the-art performance on six audio and speech classification tasks. We have drawn four interesting observations: First, a simple MAE approach works surprisingly well for audio spectrograms. Second, we find that it is possible to learn stronger representations with local self-attention in the decoder. Third, we show that masking can be applied to both pre-training and fine-tuning, improving accuracy and reducing training computation. The optimal strategy depends on the nature of the data (audio, image, etc.) and the learning type (self-/supervised). Fourth, the best performance can be achieved by pre-training and fine-tuning under the same modality, without reliance on cross-modality transfer learning. In future work, we aim to explore multimodal self-supervised learning with a joint audio-visual MAE approach as these domains share natural correspondences in video data.
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Acknowledgements. We thank Kaiming He and Luke Zettlemoyer for their feedback and discussions.
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# References
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[
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{
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"type": "text",
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"text": "Masked Autoencoders that Listen ",
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"text_level": 1,
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"type": "text",
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"text": "Po-Yao Huang1 Hu Xu1 Juncheng Li2 Alexei Baevski1 Michael Auli1 Wojciech Galuba1 Florian Metze1 Christoph Feichtenhofer1 ",
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"type": "text",
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"text": "1Meta AI 2Carnegie Mellon University ",
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"bbox": [
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"type": "text",
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"text": "Abstract ",
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"text_level": 1,
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"text": "This paper studies a simple extension of image-based Masked Autoencoders (MAE) [1] to self-supervised representation learning from audio spectrograms. Following the Transformer encoder-decoder design in MAE, our Audio-MAE first encodes audio spectrogram patches with a high masking ratio, feeding only the non-masked tokens through encoder layers. The decoder then re-orders and decodes the encoded context padded with mask tokens, in order to reconstruct the input spectrogram. We find it beneficial to incorporate local window attention in the decoder, as audio spectrograms are highly correlated in local time and frequency bands. We then fine-tune the encoder with a lower masking ratio on target datasets. Empirically, Audio-MAE sets new state-of-the-art performance on six audio and speech classification tasks, outperforming other recent models that use external supervised pre-training. Our code and models is available at https://github.com/facebookresearch/AudioMAE. ",
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"type": "text",
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"text": "1 Introduction ",
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"text_level": 1,
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"type": "text",
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"text": "Transformers [2] and self-supervised learning [3, 4, 5, 6, 7, 1] are dominating computer vision (CV) and natural language processing (NLP) research. The revolution firstly started in NLP with the invention of the Transformer architecture and self-attention [8]. Masked autoencoding with BERT [3] set a new state-of-the-art on various NLP tasks by self-supervised pre-training on large-scale language corpus. Similarly in the CV community, Vision Transformers (ViT) [9] have become popular for CV tasks, and, for self-supervised image representation learning, Masked Autoencoders (MAE) [1] have brought the CV community closer to the success of BERT in NLP. In addition to the existing masked autoencoders that can read (BERT) or see (MAE), in this work we study those that can listen. ",
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"type": "text",
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"text": "Transformer-based models have recently refreshed leaderboards for audio understanding tasks. For example, AST [10] and MBT [11] improved the audio classification performance on the AudioSet [12], Event Sound Classification [13], etc. The key technique behind this is initialization of audio model weights with ImageNet pre-trained supervised models (e.g., DeiT [14]) by deflating patch embeddings and interpolating positional embeddings for encoding audio spectrograms. However, exploiting ImageNet pre-trained models could be sub-optimal. Unlike initializing video models with weights from image models (e.g., the initial weights of I3D [15] or 3D-ResNets [16] are inflated from ImageNet pre-trained image models), there are clear and notable discrepancies between spectrograms representing audio content and natural images. It remains unclear why such heterogeneous image-toaudio transfer is useful beyond arguably similar low-level semantics such as shapes of spectrograms and shapes of visual objects. Further, any label bias would inevitably be transferred to audio models. ",
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"text": "Addressing these concerns, self-supervised audio representation learning has recently attracted much research attention. Based on BEiT [17] that learns to reconstruct image patches or learnt patch tokens, SS-AST [18] extends to the audio domain and exploits spectrograms (akin to 1-channel 2D images) and use both contrastive and reconstruction objective as self-supervision. Without using any labels, the key enabler to effective self-supervised representation learning is large-scale pre-training data. In this work we use AudioSet [12] for pre-training, a common dataset containing ${ \\sim } 2$ million audio recordings. Performing large-scale training with Transformer architectures is challenging as self-attention in Transformers has quadratic complexity w.r.t. the length of input sequence. ",
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"type": "image",
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"img_path": "images/7b578eaf9796ad13f1638cd79725ff0dce34d674e35e6e70f80938d322ab078e.jpg",
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"image_caption": [
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"Figure 1: Audio-MAE for audio self-supervised learning. An audio recording is first transformed into a spectrogram and split into patches. We embed patches and mask out a large subset $( 8 0 \\% )$ . An encoder then operates on the visible $( 2 0 \\% )$ patch embeddings. Finally, a decoder processes the order-restored embeddings and mask tokens to reconstruct the input. Audio-MAE is minimizing the mean square error (MSE) on the masked portion of the reconstruction and the input spectrogram. "
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"image_footnote": [],
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"text": "This computational burden has been addressed in different ways. A popular approach is to reduce the sequence length in self-attention. Various ViT-based architectures have been developed to alleviate such issues for image and video understanding. For example, Swin-Transformer [19] only performs local attention within windows that shift across layers. MViT [20] employs pooling attention to construct a hierarchy of Transformers where sequence lengths are downsampled. For self-supervised learning, MAE [1] efficiently encodes only a small portion $( 2 5 \\% )$ of visual patches while the majority of patches is discarded. The simplicity and scalability in MAE make it a promising framework for large-scale self-supervised learning. ",
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"type": "text",
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"text": "In this work, we study MAE for sound recognition and the unique challenges of the audio domain. We present Audio-MAE (Fig. 1) as unified and scalable framework for learning self-supervised audio representations. Similar to MAE, it is composed of a pair of a Transformer encoder and decoder. Sound is first transformed and embedded into spectrogram patches. Before feeding them into the Transformer encoder, we mask and discard the majority and only feed a small number of non-masked embeddings into the encoder for efficient encoding. After padding encoded patches with learnable embeddings to represent masked patches, it then restores the order of these patches in frequency and time and propagates them through a Transformer decoder to reconstruct the audio spectrogram. ",
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"type": "text",
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"text": "Different from image patches, spectrogram patches are comparably local-correlated. For example, formants, the vocal tract resonances, are typically grouped and continuous locally in the spectrogram. The location in frequency and time embeds essential information that determines the semantics of a spectrogram patch and how it sounds like. To this end, we further investigate using localized attention and a hybrid architecture in the Transformer decoder to properly decode for reconstruction. This simple-yet-effective upgrade leads to improved performance for Audio-MAE. ",
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"type": "text",
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"text": "Similar to MAE for images, we minimize the patch-normalized mean square error. At the fine-tuning stage, we discard the decoder and fine-tune the encoder with patch-masking. Empirically, AudioMAE sets a new state-of-the-art performance on six audio and speech classification tasks. It is the first audio-only self-supervised model that achieves state-of-the-art mAP on AudioSet-2M, outperforming other recent models with external supervision. We further provide the visualization and audible examples to qualitatively demonstrate the effectiveness of the Audio-MAE decoder. ",
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"type": "text",
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"text": "2 Related Work ",
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"text_level": 1,
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"type": "text",
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"text": "Visual masked pre-training. Masked/Denoising autoencoders [21, 22, 3] are a general representation learning methodology by reconstructing source from masked or corrupted inputs. In CV, visual masked pre-training has made recent progress [23, 24, 1, 20]. Based on ViT [9] that applies Transformers to image patches, BEiT [17] and MAE [1] present masked image modeling frameworks. BEiT [17] learns to predict discrete visual tokens generated by VAE [25] in masked patches. MAE [1] reduces sequence length by masking a large portion of image patches randomly and encoding only non-masked ones for reconstruction of pixel color information. MaskFeat [20] studies features for masked pre-training and finds that Histograms of Oriented Gradients (HoG) [26], which are in turn related to spectrogram features, perform strongly for image and video classification models. Our work extends the MAE framework for representation learning with audio spectrograms. ",
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"type": "text",
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"text": "Out-of-domain pre-training for audio. Transferring ImageNet supervised pre-trained ViT [9] or ResNet [27] has become a popular practice for audio models [10, 28, 11, 29, 30, 31]. After pre-training, these models operate over audio spectrograms by deflating from 3-channels (RGB) into 1-channel (spectrogram) in the pre-trained patch embedding in ViT and employing the rest of the transformer blocks on top. For example, HTS-AT [29] encodes spectrograms with hierarchical Transformer initialized from the Swin Transformer [19]. MBT [11] uses ImageNet-21K pre-trained ViT; AST [10] and PaSST [28] employ DeiT [14] as the Transformer backbone. Without using out-of-domain (non-audio) data, the proposed Audio-MAE focuses on audio-only self-supervised pre-training from scratch. ",
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"text": "In-domain pre-training for audio. Existing in-domain (i.e., audio-only) self-supervised methods can be broadly categorized by the input signal type (e.g., raw waveform [32, 33, 34], frame-level features [35, 36, 37], or spectrogram patches [18, 38]); and the objective used for self-supervision (e.g., contrastive [39, 33, 40, 41, 35] or prediction/reconstruction [18, 34, 37, 36]). For example, wav2vec 2.0 [33] takes raw waveform as inputs and exploits contrastive learning to discriminate contextualized representations in different time segments. Mockingjay [42] proposed a masked acoustic model pretext task to reconstruct frame-level Mel-features of masked time frames. SSAST [18] is the closest work to Audio-MAE and is our main benchmark. Inspired by the success of BERT [3], SS-AST proposed a self-supervised learning method which operates over spectrogram patches and employs joint contrastive and reconstructive objectives on masked patches. These previous methods generate audio representations by encoding full-view of both masked and nonmasked time or spectrogram segments for self-supervised pre-training. In contrast, Audio-MAE encodes only the non-masked spectrogram patches. ",
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"text": "Our work is done independently and concurrently with [38, 43, 44] related methods. We also compare our model to these concurrent works in the experiments and showcase the superiority of Audio-MAE. ",
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"text": "3 Audio Masked Autoencoders (Audio-MAE) ",
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"text_level": 1,
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"type": "text",
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"text": "Audio-MAE is a conceptually simple extension of MAE to learn self-supervised representations from audio spectrograms. Fig. 1 depicts an overview. The details of each component are as follows. ",
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"type": "text",
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"text": "Spectrogram Patch Embeddings. Following [10, 18], we transform audio recordings into Melspectrograms and divide them into non-overlapped regular grid patches. These patches are then flattened and embedded by a linear projection. Similar to MAE [1], we add fixed sinusoidal positional embeddings to the embedded patches. ",
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"type": "image",
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"img_path": "images/31a937966647bc9c70a9fc197b7e10a2aa38720c7ea2a23229a1c5f045f9bb94.jpg",
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"image_caption": [
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"Figure 2: Audio-MAE’s masking strategies on Mel-spectrograms. "
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"text": "Masking Strategies. Audio-MAE masks out a large subset of spectrogram patches. As a spectrogram can be viewed as a 2D representation of time and frequency components of a sound, it is reasonable to explore treating time and frequency differently during masking. In this work, we investigate both the unstructured (i.e., random masking without any prior) and structured (i.e., randomly masking a portion of time, frequency, or time $^ +$ frequency of a spectrogram) in the pre-training and fine-tuning phase. Illustrative examples are shown in Fig. 2. We show masked regions with dark overlay. ",
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"type": "text",
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"text": "The masking mechanism, as introduced in MAE [1], is the key ingredient for efficient self-supervised learning. For a input patch sequence, this can be regarded as a Bernoulli process where each patch is masked/dropped with probability $p$ (masking ratio). Masking reduces input patch sequence length and encourages learning global, contextualized representations from limited “visible” patches. We observe that akin to images, a large masking rate ( $80 \\%$ in our experiments for spectrogram patches, which is similar to $7 5 \\%$ in MAE for images) is feasible for learning self-supervised audio representations. Unlike BERT [3] that uses $15 \\%$ masking rate for self-supervised learning in NLP, most of the tokens/patches can be discarded for spectrograms as well as images due to high redundancy in these modalities. Beyond self-supervised pre-training, we further explore the effectiveness of masking in the supervised fine-tuning stage. Empirically, we found unstructured (random) masking at a higher ratio for pre-training and structured (time+frequency masking) at a lower ratio for fine-tuning provide best accuracy (ablations are in $\\ S \\_ 4 )$ ). ",
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"type": "text",
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"text": "",
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"type": "text",
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"text": "Encoder. Audio-MAE uses a stack of standard Transformers [2] as its encoder. The encoder only processes $( 2 0 \\% )$ non-masked patches to reduce computation overhead which is quadratic to the input sequence length. We use the 12-layer ViT-Base (ViT-B) [9] Transformer as our default. ",
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"type": "text",
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"text": "Decoder with Local Attention. The decoder is also composed of standard Transformer blocks. The encoded patches from the encoder are padded with trainable masked tokens. After restoring the original time-frequency order in the audio spectrogram, we add the decoder’s (fixed sinusoidal) positional embeddings and feed the restored sequence into the decoder. At the top of the decoder stack, we add a linear head to predict and reconstruct the input spectrogram. ",
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],
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{
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"type": "text",
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"text": "To address the unique characteristics of audio spectrograms, our work investigates an enhancement to the vanilla MAE decoder. Image-based MAE uses global self-attention in the Transformer decoder which is appropriate for visual context, because visual objects are typically invariant under translation or scaling, and their exact position may not affect the semantics of an image. In contrast, the position, scale, and translation of spectrogram features however directly affects the sound or semantics of an audio recording. Consequently, global self-attention is sub-optimal for spectrograms if the timefrequency components is predominantly local. For instance, we would have better success to use the harmonics (e.g., Fig. 2a) in lower bands of a vowel to predict the spectrogram patch vertically in a higher frequency band rather than horizontally in the time domain. Similarly, a frictional sound of a consonant likely only correlates to other part of the consonant, and is without dependency to other silence segments in the audio recording. Compared to images, the spectrogram patches are more similar to speech or text tokens where its order and position is more relevant. ",
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"type": "text",
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"text": "To address the nature of audio spectrograms, in addition to using Transformers with global self-attention as in vanilla MAE, we incorporate the local attention mechanism which groups and separates the spectrogram patches in to local windows in self-attention for decoding. We investigate two types of local attention: (1) Shifted window location: Inspired by the shifted-window in Swin Transformers [19], we shift window attention by $50 \\%$ between consecutive Transformer decoder layers. For padding the margin when shifting, we cyclically shift the spectrogram to the top-left direction. Fig. 3 illustrates the localized decoder attention by shifted windows. (2) Hybrid window attention (global+local attention): Inspired by [45], to add better cross-window connections, we design a simple hybrid (global+local) attention that computes local attention within a window in all but the last few top layers. In this way, the input feature maps for the final reconstruction layer also contain global information. For simplicity, we use $_ { n o }$ pooling or hierarchical structure. Decoders with different attention types are compared in $\\ S \\ O = 4$ . ",
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"type": "image",
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"img_path": "images/eac4e377de5817b96d0854d87b3e709eb9a487a2db0842240cefe54d8a061b6c.jpg",
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| 348 |
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"image_caption": [
|
| 349 |
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"Figure 3: Decoder’s local attention and shifted window (right). "
|
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],
|
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"type": "text",
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"text": "",
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"type": "text",
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| 373 |
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"text": "Objective. The Audio-MAE decoder learns to reconstruct the input spectrogram by predicting the values in the spectrogram patches or their per-patch normalized ones. The objective is the mean squared error (MSE) between the prediction and the input spectrogram, averaged over unknown patches. Empirically we found employing the reconstruction loss alone is sufficient while including additional contrastive objectives (e.g., InfoNCE loss [46]) does not improve Audio-MAE. ",
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"bbox": [
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"type": "text",
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"text": "Fine-tuning for Downstream Tasks. In the fine-tuning stage, we only keep and fine-tune the AudioMAE encoder and discard the decoder. Different from the original MAE, and inspired by [47, 28], we also explore to employ masking in the fine-tuning stage to remove a portion of patches to further regularize learning from a limited view of spectrogram inputs, which, as a side effect, also reduces computation during fine-tuning. Compared to SpecAug [48] which takes full-length input with the masked portion set to zero as data augmentation, Audio-MAE sees only a subset of real-valued input patches without the nullified ones. Audio-MAE then encodes these non-masked patches and applies an average pooling layer followed by a linear layer on top for fine-tuning in classification tasks. ",
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"type": "text",
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"text": "4 Experiments ",
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| 396 |
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"text_level": 1,
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"type": "text",
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"text": "We perform an extensive evaluation on six tasks, including audio classification on AudioSet (AS-2M, AS-20K) and Environmental Sound Classification (ESC-50), and speech classification on Speech Commands (SPC-1 and SPC-2) and VoxCeleb (SID). We use AudioSet for ablation studies. ",
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"type": "text",
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"text": "4.1 Datasets and Tasks ",
|
| 419 |
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"text_level": 1,
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| 420 |
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"bbox": [
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"type": "text",
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"text": "AudioSet [12] (AS-2M, AS-20K) contains ${ \\sim } 2$ million 10-second YouTube clips for audio classification. 527 types of audio events are weakly annotated [49, 50, 51] for each clip. There could be multiple events in a clip. The full training set has 2 subsets: A class-wise balanced (22,176 clips) and an unbalanced (2,042,985 clips) set. The eval set has 20,383 clips. We downloaded and processed around 1.96M unbalanced training, 21K balanced training, and 19K evaluation clips. ",
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| 431 |
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| 440 |
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"type": "text",
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| 441 |
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"text": "For the AS-2M experiments, we use the union of unbalanced and balanced training audio for pretraining and fine-tuning. For the AS-20K experiments, we use AS-2M for pre-training and the 20K balanced set for fine-tuning. We report the testing mAP on the 19K eval set used by AST [10]. ",
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| 442 |
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| 450 |
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| 451 |
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"type": "text",
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| 452 |
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"text": "Environmental Sound Classification (ESC-50) [13] is an audio classification dataset consists of 2,000 5-second environmental sound recordings. There are 50 classes in ESC. We report accuracy under 5-fold cross-validation with the same split used by [10]. ",
|
| 453 |
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| 459 |
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| 460 |
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{
|
| 462 |
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"type": "text",
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| 463 |
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"text": "Speech Commands (SPC-2, SPC-1) [52] are two keyword spotting tasks. In SPC-2, there are 35 speech commands. The training/validation/testing set has 84,843/9,981/11,005 1-second recordings, respectively. In SPC-1, there are 10 classes of keywords, 1 silence class, and 1 unknown class that includes all the other 20 common speech commands. We use the data and split provided in the SUPERB [53] benchmark to report the testing accuracy. ",
|
| 464 |
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| 470 |
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| 471 |
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|
| 472 |
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{
|
| 473 |
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"type": "text",
|
| 474 |
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"text": "VoxCeleb (SID) [54] contains 150K utterances from 1,251 speakers. The speaker identification task (SID) is to classify the utterances to identify its original speaker. We use the V1 standard train (138,361), validation (6,904), testing (8,251) sets and report the testing accuracy. ",
|
| 475 |
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"bbox": [
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| 482 |
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| 483 |
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{
|
| 484 |
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"type": "text",
|
| 485 |
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"text": "4.2 Implementation Details ",
|
| 486 |
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"text_level": 1,
|
| 487 |
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"bbox": [
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| 488 |
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| 490 |
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| 491 |
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| 493 |
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"page_idx": 4
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| 494 |
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| 495 |
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| 496 |
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"type": "text",
|
| 497 |
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"text": "We use a vanilla 12-layer ViT-B by default as the Transformer encoder. For the decoder, we use a 16-layer Transformer with shifted local attention. We investigate the vanilla (global attention) and hybrid (global+local attention) decoder variants (see Table. 1c). ",
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| 498 |
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"bbox": [
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| 505 |
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| 506 |
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| 507 |
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"type": "text",
|
| 508 |
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"text": "Following [10, 11], we transform raw waveform (pre-processed as mono channel under 16,000 sampling rate) into 128 Kaldi [55]-compatible Mel-frequency bands with a $2 5 \\mathrm { m s }$ Hanning window that shifts every $1 0 ~ \\mathrm { m s }$ . For a 10-second recording in AudioSet, the resulting spectrogram is of $1 \\times 1 0 2 4 \\times 1 2 8$ dimension. ",
|
| 509 |
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"bbox": [
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| 515 |
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"page_idx": 4
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| 516 |
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| 517 |
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| 518 |
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"type": "text",
|
| 519 |
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"text": "For patch embedding, we use convolutional kernels with (16, 16) size and stride in time and frequency (thus, patches are non-overlapping) to avoid short-cuts via overlap in self-supervision (though, at high masking ratios such short-cuts are less severe). By default, we use a masking ratio of 0.8 with (unstructured) random masking for pre-training. During fine-tuning, we employ a lower masking ratio (0.3 in time and 0.3 in frequency). Ablations on these design choices are given in $\\ S \\ O = 4$ . ",
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| 520 |
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| 528 |
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{
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| 529 |
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"type": "text",
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| 530 |
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"text": "4.3 Pre-training and Fine-tuning ",
|
| 531 |
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"text_level": 1,
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| 532 |
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| 541 |
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"type": "text",
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| 542 |
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"text": "We use AudioSet-2M for pre-training and randomly iterate over all audio recordings. We train for 32 epochs with a batch size of 512 and a 0.0002 learning rate. We distribute the training load over 64 V100 GPUs and the total training time is ${ \\sim } 3 6$ hours. For each audio, we randomly sample the starting time, cyclically extract 10-second audio, and randomly jitter its magnitude by up to $\\pm 6 \\mathrm { d B }$ . We use only natural audio spectrograms and apply no augmentations (e.g., [48, 56, 57]) as we do not find these strong augmentations helpful in the pre-training phase. ",
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| 552 |
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"type": "text",
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| 553 |
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"text": "In the fine-tuning phase, we remove the decoder and only fine-tune the encoder. For the supervised fine-tuning on AudioSet-2M, since the size of training samples are uneven across classes (unbalanced), we follow the common practice of using a weighted sampling to balance the classes during training. In each epoch, we sample 200K instances ( $\\mathord { \\sim } 1 0 \\%$ of AudioSet-2M) without replacement. We fine-tune for 100 epochs, which aggregate to ${ \\sim } 1 0$ full epochs of AudioSet-2M. The probability of sampling an instance is inversely proportional to the dataset-wise occurrences of its classes. Fine-tuning on 64 GPUs takes ${ \\sim } 1 2$ hours. For the smaller balanced AudioSet-20K, we fine-tune on 4 GPUs for 60 epochs without weighted sampling. Please see Supplementary for the details on other datasets. ",
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| 554 |
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| 562 |
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{
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| 563 |
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"type": "image",
|
| 564 |
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"img_path": "images/77981a7649efa2be98251d63c87ce0bb29948d0455d85ac60829270b7d834094.jpg",
|
| 565 |
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"image_caption": [
|
| 566 |
+
"Figure 4: Masking strategy. For pre-training, a higher ratio and unstructured masking (random) is preferred. For fine-tuning, a lower ratio and structured masking (time $^ +$ frequency) is better. The y-axes are mAP on AS-2M and the $\\mathbf { X }$ -axes are masking ratio. This ablation format follows [1]. "
|
| 567 |
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],
|
| 568 |
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"image_footnote": [],
|
| 569 |
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"bbox": [
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| 575 |
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| 576 |
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| 577 |
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| 578 |
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"type": "text",
|
| 579 |
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"text": "",
|
| 580 |
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| 589 |
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"type": "text",
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"text": "4.4 Ablations and Model Properties ",
|
| 591 |
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"text_level": 1,
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| 592 |
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"type": "text",
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"text": "Masking Strategies in Pre-training and Fine-tuning. In Fig. 4, we compare different pre-training and fine-tuning masking strategies for Audio-MAE. First, in Fig. 4a we explore the pre-training masking ratio. We observe, similar as in MAE for images [1], that a high pre-training masking ratio $80 \\%$ in our case) is optimal for audio spectrograms. This is due to the fact that both audio spectrograms and images are continuous signals with significant redundancy. Further, we find the unstructured random masking works the best for self-supervised pre-training over more structured masking (e.g., time+frequency). ",
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| 612 |
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"type": "text",
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| 613 |
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"text": "Unlike MAE for images, there are clear performance differences among masking strategies when pre-training with audio spectrograms. Comparing Audio-MAE reconstructions between Fig. 6a to 6e and 6d to 6h, under the same masking ratio, we observe the unstructured random masking is comparably easier than structured masking (i.e., time and/or frequency) as the model can guess the missing component by extrapolating nearby context (e.g., formants in vowels and frictional sounds in consonants around). We also observe that for higher masking ratios, the structured masking alternatives drop in performance, presumably because the task becomes too difficult while random masking improves steadily up to $80 \\%$ . This result show that designing a pretext task with proper hardness is important for effective self-supervised learning of audio representations. We therefore use random masking with ratio of $80 \\%$ as our default for pre-training. ",
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| 614 |
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"type": "text",
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"text": "Fig. 4b studies the effect of masking during the fine-tuning phase. We see that in this case, it is more beneficial to use structured masking: time+frequency performs better than time- or frequency-based masking, and these perform better than unstructured masking. Overall, we see that the optimal masking ratios are lower than for pre-training and we use 0.3 as our default in the fine-tuning phase. ",
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| 625 |
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| 634 |
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"type": "text",
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| 635 |
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"text": "In general, we observe that for task-agnostic pre-training, unstructured masking with a higher ratio is preferred. While in task-specific fine-tuning, structured masking with lower ratios performs better. ",
|
| 636 |
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"type": "text",
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"text": "Impact of Patch Size and Stride. We compare the performance of Audio-MAE trained with different patch sizes and strides in Table 1a. A non-zero overlap (i.e., stride $<$ patch size) between patches will increase the number of patches and quadratically increase computation in floating point operations (FLOPs), as reported in the table. Most prior works follow AST [10] to use overlapped patches (patch $= 1 6$ and stride $= 1 0$ ) to boost end task performance. As shown in Table 1a, we do not observe a performance improvement using overlapped patches for Audio-MAE (both $4 7 . 3 \\mathrm { m A P }$ ), presumably because due to overlap, the patch embedding can leak information into the masked patches. The non-overlapped $1 6 \\times 1 6$ patches achieve a good balance between computation and performance. By default, we use this setup in our experiments. ",
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| 647 |
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"type": "text",
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"text": "Encoder. We investigate the design choices of encoder and decoder architectures in Audio-MAE. Table 1b shows the trade-off between encoder model size and performance. As expected, larger models achieve better performance, at a cost of computation and memory. The accuracy gain of ViT-L over ViT-B/S is more significant on the smaller and balanced AS-20K. For ViT-S, the performance ",
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"type": "table",
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"img_path": "images/6f59a1c28e76f7aa6d92f54dc2336e032fe1fec05ebb7a82d7a9a980d84c69bf.jpg",
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"table_caption": [],
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"table_body": "<table><tr><td>(16,16), (16,16)</td><td>64×8</td><td>48.647.3</td><td></td></tr><tr><td>(16,16), (10,10)</td><td>101×12</td><td>130.5</td><td>47.3</td></tr><tr><td>(32,16), (16,16)</td><td>63×8</td><td>47.8</td><td>46.6</td></tr><tr><td>(16,32), (16,16)</td><td>64×7</td><td>42.1</td><td>46.8</td></tr></table>",
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"img_path": "images/cd323607a9ef4d1435f53f5a4694198cfcaa19480ab62f7674c6087d91c726d9.jpg",
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"table_body": "<table><tr><td>ViT-S</td><td>22M</td><td>32.1</td><td>45.0</td></tr><tr><td>ViT-B</td><td>86M</td><td>37.1</td><td>47.3</td></tr><tr><td>ViT-L</td><td>304M</td><td>37.6</td><td>47.4</td></tr></table>",
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"img_path": "images/2e64e580b9f04e22b287bd69d5bfdd39254f01c2e6f243ca7c94c7792437d8fd.jpg",
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"table_caption": [
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"scenario IN-SSL IN-SL AS-SSL AS-20K AS-2M "
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],
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"table_footnote": [],
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"table_body": "<table><tr><td>Attention type</td><td>AS-20K AS-2M ESC-50 SID</td></tr><tr><td>Global(8) (vanilla)</td><td>36.6 46.8</td></tr><tr><td>93.6 94.1 47.3 94.1</td><td>Local(16) (shifted) 37.1</td></tr><tr><td>Hwin (local(8)+ global(4) 36.8</td><td>94.8 47.3 93.8 95.0</td></tr></table>",
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"img_path": "images/c8970b78f179014b4562bee38cb0d12fbbb43623ba5e47ab3c3b6f7e874f2872.jpg",
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"image_caption": [
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"(h) External ImageNet (IN) pre-training. SSL: w/ selfsupervised MAE. SL: w/ supervised (fine-tuned) MAE. "
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"type": "text",
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"text": "Table 1: Ablation studies on AS-2M. The gray entries are the default Audio-MAE setup (ViT-B encoder, decoder with shifted local attention, pre-trained for 32 epochs). Table format follows [1]. ",
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"type": "text",
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"text": "gap to ViT-B can be significantly closed $\\mathrm { 5 . 0 \\to 2 . 3 \\ m A P }$ ) when fine-tuning with more in-domain data $( \\mathrm { A S } - 2 0 \\mathrm { K } \\mathrm { A S } - 2 \\mathrm { M } )$ ). ",
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"type": "text",
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"text": "Decoder. Table 1c compares decoder attention types in Audio-MAE. Note that decoders are discarded after pretraining and only the equal-sized ViT-B encoders are fine-tuned for the end task. Our results show that local attention with shifted window achieves the best performance. Combining local and global attention (i.e., hybrid attention, Hwin) also improves vanilla global self-attention. Fig. 5 shows the qualitative reconstruction comparison. In the spectrogram of vowels, the decoder with local attention reconstructs better harmonics and recovers more context in the spectrogram. Similar phenomena are observed in the frictional sound in the middle consonant. ",
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"type": "image",
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"img_path": "images/2eac13304af84b06c5760b4abdf221924cb45af9f00f2bcb95dca8f6af1aa8b1.jpg",
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"image_caption": [
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"Figure 5: Decoder reconstruction comparison. "
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"type": "text",
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"text": "Table 1d ablates the impact of decoder depth on mAP. A deeper 16-layer decoder achieves better performance against its shallower variants. Note that our decoder uses local window attention by default where only a fraction of tokens $4 { \\times } 4$ local windows vs. $6 4 \\times 8$ with global attention) are attended. For global attention we find 8-layer decoders to perform better than 16-layer. Table 1e compares decoder width (embedding dimension). A 512-dimension decoder achieves a good trade-off between computation and performance as a wider one is not better. ",
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"type": "text",
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"text": "Pre-training Data and Setup. Table 1f summarizes the impact of pre-training dataset size. Overall the model performance is monotonically increasing when using more data for pre-training. Comparing the performance of using $1 \\%$ well-annotated AS-20K balanced data to using randomly sampled 20K unbalanced data for pre-training, the similar mAPs (39.4 vs 39.6) suggest that the distribution of data classes (balanced vs. unbalanced) is less important for pre-training. Meanwhile, as shown in Table $1 \\mathrm { g }$ , training for longer is beneficial yet the performance saturates after the 24-th epoch. ",
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"type": "text",
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"text": "Out-of-domain Pre-training on ImageNet. Initializing audio models from ImageNet pre-trained weights has become popular for audio classification. However, as there are significant discrepancies between image and audio modalities, it is questionable if out-of-domain pre-training benefits audio representation learning. In Table 1h we design 3 scenarios to investigate this for Audio-MAE: (1) ",
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"type": "table",
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"img_path": "images/e0146f12659732d22bc5a656b8f385365a1efb9fcc9883c795d053f067db9e94.jpg",
|
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"table_caption": [
|
| 810 |
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"Table 2: Comparison with other state-of-the-art models on audio and speech classification tasks. Metrics are mAP for AS and accuracy $( \\% )$ for ESC/SPC/SID. For pre-training (PT) dataset, AS:AudioSet, LS:LibriSpeech, and IN:ImageNet. †: Fine-tuning results with additional supervised training on AS-2M. We gray-out models pre-trained with external non-audio datasets (e.g., ImageNet). Best single models in AS-2M are compared (no ensembles). \\*: linear evaluation results from [53]. "
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| 812 |
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"table_footnote": [],
|
| 813 |
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"table_body": "<table><tr><td>Moder</td><td>Backbone</td><td></td><td>P1-DataAS-20K</td><td>AS-ZMI</td><td>ESC-30</td><td>SPC-2</td><td>SPC-1</td><td>SID</td></tr><tr><td>No pre-training</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ERANN [58]</td><td>CNN</td><td></td><td></td><td>45.0</td><td>89.2</td><td></td><td></td><td></td></tr><tr><td>PANN [59]</td><td>CNN</td><td></td><td>27.8</td><td>43.1</td><td>83.3</td><td>61.8</td><td></td><td></td></tr><tr><td colspan=\"9\">In-domain self-supervised pre-training</td></tr><tr><td>wav2vec 2.0 [33]</td><td>Transformer</td><td>LS</td><td></td><td></td><td></td><td></td><td>96.2*</td><td>75.2*</td></tr><tr><td>HuBERT[35]</td><td>Transformer</td><td>LS</td><td></td><td></td><td></td><td></td><td>96.3*</td><td>81.4*</td></tr><tr><td>Conformer [37]</td><td>Conformer</td><td>AS</td><td>=</td><td>41.1</td><td>88.0</td><td>=</td><td>-</td><td>-</td></tr><tr><td>SS-AST[18]</td><td>ViT-B</td><td>AS+LS</td><td>31.0</td><td>1</td><td>88.8</td><td>98.0</td><td>96.0</td><td>64.3</td></tr><tr><td colspan=\"9\">Concurrent MAE-based works</td></tr><tr><td>MaskSpec [43]</td><td>ViT-B</td><td>AS</td><td>32.3</td><td>47.1</td><td>89.6</td><td>97.7</td><td>=</td><td></td></tr><tr><td>MAE-AST[38]</td><td>ViT-B</td><td>AS+LS</td><td>30.6</td><td>-</td><td>90.0</td><td>97.9</td><td>95.8</td><td>63.3</td></tr><tr><td>Audio-MAE (global)</td><td>ViT-B</td><td>AS</td><td>36.6±.11</td><td>46.8±.06</td><td>93.6±.11</td><td>98.3±.06</td><td>97.6±.06</td><td>94.1±.06</td></tr><tr><td>Audio-MAE (local)</td><td>ViT-B</td><td>AS</td><td>37.0±.11</td><td>47.3±.11</td><td>94.1±.10</td><td>98.3±.06</td><td>96.9±.00</td><td>94.8± .11</td></tr><tr><td colspan=\"9\">Out-of-domain supervised pre-training</td></tr><tr><td>PSLA [30]</td><td>EffNet [60]</td><td>IN</td><td>31.9</td><td>44.4</td><td>=</td><td>96.3</td><td>=</td><td></td></tr><tr><td>AST[10]</td><td>DeiT-B</td><td>IN</td><td>34.7</td><td>45.9</td><td>88.7</td><td>98.1</td><td>95.5</td><td>41.1</td></tr><tr><td>MBT[11]</td><td>ViT-B</td><td>IN-21K</td><td>31.3</td><td>44.3</td><td>1</td><td>-</td><td>=</td><td></td></tr><tr><td>HTS-AT [29]</td><td>Swin-B</td><td>IN</td><td>=</td><td>47.1</td><td>97.0t</td><td>98.0</td><td></td><td></td></tr><tr><td>PaSST[28]</td><td>DeiT-B</td><td>IN</td><td></td><td>47.1</td><td>96.8†</td><td>-</td><td></td><td></td></tr></table>",
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"type": "text",
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"text": "Audio-only pre-training (AS-SSL) from scratch. We consider this the ideal schema for learning audio representations as it is a simple and clean setup that prevents uncontrollable bias transfer from other modalities. (2) Directly using self-supervised ImageNet MAE models (IN-SSL) and its fine-tuned variant (IN-SL). (3) Audio-MAE self-supervised pre-training on top of these ImageNet weights. ",
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"text": "The results show that (1) from-scratch audio-only pre-training is the best. For scenarios (2) and (3), we observe that ImageNet pre-training alone (2) is not sufficient (especially when the downstream data is smaller, AS-20K), and, in self-supervised pre-training on AudioSet, ImageNet initialization (3) does not help but degrades accuracy. Also in (3), supervised ImageNet pre-training (IN-SL) seems harmful. Consequently, the result suggests that out-of-domain pre-training (i.e., ImageNet) is not helpful for Audio-MAE, possibly due to domain shift. ",
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"type": "text",
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"text": "4.5 Comparison with the State-of-the-art ",
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"text_level": 1,
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"type": "text",
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"text": "Table 2 compares Audio-MAE (with 3-run error bars) to prior state-of-the-art. We categorize the comparison into 3 groups. For fair comparison, our main benchmark is the models in the middle group with self-supervised pre-training on in-domain (audio) datasets (AudioSet and LibriSpeech). For reference we also list other models without pre-training (the top group) and other models with supervised pre-training on out-of-domain ImageNet (the bottom group), where the latter contains previous best systems on the datasets. ",
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"type": "text",
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"text": "Pre-trained on AudioSet, Audio-MAE achieves the best performance across all tasks compared to other models with in-domain self-supervised pre-training. On AudioSet-20K, its $3 7 . 1 \\ \\mathrm { m A P }$ significantly outperforms all other approaches including concurrent works and other models with outof-domain pre-training. On AudioSet-2M and ESC-50, our method also outperforms Conformer [37] and SS-AST [18]. Notably, unlike SS-AST and concurrent MAE-AST [38], which trained with additional 1,000 hours of speech in Librispeech, we use only AudioSet for pre-training. ",
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"type": "text",
|
| 880 |
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"text": "In the bottom group of Table 2, Audio-MAE also outperforms previous state-of-the-art models with ImageNet supervised pre-training. Note that the proposed Audio-MAE does not rely on any out-ofdomain data and labels, nor using knowledge distillation (e.g., DeiT) from additional CNN-based models. Also, compared to HTS-AT [29] and PaSST [28], Audio-MAE is trained with audio under 16K sampling rate. As experimented in [59], there could be up to 0.4 potential mAP improvement for Audio-MAE if audio with 32K sampling rate are available. ",
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"type": "image",
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"img_path": "images/6244fd1a7a46c5c39262c96d30a4dfd6f022b65c3eb7f73ba45382c9f667a734.jpg",
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"image_caption": [
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| 893 |
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"Figure 6: Spectrogram reconstruction visualizations on the AudioSet eval set. Column-wise type: speech, music, event, others. Masking type: (a-d) unstructured (random); (e-h) structured (time $^ +$ frequency). Masking Ratio: $70 \\%$ . In each group, we show the original spectrogram (1, top), masked input (2, middle), and MAE output (3, bottom). The spectrogram size is $1 0 2 4 \\times 1 2 8$ ; patch size is $1 6 \\times 1 6$ . Each sample has $6 4 \\times 8 = 5 1 2$ patches with 154 ( $70 \\%$ masked) patches being visible to Audio-MAE. Please click (1 2 3) for audible .wavs. More audible examples are in Supplementary. "
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"type": "text",
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"text": "For the speech tasks (SPC-1, SPC-2, and SID), Audio-MAE outperforms other models without pre-training (ERANN [58], PANN [59]), supervised (AST) and self-supervised models (SS-AST, MAE-AST). We further list other works (marked with \\*) to include the latest results introduced in the SUPERB [53] benchmark. But note that these results are not strictly comparable since SUPERB employs linear evaluation where the underlying pre-trained models are not end-to-end fine-tuned. ",
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"text": "In summary, with audio-only from-scratch pre-training on AudioSet, our Audio-MAE performs well for both the audio and speech classification tasks. ",
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"text": "4.6 Visualization and Audible Examples by Audio-MAE Decoder ",
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"text": "For better visualization, we follow MAE [1] to use MSE over non-normalized spectrograms as the selfsupervised objective. We use ViT-L as the Audio-MAE encoder for visualization. Fig. 6 illustrates the reconstruction results sampled from the AudioSet-2M eval set. We further reconstruct .wavs using the Griffin-Lim [61] algorithm, audible under the anonymous links (accessible in respective 1 2 3). ",
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"text": "As can be seen and heard, for various masking strategies and different sounds, our Audio-MAE generates reasonable reconstruction. It works well for noisy event sounds (e.g., the reconstructed siren in Fig. 6c-3), as well as speech and music (e.g., the reconstructed singing in Fig. 6b-3). Notably, unlike visual contents that are typically scale/translation/position invariant [19], absolute positions and arrangement of spectrogram components are critical for humans to understand sound [62]. For example, shifting a pitch will make an audio sounds completely different. Also, phoneme sequences in time are important cues for speech understanding. Consequently, unstructured masking produces better aligned outputs that are closer to the ground-truth (top row in each subfigure) as the model can make better predictions based on nearby spectrogram patches; while structured masking is harder (less accurate or with words missing), especially when masking is performed over the time axis. A failure example (missing words) is the reconstructed speech in Fig. 6e-3. ",
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"text": "5 Conclusion ",
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"text": "We have explored a simple extension of MAE [1] to audio data. Our Audio-MAE learns to reconstruct masked spectrogram patches from audio recordings and achieves state-of-the-art performance on six audio and speech classification tasks. We have drawn four interesting observations: First, a simple MAE approach works surprisingly well for audio spectrograms. Second, we find that it is possible to learn stronger representations with local self-attention in the decoder. Third, we show that masking can be applied to both pre-training and fine-tuning, improving accuracy and reducing training computation. The optimal strategy depends on the nature of the data (audio, image, etc.) and the learning type (self-/supervised). Fourth, the best performance can be achieved by pre-training and fine-tuning under the same modality, without reliance on cross-modality transfer learning. In future work, we aim to explore multimodal self-supervised learning with a joint audio-visual MAE approach as these domains share natural correspondences in video data. ",
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"text": "Acknowledgements. We thank Kaiming He and Luke Zettlemoyer for their feedback and discussions. ",
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"text": "References ",
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| 1 |
+
[
|
| 2 |
+
{
|
| 3 |
+
"type": "text",
|
| 4 |
+
"text": "TEMPORAL EFFICIENT TRAINING OF SPIKINGNEURAL NETWORK VIA GRADIENT RE-WEIGHTING",
|
| 5 |
+
"text_level": 1,
|
| 6 |
+
"bbox": [
|
| 7 |
+
176,
|
| 8 |
+
99,
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| 9 |
+
797,
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| 10 |
+
146
|
| 11 |
+
],
|
| 12 |
+
"page_idx": 0
|
| 13 |
+
},
|
| 14 |
+
{
|
| 15 |
+
"type": "text",
|
| 16 |
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"text": "Shikuang Deng1,2, Yuhang $\\mathbf { L i ^ { 3 } }$ , Shanghang Zhang4 & Shi $\\mathbf { G u } ^ { 1 , 2 , 5 \\boxtimes }$ ",
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"text": "1University of Electronic Science and Technology of China, \n2Shenzhen Institute for Advanced Study, UESTC \n3Yale University, 4Peking University ,5Peng Cheng Laboratory \ndengsk119@std.uestc.edu.cn, yuhang.li@yale.edu, gus@uestc.edu.cn ",
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"type": "text",
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"text": "ABSTRACT ",
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"text": "Recently, brain-inspired spiking neuron networks (SNNs) have attracted widespread research interest because of their event-driven and energy-efficient characteristics. Still, it is difficult to efficiently train deep SNNs due to the nondifferentiability of its activation function, which disables the typically used gradient descent approaches for traditional artificial neural networks (ANNs). Although the adoption of surrogate gradient (SG) formally allows for the back-propagation of losses, the discrete spiking mechanism actually differentiates the loss landscape of SNNs from that of ANNs, failing the surrogate gradient methods to achieve comparable accuracy as for ANNs. In this paper, we first analyze why the current direct training approach with surrogate gradient results in SNNs with poor generalizability. Then we introduce the temporal efficient training (TET) approach to compensate for the loss of momentum in the gradient descent with SG so that the training process can converge into flatter minima with better generalizability. Meanwhile, we demonstrate that TET improves the temporal scalability of SNN and induces a temporal inheritable training for acceleration. Our method consistently outperforms the SOTA on all reported mainstream datasets, including CIFAR-10/100 and ImageNet. Remarkably on DVS-CIFAR10, we obtained $8 3 \\%$ top-1 accuracy, over $\\bar { 1 0 \\% }$ improvement compared to existing state of the art. Codes are available at https://github.com/Gus-Lab/temporal_ efficient_training. ",
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"text": "1 INTRODUCTION ",
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"text": "The advantages of Spiking neuron networks (SNNs) lie in their energy-saving and fast-inference computation when embedded on neuromorphic hardware such as TrueNorth (DeBole et al., 2019) and Loihi (Davies et al., 2018). Such advantages originate from the biology-inspired binary spike transmitted mechanism, by which the networks avoid multiplication during inference. On the other hand, this mechanism also leads to difficulty in training very deep SNNs from scratch because the non-differentiable spike transmission hinders the powerful back-propagation approaches like gradient descents. Recently, many studies on converting artificial neuron networks (ANNs) to SNNs have demonstrated SNNs’ comparable power in feature representation as ANNs (Han & Roy, 2020; Deng & Gu, 2020; Li et al., 2021a). Nevertheless, it is commonly agreed that the direct training method for high-performance SNN is still crucial since it distinguishes SNNs from converted ANNs, especially on neuromorphic datasets. ",
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"text": "The output layer’s spike frequency or the average membrane potential increment is commonly used as inference indicators in SNNs (Shrestha & Orchard, 2018; Kim et al., 2019). The current standard direct training (SDT) methods regard the SNN as RNN and optimize inference indicators’ distribution (Wu et al., 2018). They adopt surrogate gradients (SG) to relieve the non-differentiability (Lee et al., 2016; Wu et al., 2018; Zheng et al., 2021). However, the gradient descent with SG does not match with the loss landscape in SNN and is easy to get trapped in a local minimum with low generalizability. Although using suitable optimizers and weight decay help ease this problem, the performance of deep SNNs trained from scratch still suffers a big deficit compared to that of ANNs Deng et al. (2020). Another training issue is the memory and time consumption, which increases linearly with the simulation time. Rathi & Roy (2020) initializes the target network by a converted SNN to shorten the training epochs, indicating the possibility of high-performance SNN with limited activation time. The training problem due to the non-differentiable activation function has become the main obstruction of spiking neural network development. ",
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"type": "image",
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"img_path": "images/1c0df3e5e42eb5f12b364ae3e1b86c171367176d7d8e201b7cccf8c9ba08687d.jpg",
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"image_caption": [
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"Figure 1: Workflow of temporal efficient training (TET). To obtain a more generalized SNN, we modify the optimization target to adjust each moment’s output distribution. "
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"text": "",
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| 111 |
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"text": "In this work, we examine the limitation of the traditional direct training approach with SG and propose the temporal efficient training (TET) algorithm. Instead of directly optimizing the integrated potential, TET optimizes every moment’s pre-synaptic inputs. As a result, it avoids the trap into local minima with low prediction error but a high second-order moment. Furthermore, since the TET applies optimization on each time point, the network naturally has more robust time scalability. Based on this characteristic, we propose the time inheritance training (TIT), which reduces the training time by initializing the SNN with a smaller simulation length. With the help of TET, the performance of SNNs has improved on both static datasets and neuromorphic datasets. Figure 1 depicts the workflow of our approach. ",
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"text": "The following summarizes our main contributions: ",
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"text": "• We analyze the problem of training SNN with SG and propose the TET method, a new loss and gradient descent regime that succeeds in obtaining more generalizable SNNs. • We analyze the feasibility of TET and picture the loss landscape under both the SDT and TET setups to demonstrate TET’s advantage in better generalization. • Our sufficient experiments on both static datasets and neuromorphic datasets prove the effectiveness of the TET method. Especially on DVS-CIFAR10, we report $8 3 . 1 \\bar { 7 } \\%$ top-1 accuracy for the first time, which is over $1 0 \\%$ better than the current state-of-the-art result. ",
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"text": "2 RELATED WORK ",
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| 155 |
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"text": "In recent years, SNNs have developed rapidly and received more and more attention from the research community. However, lots of challenging problems remain to be unsolved. In general, most works on SNN training have been carried out in two strategies: ANN-to-SNN conversion and direct training from scratch. ",
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"text": "ANN-to-SNN Conversion. Conversion approaches avoid the training problem by trading high accuracy through high latency. They convert a high-performing ANN to SNN and adjust the SNN parameters w.r.t the ANN activation value layer-by-layer (Diehl et al., 2015; 2016). Some special techniques have been proposed to reduce the inference latency, such as the subtraction mechanism (Rueckauer et al., 2016; Han et al., 2020), robust normalization Rueckauer et al. (2016), spike-norm (Sengupta et al., 2018), and channel-wise normalization (Kim et al., 2019). Recently, Deng & Gu (2020) decompose the conversion error to each layer and reduce it by bias shift. Li et al. (2021a) suggest using adaptive threshold and layer-wise calibration to obtain high-performance SNNs that require a simulation length of less than 50. However, converted methods significantly extend the inference latency, and they are not suitable for neuromorphic data (Deng et al., 2020). ",
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"text": "",
|
| 189 |
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"text": "Direct training. In this area, SNNs are regarded as special RNNs and training with BPTT (Neftci et al., 2019). On the backpropagation process, The non-differentiable activation term is replaced with a surrogate gradient (Lee et al., 2016). Compared with ANN-to-SNN conversion, direct training achieves high accuracy with few time steps but suffers more training costs (Deng et al., 2020). Several studies suggest that surrogate gradient (SG) is helpful to obtain high-performance SNNs on both static datasets and neuromorphic datasets (Wu et al., 2019; Shrestha & Orchard, 2018; Li et al., 2021b). On the backpropagation process, SG replaces the Dirac function with various shapes of curves. Exceptionally, Wu et al. (2018) first propose the STBP method and train SNNs on the ANN programming platform, which significantly promotes direct training development. Zheng et al. (2021) further proposes the tdBN algorithm to smooth the loss function and first realize training a large-scale SNN on ImageNet. Zhang & Li (2020) proposes TSSL-BP to break down error backpropagation across two types of inter-neuron and intra-neuron dependencies and achieve low-latency and high accuracy SNNs. Recently, Yang et al. (2021) designed a neighborhood aggregation (NA) method to use the multiple perturbed membrane potential waveforms in the neighborhood to compute the finite difference gradients and guide the weight updates. They significantly decrease the required training iterations and improve the SNN performance. ",
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| 200 |
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"text": "3 PRELIMINARY ",
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| 211 |
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"text": "3.1 ITERATIVE LIF MODEL ",
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"text": "We adopt the Leaky Integrate-and-Fire (LIF) model and translate it to an iterative expression with the Euler method (Wu et al., 2019). Mathematically, the membrane potential is updated as ",
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"type": "equation",
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"img_path": "images/79d0ddccc8ccc58411e76edbec4fc81d48d5beb97e2427fcc4feed59b3981d00.jpg",
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"text": "$$\n\\begin{array} { r } { \\pmb { u } ( t + 1 ) = \\tau \\pmb { u } ( t ) + \\pmb { I } ( t ) , } \\end{array}\n$$",
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"text": "where $\\tau$ is the constant leaky factor, ${ \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf { } \\mathbf \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf \\mathbf \\Psi \\Psi \\mathbf { \\mathbf } \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf $ is the membrane potential at time $t$ , and $\\mathbf { } I ( t )$ denotes the pre-synaptic inputs, which is the product of synaptic weight $\\mathbf { W }$ and spiking input ${ \\mathbf { } } x ( t )$ . Given a specific threshold $V _ { t h }$ , the neuron fires a spike and ${ \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\Psi \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf \\Psi { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf { } \\mathbf \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\Psi \\mathbf \\Psi \\mathbf { \\mathbf } \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf $ reset to 0 when the ${ \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } { \\mathbf { } } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf { } \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf { } \\mathbf \\Psi \\mathbf { } \\mathbf \\mathbf { } \\mathbf \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf \\mathbf \\Psi \\Psi \\mathbf { } \\mathbf \\mathbf \\mathbf { } \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf { \\Psi \\mathbf } \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\Psi \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf \\mathbf $ exceeds the threshold. So the firing function and hard reset mechanism can be described as ",
|
| 259 |
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"bbox": [
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| 260 |
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| 261 |
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| 262 |
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| 264 |
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|
| 265 |
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"page_idx": 2
|
| 266 |
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},
|
| 267 |
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{
|
| 268 |
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"type": "equation",
|
| 269 |
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"img_path": "images/20e0ed1a52553143a3bef8068e7733454312aa974301f895a48de2c6e6b19bc9.jpg",
|
| 270 |
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"text": "$$\n\\pmb { a } ( t + 1 ) = \\pmb { \\Theta } ( \\pmb { u } ( t + 1 ) - V _ { t h } )\n$$",
|
| 271 |
+
"text_format": "latex",
|
| 272 |
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"bbox": [
|
| 273 |
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| 274 |
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| 276 |
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| 277 |
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],
|
| 278 |
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|
| 279 |
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},
|
| 280 |
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{
|
| 281 |
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"type": "equation",
|
| 282 |
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"img_path": "images/2aa71469768ad37328e20be11ce6b924f417ac2ecbe65d9957fbda1dc4dbcc1c.jpg",
|
| 283 |
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"text": "$$\n\\pmb { u } ( t + 1 ) = \\pmb { u } ( t + 1 ) \\cdot ( 1 - \\pmb { a } ( t + 1 ) ) ,\n$$",
|
| 284 |
+
"text_format": "latex",
|
| 285 |
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"bbox": [
|
| 286 |
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370,
|
| 287 |
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|
| 289 |
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|
| 290 |
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],
|
| 291 |
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"page_idx": 2
|
| 292 |
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},
|
| 293 |
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{
|
| 294 |
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"type": "text",
|
| 295 |
+
"text": "where $\\Theta$ denotes the Heaviside step function. The output spike $\\mathbf { \\delta } \\mathbf { \\ } \\mathbf { \\em a } ( t + 1 )$ will become the post synaptic spike and propagate to the next layer. In this study, we set the starting membrane $\\pmb { u } ( 0 )$ to 0, the threshold $V _ { t h }$ to 1, and the leaky factor $\\tau$ to 0.5 for all experiments. ",
|
| 296 |
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"bbox": [
|
| 297 |
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| 298 |
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| 301 |
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],
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| 302 |
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"page_idx": 2
|
| 303 |
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},
|
| 304 |
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{
|
| 305 |
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"type": "text",
|
| 306 |
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"text": "The last layer’s spike frequency is typically used as the final classification index. However, adopting the LIF model on the last layer will lose information on the membrane potential and damage the performance, especially on complex tasks (Kim et al., 2019). Instead, we integrate the pre-synaptic inputs $\\mathbf { } I ( t )$ with no decay or firing (Rathi & Roy, 2020; Fang et al., 2021). Finally, we set the average membrane potential as the classification index and calculate the cross-entropy loss for training. ",
|
| 307 |
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"bbox": [
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| 308 |
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| 309 |
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| 312 |
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|
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|
| 314 |
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},
|
| 315 |
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{
|
| 316 |
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"type": "text",
|
| 317 |
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"text": "3.2 SURROGATE GRADIENT ",
|
| 318 |
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"text_level": 1,
|
| 319 |
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"bbox": [
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| 320 |
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| 324 |
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],
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|
| 326 |
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},
|
| 327 |
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{
|
| 328 |
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"type": "text",
|
| 329 |
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"text": "Following the concept of direct training, we regard the SNN as RNN and calculate the gradients through spatial-temporal backpropagation (STBP) (Wu et al., 2018): ",
|
| 330 |
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"bbox": [
|
| 331 |
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|
| 332 |
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| 333 |
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821,
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| 334 |
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| 335 |
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],
|
| 336 |
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|
| 337 |
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},
|
| 338 |
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{
|
| 339 |
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"type": "equation",
|
| 340 |
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"img_path": "images/cd21c6adb4f30e317bf469128694fc231f872f68c84c7a80998a1e60e25c08bb.jpg",
|
| 341 |
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"text": "$$\n\\frac { \\partial L } { \\partial \\mathbf { W } } = \\sum _ { t } \\frac { \\partial L } { \\partial \\pmb { a } ( t ) } \\frac { \\partial \\pmb { a } ( t ) } { \\partial \\pmb { a } ( t ) } \\frac { \\partial \\pmb { u } ( t ) } { \\partial \\pmb { I } ( t ) } \\frac { \\partial \\pmb { I } ( t ) } { \\partial \\mathbf { W } } ,\n$$",
|
| 342 |
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"text_format": "latex",
|
| 343 |
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"bbox": [
|
| 344 |
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369,
|
| 345 |
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| 346 |
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627,
|
| 347 |
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883
|
| 348 |
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],
|
| 349 |
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"page_idx": 2
|
| 350 |
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},
|
| 351 |
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{
|
| 352 |
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"type": "text",
|
| 353 |
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"text": "where the term $\\frac { \\partial \\pmb { a } ( t ) } { \\partial \\pmb { u } ( t ) }$ is the gradient of the non-differentiability step function involving the derivative of Dirac’s $\\delta$ -function that is typically replaced by surrogate gradients with a derivable curve. So far, ",
|
| 354 |
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"bbox": [
|
| 355 |
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| 356 |
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| 357 |
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| 358 |
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| 359 |
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],
|
| 360 |
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"page_idx": 2
|
| 361 |
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},
|
| 362 |
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{
|
| 363 |
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"type": "text",
|
| 364 |
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"text": "there are various shapes of surrogate gradients, such as rectangular (Wu et al., 2018; 2019), triangle (Esser et al., 2016; Rathi & Roy, 2020), and exponential (Shrestha & Orchard, 2018) curve. In this work, we choose the surrogate gradients shaped like triangles. Mathematically, it can describe as ",
|
| 365 |
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"bbox": [
|
| 366 |
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|
| 367 |
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| 368 |
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| 369 |
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| 370 |
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],
|
| 371 |
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"page_idx": 3
|
| 372 |
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},
|
| 373 |
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{
|
| 374 |
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"type": "equation",
|
| 375 |
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"img_path": "images/0d996846155207901ccfa55f7bd0020fc5d421b0bad5b204f7ff5dc37acc1d79.jpg",
|
| 376 |
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"text": "$$\n\\frac { \\partial \\pmb { a } ( t ) } { \\partial \\pmb { u } ( t ) } = \\frac { 1 } { \\gamma ^ { 2 } } \\mathrm { m a x } ( 0 , \\gamma - | \\pmb { u } ( t ) - V _ { t h } | ) ,\n$$",
|
| 377 |
+
"text_format": "latex",
|
| 378 |
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"bbox": [
|
| 379 |
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| 380 |
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| 381 |
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| 382 |
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|
| 383 |
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],
|
| 384 |
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"page_idx": 3
|
| 385 |
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},
|
| 386 |
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{
|
| 387 |
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"type": "text",
|
| 388 |
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"text": "where the $\\gamma$ denotes the constraint factor that determines the sample range to activate the gradient. ",
|
| 389 |
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"bbox": [
|
| 390 |
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| 391 |
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| 392 |
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| 393 |
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|
| 394 |
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],
|
| 395 |
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"page_idx": 3
|
| 396 |
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},
|
| 397 |
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{
|
| 398 |
+
"type": "text",
|
| 399 |
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"text": "3.3 BATCH NORMALIZATION FOR SNN ",
|
| 400 |
+
"text_level": 1,
|
| 401 |
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"bbox": [
|
| 402 |
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| 403 |
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|
| 404 |
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|
| 405 |
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|
| 406 |
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],
|
| 407 |
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"page_idx": 3
|
| 408 |
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},
|
| 409 |
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{
|
| 410 |
+
"type": "text",
|
| 411 |
+
"text": "Batch Normalization (BN) (Ioffe & Szegedy, 2015) is beneficial to accelerate training and increase performance since it can smooth the loss landscape during training (Santurkar et al., 2018). Zheng et al. (2021) modified the forward time loop form and proposed threshold-dependent Batch Normalization (tdBN) to normalize the pre-synaptic inputs $\\pmb { I }$ in both spatial and temporal paradigms so that the BN can support spatial-temporal input. We adopt this setup with the extension of the time dimension to batch dimension 1. In the inference process, the BN layer will be merged into the pre-convolutional layer, thus the inference rule of SNN remain the same but with modified weight: ",
|
| 412 |
+
"bbox": [
|
| 413 |
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173,
|
| 414 |
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262,
|
| 415 |
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|
| 416 |
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361
|
| 417 |
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],
|
| 418 |
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"page_idx": 3
|
| 419 |
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},
|
| 420 |
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{
|
| 421 |
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"type": "equation",
|
| 422 |
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"img_path": "images/73c9e2e71e72668daac6ce033bd93a8a69776856e2f35751fa47b8f51dec6235.jpg",
|
| 423 |
+
"text": "$$\n\\hat { \\mathbf { W } } \\gets \\mathbf { W } \\frac { \\gamma } { \\alpha } , \\hat { \\pmb { b } } \\gets \\beta + ( \\pmb { b } - \\mu ) \\frac { \\gamma } { \\alpha } ,\n$$",
|
| 424 |
+
"text_format": "latex",
|
| 425 |
+
"bbox": [
|
| 426 |
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385,
|
| 427 |
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| 428 |
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| 429 |
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|
| 430 |
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],
|
| 431 |
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"page_idx": 3
|
| 432 |
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},
|
| 433 |
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{
|
| 434 |
+
"type": "text",
|
| 435 |
+
"text": "where $\\mu , \\alpha$ are the running mean and standard deviation on both spatial and temporal paradigm, $\\gamma , \\beta$ are the affine transformation parameters, and $\\mathbf { W } , b$ are the parameters of the pre-convolutional layer. ",
|
| 436 |
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"bbox": [
|
| 437 |
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176,
|
| 438 |
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|
| 439 |
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| 440 |
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|
| 441 |
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],
|
| 442 |
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"page_idx": 3
|
| 443 |
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},
|
| 444 |
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{
|
| 445 |
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"type": "text",
|
| 446 |
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"text": "4 METHODOLOGY ",
|
| 447 |
+
"text_level": 1,
|
| 448 |
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"bbox": [
|
| 449 |
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| 450 |
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| 451 |
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| 452 |
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|
| 453 |
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],
|
| 454 |
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"page_idx": 3
|
| 455 |
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},
|
| 456 |
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{
|
| 457 |
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"type": "text",
|
| 458 |
+
"text": "4.1 FORMULA OF TRAINING SNN WITH SURROGATE GRADIENTS",
|
| 459 |
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"text_level": 1,
|
| 460 |
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"bbox": [
|
| 461 |
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| 462 |
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| 463 |
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| 464 |
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|
| 465 |
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],
|
| 466 |
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"page_idx": 3
|
| 467 |
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},
|
| 468 |
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{
|
| 469 |
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"type": "text",
|
| 470 |
+
"text": "Standard Direct Training. We use $O ( t )$ to represent pre-synaptic input $\\mathbf { } I ( t )$ of the output layer and calculate the cross-entropy loss. The loss function of standard direct training ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ is: ",
|
| 471 |
+
"bbox": [
|
| 472 |
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173,
|
| 473 |
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520,
|
| 474 |
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828,
|
| 475 |
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550
|
| 476 |
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],
|
| 477 |
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"page_idx": 3
|
| 478 |
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},
|
| 479 |
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{
|
| 480 |
+
"type": "equation",
|
| 481 |
+
"img_path": "images/8f4533824d324c069c3603f39de4b247d351ea6cf666d20b7c5b6f05cc4ffc71.jpg",
|
| 482 |
+
"text": "$$\n\\mathcal { L } _ { \\mathrm { S D T } } = \\mathcal { L } _ { \\mathrm { C E } } \\big ( \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } O ( t ) , { \\pmb y } \\big ) ,\n$$",
|
| 483 |
+
"text_format": "latex",
|
| 484 |
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"bbox": [
|
| 485 |
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398,
|
| 486 |
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| 487 |
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598,
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| 488 |
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|
| 489 |
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],
|
| 490 |
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"page_idx": 3
|
| 491 |
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},
|
| 492 |
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{
|
| 493 |
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"type": "text",
|
| 494 |
+
"text": "where $T$ is the total simulation time, $\\mathcal { L } _ { \\mathrm { C E } }$ denotes the cross-entropy loss, and $\\textbf { { y } }$ represents the target label. Following the chain rule, we obtain the gradient of $\\mathbf { W }$ with softmax $S ( \\cdot )$ inference function : ",
|
| 495 |
+
"bbox": [
|
| 496 |
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173,
|
| 497 |
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612,
|
| 498 |
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826,
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| 499 |
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641
|
| 500 |
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],
|
| 501 |
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"page_idx": 3
|
| 502 |
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},
|
| 503 |
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{
|
| 504 |
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"type": "equation",
|
| 505 |
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"img_path": "images/2291a0db108c1baa17edc7f234f088fa3a88711355c3d68e0d15b610f7cddd0d.jpg",
|
| 506 |
+
"text": "$$\n\\frac { \\partial \\mathcal { L } _ { \\mathrm { S D T } } } { \\partial { \\bf W } } = \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } [ S ( O _ { \\mathrm { m e a n } } ) - \\hat { \\pmb { y } } ] \\frac { \\partial O ( t ) } { \\partial { \\bf W } } ,\n$$",
|
| 507 |
+
"text_format": "latex",
|
| 508 |
+
"bbox": [
|
| 509 |
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364,
|
| 510 |
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|
| 511 |
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|
| 512 |
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695
|
| 513 |
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],
|
| 514 |
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"page_idx": 3
|
| 515 |
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},
|
| 516 |
+
{
|
| 517 |
+
"type": "text",
|
| 518 |
+
"text": "where $O _ { \\mathrm { m e a n } }$ denotes the average of the output $O ( t )$ over time, and $\\hat { y }$ is the one-hot coding of $\\textbf { { y } }$ . ",
|
| 519 |
+
"bbox": [
|
| 520 |
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173,
|
| 521 |
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704,
|
| 522 |
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803,
|
| 523 |
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720
|
| 524 |
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],
|
| 525 |
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"page_idx": 3
|
| 526 |
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},
|
| 527 |
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{
|
| 528 |
+
"type": "text",
|
| 529 |
+
"text": "Temporal Efficient Training. In this section, we come up with a new kind of loss function ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ to realize temporal efficient training (TET). It constrains the output (pre-synaptic inputs) at each moment to be close to the target distribution. It is described as: ",
|
| 530 |
+
"bbox": [
|
| 531 |
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174,
|
| 532 |
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727,
|
| 533 |
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820,
|
| 534 |
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768
|
| 535 |
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],
|
| 536 |
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"page_idx": 3
|
| 537 |
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},
|
| 538 |
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{
|
| 539 |
+
"type": "equation",
|
| 540 |
+
"img_path": "images/5b2fde9662b1a8301b77818a0131d21844eaca42707e3ef63dd52e680943a97b.jpg",
|
| 541 |
+
"text": "$$\n\\mathcal { L } _ { \\mathrm { T E T } } = \\frac { 1 } { T } \\cdot \\sum _ { t = 1 } ^ { T } \\mathcal { L } _ { \\mathrm { C E } } [ O ( t ) , { \\pmb y } ] .\n$$",
|
| 542 |
+
"text_format": "latex",
|
| 543 |
+
"bbox": [
|
| 544 |
+
397,
|
| 545 |
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779,
|
| 546 |
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601,
|
| 547 |
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823
|
| 548 |
+
],
|
| 549 |
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"page_idx": 3
|
| 550 |
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},
|
| 551 |
+
{
|
| 552 |
+
"type": "text",
|
| 553 |
+
"text": "Recalculate the gradient of weights under the loss function ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ , and we have: ",
|
| 554 |
+
"bbox": [
|
| 555 |
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173,
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| 556 |
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832,
|
| 557 |
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687,
|
| 558 |
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847
|
| 559 |
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],
|
| 560 |
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"page_idx": 3
|
| 561 |
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},
|
| 562 |
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{
|
| 563 |
+
"type": "equation",
|
| 564 |
+
"img_path": "images/c30cf63716931d277601336b8854b8a69f7d6fe85744cd096f5dd6904c14578f.jpg",
|
| 565 |
+
"text": "$$\n\\frac { \\partial \\mathcal { L } _ { \\mathrm { T E T } } } { \\partial { \\bf W } } = \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } [ S ( \\pmb { O } ( t ) ) - \\pmb { \\hat { y } } ] \\cdot \\frac { \\partial \\pmb { O } ( t ) } { \\partial { \\bf W } } .\n$$",
|
| 566 |
+
"text_format": "latex",
|
| 567 |
+
"bbox": [
|
| 568 |
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362,
|
| 569 |
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856,
|
| 570 |
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635,
|
| 571 |
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900
|
| 572 |
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"type": "text",
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"text": "4.2 CONVERGENCE OF GRADIENT DESCENT FOR SDT V.S. TET ",
|
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"text": "In the case of SDT, the gradient consists of two parts, the error term $( S ( O _ { \\mathrm { m e a n } } ) - \\hat { \\pmb y } )$ and the partial derivative of output $\\partial { \\cal O } \\bar { ( } t ) / \\partial { \\bf W }$ . When the training process reaches near a local minimum, the term $( S ( O _ { \\mathrm { m e a n } } ) - \\hat { \\pmb y } )$ approximates 0 for all $t = 1 , . . . , T$ , ignorant of the term $\\partial O ( t ) / \\partial \\mathbf { W }$ . For traditional ANNs, the accumulated momentum may help get out of the local minima (e.g. saddle point) that typically implies bad generalizability (Kingma & Ba, 2014; Kidambi et al., 2018). However, when the SNN is trained with surrogate gradients, the accumulated momentum could be extremely small, considering the mismatch of gradients and losses. The fact that the activation function is a step one while the SG is bounded with integral constraints. This mismatch dissipates the momentum around a local minimum and stops the SDT from searching for a flatter minimum that may suggest better generalizability. ",
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"text": "In the case of TET, this issue of mismatch is relieved by reweighting the contribution of $\\partial { \\cal O } ( t ) / \\partial { \\bf W }$ . Indeed, considering the fact that the first term $( S ( O ( t ) ) - \\hat { { \\mathbf { y } } } )$ is impossible to be 0 at every moment of SNN since the early output accuracy on the training set is not $1 0 0 \\%$ . So TET needs the second term $\\partial { \\cal O } ( t ) / \\partial { \\bf W }$ close to 0 to make the ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ convergence. This mechanism increases the norm of gradients around sharp local minima and drives the TET to search for a flat local minimum where the disturbance of weight does not cause a huge change in $O ( t )$ . ",
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"type": "text",
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"text": "Further, to ensure that the convergence with TET implies the convergence of SDT, we prove the following lemma: ",
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"type": "text",
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"text": "Lemma 4.1. $\\mathcal { L } _ { S D T }$ is upper bounded by $\\mathcal { L } _ { T E T }$ ",
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| 623 |
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"bbox": [
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"type": "text",
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"text": "Proof. Suppose $O _ { i } ( t )$ and $\\hat { y } _ { i }$ denote the i-th component of $O ( t )$ and $\\hat { y }$ , respectively. Expand Eqn.9, we have: ",
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"text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { \\mathrm { T E T } } = - \\displaystyle \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } \\sum _ { i = 1 } ^ { n } \\hat { y } _ { i } \\log S ( \\boldsymbol { O } _ { i } ( t ) ) = - \\frac { 1 } { T } \\sum _ { i = 1 } ^ { n } \\hat { y } _ { i } \\log ( \\prod _ { t = 1 } ^ { T } S ( \\boldsymbol { O } _ { i } ( t ) ) ) } \\\\ & { \\quad \\quad \\quad = - \\displaystyle \\sum _ { i = 1 } ^ { n } \\hat { y } _ { i } \\log ( \\prod _ { t = 1 } ^ { T } S ( \\boldsymbol { O } _ { i } ( t ) ) ) ^ { \\frac { 1 } { T } } \\geq - \\sum _ { i = 1 } ^ { n } \\hat { y } _ { i } \\log ( \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } S ( \\boldsymbol { O } _ { i } ( t ) ) ) } \\\\ & { \\quad \\quad \\quad \\geq - \\displaystyle \\sum _ { i = 1 } ^ { n } \\hat { y } _ { i } \\log ( S ( \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } O _ { i } ( t ) ) ) = \\mathcal { L } _ { \\mathrm { S D T } } , } \\end{array}\n$$",
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"bbox": [
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"text": "where the first inequality is given by the Arithmetic Mean-Geometric Mean Inequality, and the second one is given by Jensen Inequality since the softmax function is convex. As a corollary, once the ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ gets closed to zero, the original loss function ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ also approaches zero. □ ",
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"bbox": [
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"text": "Furthermore, the network output $O ( t )$ at a particular time point may be a particular outlier that dramatically affects the total output since the output of the SNN has the same weight at every moment under the rule of integration. Thus it is necessary to add a regularization term like $\\mathcal { L } _ { \\mathrm { M S E } }$ loss to confine each moment’s output to reduce the risk of outliers: ",
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"img_path": "images/c03a2ccbd27a1cfad5ad85cefa96a16c4c0e3ccba38d4f927a7bb4ab70ca5181.jpg",
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"text": "$$\n\\mathcal { L } _ { \\mathrm { M S E } } = \\frac { 1 } { T } \\sum _ { t = 1 } ^ { T } \\mathrm { M S E } ( \\mathbf { O } ( t ) , \\phi ) ,\n$$",
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"bbox": [
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"text": "where $\\phi$ is a constant used to regularize the membrane potential distribution. And we set $\\phi = V _ { t h }$ in our experiments. In practice, we use a hyperparameter $\\lambda$ to adjust the proportion of the regular term, we have: ",
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"img_path": "images/2d4ca1af8e92f1b5e37f29d8225e52d8f739328ae7f8fbd21a9e43ec0522cfeb.jpg",
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"text": "$$\n\\mathcal { L } _ { \\mathrm { T O T A L } } = ( 1 - \\lambda ) \\mathcal { L } _ { \\mathrm { T E T } } + \\lambda \\mathcal { L } _ { \\mathrm { M S E } } .\n$$",
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"bbox": [
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"text": "It is worth noting that we only changed the loss function in the training process and did not change SNN’s inference rules in the testing phase for a fair comparison. This algorithm is detailed in Algo.1. ",
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"type": "table",
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"img_path": "images/65e0c9778d5b8d9266b65a187986cadf1c733a981e2dc311d68d5eed5c5bed81.jpg",
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"table_caption": [
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""
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| 730 |
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"table_footnote": [],
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| 732 |
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"table_body": "<table><tr><td>Algorithm1:Temporalefficienttrainingforoneepoch Input: SNN model; Simulation length: T; Threshold: Vth; Training dataset; Validation dataset;</td></tr><tr><td>total training iteration in one epoch: Itrain; total validation iteration in one epoch: Ival</td></tr><tr><td>for all i= 1,2,...Itrain iteration do Get mini-batch training data,and class label: Yi;</td></tr><tr><td>Compute the SNN output Oi(t) of eatch time step;</td></tr><tr><td>Calculate loss function: LTOTAL = (1-λ)LTET + 入LMSE =</td></tr><tr><td>(1-λ):¹∑t=1LcE(O²(t),Yi)+>·¹∑t=1 MSE(Oi(t),𝜙);</td></tr><tr><td>Backpropagation and update model parameters;</td></tr><tr><td>end for all i= 1,2,..Ival iteration do</td></tr><tr><td>Get mini-batch validation data,and class label: Yi;</td></tr><tr><td>T</td></tr><tr><td>Compute the SNN average output Omean = ∑T=1 O(t) over al time step;</td></tr><tr><td>Compare the clasification factor Omean and Yi for classification; end</td></tr></table>",
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"type": "text",
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"text": "4.3 TIME INHERITANCE TRAINING ",
|
| 744 |
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"text_level": 1,
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"text": "SNN demands simulation length long enough to obtain a satisfying performance, but the training time consumption will increase linearly as the simulation length grows. So how to shorten the training time is also an essential problem in the direct training field. Traditional loss function ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ only optimizes the whole network output under a specific $T$ , so its temporal scalability is poor. Unlike the standard training, TET algorithm optimizes each moment’s output, enabling us to extend the simulation time naturally. We introduce Time Inheritance Training (TIT) to alleviate the training time problem. We first use long epochs to train an SNN with a short simulation time T, e.g., 2. Then, we increase the simulation time to the target value and retrain with short epochs. We discover that TIT performs better than training from scratch on accuracy and significantly saves the training time. Assuming that training an SNN with simulation length $T = 1$ cost $t s$ time per epoch, the SNN needs 300 epochs to train from scratch, and the TIT needs 50 epochs for finetuning. So we need $1 8 0 0 t s$ time to train an SNN with $T = 6$ from scratch, but following the TIT pipeline with the initial $T = 2$ only requires $9 0 0 t s$ . As a result, the TIT can reduce the training time cost by half. ",
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"type": "text",
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"text": "5 EXPERIMENTS ",
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"text_level": 1,
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"text": "We validate our proposed TET algorithm and compare it with existing works on both static and neuromorphic datasets. The network architectures in this paper include ResNet-19 (Zheng et al., 2021), Spiking-ResNet34 (Zheng et al., 2021), SEW-ResNet34 (Fang et al., 2021), SNN-5, and VGGSNN. SNN-5 (16C3-64C5-AP2-128C5-AP2-256C5-AP2-512C3-AP2-FC) is a simple convolutional SNN suitable for multiple runs to discover statistical rules (Figure A. 7). The architecture of VGGSNN (64C3-128C3-AP2-256C3-256C3-AP2-512C3-512C3-AP2-512C3-512C3-AP2- FC) is based on VGG11 with two fully connected layers removed as we found that additional fully connected layers were unnecessary for neuromorphic datasets. ",
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"text": "5.1 MODEL VALIDATION AND ABLATION STUDY",
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"text": "Effectiveness of TET over SDT with SG. We first examine whether the mismatch between SG and loss causes the convergence problem. For this purpose, we set the simulation length to 4 and change the spike function $\\Theta$ in Eqn.2 to Sigmoid $\\sigma ( \\bar { k } \\cdot \\mathrm { { i n p u t } } )$ . We find that the TET and SDT achieved similar accuracy (Table 2) when $k = 1 , 1 0 , 2 0$ . This indicates that both TET and SDT work when the gradient and loss function match each other. Next, we compare the results training with ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ and ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ on SNNs (ResNet-19 on CIFAR100) training with surrogate gradient for three runs. As shown in Table 1, our proposed new TET training strategy dramatically increases the accuracy by $3 . 2 5 \\%$ when the simulation time is 4 and $3 . 5 3 \\%$ when the simulation time is 6. These results quantitatively support the effectiveness of TET in solving the mismatch between gradient and loss in training SNNs with SG. ",
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"type": "image",
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"img_path": "images/aff831f07e0e329cffab78a14e6c6b9cb6a33fb6860a562c194fcda2f2064b92.jpg",
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"image_caption": [
|
| 814 |
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"Figure 2: Loss landscape of VGGSNN. The 2D landscape of ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ and ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ from two different training methods. "
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"table_caption": [
|
| 829 |
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"Table 1: Comparison between SDT and TET. We adopt the SNN architecture ResNet-19 with SG on CIFAR100 and record the results with three different simulation lengths 2, 4, and 6. "
|
| 830 |
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],
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| 832 |
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"table_body": "<table><tr><td>Method</td><td>T=2</td><td>T=4</td><td>T=6</td></tr><tr><td>Direct training</td><td>69.41±0.08</td><td>70.86±0.22</td><td>71.12±0.57</td></tr><tr><td>TET</td><td>72.37±0.21</td><td>74.11±0.18</td><td>74.65±0.12</td></tr></table>",
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"img_path": "images/2b28a47a94520362d7566ceb1821586f201923734a5ba4241ac94a4a29bed241.jpg",
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"table_caption": [
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| 845 |
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"Table 2: Comparison of SDT and TET with sigmoid function $\\sigma ( k { \\cdot } \\mathrm { i n p u t } )$ . We fix the simulation length to 4 and record the results of CNN-5 under three different $k$ on CIFAR10. "
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"table_body": "<table><tr><td>Method</td><td>k=1</td><td>k=10</td><td>k=20</td></tr><tr><td>Direct training</td><td>88.00±0.15</td><td>88.83±0.32</td><td>88.50±0.32</td></tr><tr><td>TET</td><td>87.63±0.38</td><td>89.31±0.15</td><td>88.64±0.28</td></tr></table>",
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"text": "Loss Landscape around Local Minima. We further inspect the 2D landscapes (Li et al., 2018) of $\\mathcal { L } _ { \\mathrm { S D T } }$ and ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ around their local minima (see Figure. 2) to demonstrate why TET generalizes better than SDT and how TET helps the training process jump out of the sharp local minima typically found by SDT. First, comparing Figure. $2 \\textrm { A }$ and C, we can see that although the values of local minima achieved by SDT and TET are similar in $\\mathcal { L } _ { \\mathrm { S D T } }$ , the local minima of TET (Figure. $2 \\textrm { C }$ ) is flatter than that of SDT (Figure. $2 \\mathrm { \\ A }$ ). This indicates that the TET is effective in finding flatter minima that are typically more generalizable even w.r.t the original loss in TET. Next, we examine the two local minima under ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ to see how it helps jump out the local minima found by SDT. When comparing Figure. 2 B and D, we observe that the local minima found by SDT (Figure. 2 B) is not only sharper than that found by TET (Figure. $2 \\mathbf { D }$ ) under ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ but also maintains a higher loss value. This supports our claim that TET loss cannot be easily minimized around sharp local minima (Figure. $2 \\mathrm { \\ B }$ ), thus preferable to converge into flatter local minima (Figure. $2 \\mathrm { D }$ ). Put together, the results here provide evidence for our reasoning in Section 4.2. ",
|
| 860 |
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"bbox": [
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| 866 |
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"page_idx": 6
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| 868 |
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{
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| 869 |
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"type": "text",
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| 870 |
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"text": "Training from SDT to TET. In this part, we further validate the ability of TET to escape from the local minimum found by SDT. We adopt the VGGSNN with 300 epochs training on DVS-CIFAR10. First, we optimize ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ for 200 epochs and then change the loss function to ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ after epoch 200. Figure 3 demonstrates the accuracy and loss change on the test set. After 200 epochs training, SDT gets trapped into a local minimum, and the ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ no longer decreases. The ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ is much higher than $\\mathcal { L } _ { \\mathrm { S D T } }$ since SDT does not optimize it. Nevertheless, after we change the loss function to ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ , the ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ and $\\mathcal { L } _ { \\mathrm { S D T } }$ on the test set both have a rapid decline. This phenomenon illustrates the TET ability to help the SNN efficiently jump out of the local minimum with poor generalization and find another flatter local minimum. ",
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"page_idx": 6
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| 879 |
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"type": "image",
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"img_path": "images/3337c633c01451316aa0cc30732fe1eaeb582425bcdf30fbe135431d8bf36214.jpg",
|
| 882 |
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"image_caption": [
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| 883 |
+
"Figure 3: TET helps to jump out the local minimum point. We provide the test accuracy (A) and loss $( B )$ change after changing the SDT to TET at epoch 200. TET efficiently improves the test performance and reduces the two kinds of loss. "
|
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| 885 |
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"image_footnote": [],
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"type": "image",
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"img_path": "images/086a43f62fe160235967e86bf1fd8d81f8153af1874a2e9a74e352d77d8e5e20.jpg",
|
| 897 |
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"image_caption": [
|
| 898 |
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"Figure 4: Time scalability robustness and network efficiency of ResNet-19 on CIFAR100. (A) The comparison of training from scratch (dots) and inheriting from a small simulation length (lines). $( B )$ SNN network performance changes with energy consumption. "
|
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"type": "text",
|
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"text": "",
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"bbox": [
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"type": "text",
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| 922 |
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"text": "Time Scalability Robustness. Here, we study the time scalability robustness of SNNs trained with TET $( \\mathcal { L } _ { \\mathrm { T E T } } )$ . First, we use 300 epochs to train a small simulation length ResNet-19 on CIFAR100 as the initial SNN. Then, we directly change the simulation length from 2 to 8 without finetuning and report the network accuracy on the test set. Figure. 4. A displays the results after changing the simulation length. We use 2, 3, and 4, respectively, as the simulation length of the initial network. When we increase the simulation length, the accuracy of all networks gradually increases. After the simulation time reaches a certain value, the network performance will slightly decrease. Interestingly, SNNs trained from scratch ( $\\mathrm { T } { = } 4$ and ${ \\mathrm { T } } { = } 6$ ) are not as good as those trained following the TIT procedure. ",
|
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{
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"type": "text",
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"text": "Network Efficiency. In this section, we measure the relationship between energy consumption and network performance. SNN avoids multiplication on the inference since its binary activation and event-based operation. The addition operation in SNN costs $0 . 9 p J$ energy while multiplication operation consumes $4 . 6 p J$ measured in $4 5 \\mathrm { n m }$ CMOS technology (Rathi & Roy, 2020). In our SNN model, the first layer has multiplication operations, while the other layers only have addition operations. Figure 4. B summarizes the results of different simulation times. In all cases, the SNN obtained by TET has higher efficiency. ",
|
| 934 |
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{
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"type": "text",
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| 944 |
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"text": "5.2 COMPARISON TO EXITING WORKS ",
|
| 945 |
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"text_level": 1,
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| 946 |
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{
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| 955 |
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"type": "text",
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| 956 |
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"text": "In this section, we compare our experimental results with previous works. We validate the full TIT algorithm $( \\mathcal { L } _ { \\mathrm { T O T A L } } )$ both on the static dataset and neuromorphic dataset. All of the experiment results are summarized in Table 5.2. We specify all the training details in the appendix A.1. ",
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"bbox": [
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"type": "text",
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| 967 |
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"text": "CIFAR. We apply TET and TIT algorithm on CIFAR (Krizhevsky et al., 2009), and report the mean and standard deviation of 3 runs under different random seeds. The $\\lambda$ is set to 0.05. On CIFAR10, our TET method achieves the highest accuracy above all existing approaches. Even when $T = 2$ , there is a $1 . 8 2 \\%$ increment compare to STBP-tdBN with simulation length $T = 6$ . It is worth noting that our method is only $0 . 4 7 \\%$ lower than the ANN performance. TET algorithm demonstrates a more excellent ability on CIFAR100. It has an accuracy increase greater than $3 \\%$ on all report simulation lengths. In addition, when $T = 6$ , the reported accuracy is only $0 . 6 3 \\%$ lower than that of ANN. We can see that the proposed TET’s improvement is even higher on complex data like CIFAR100, where the generalizability of the model distinguishes a lot among minima with different flatness. ",
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| 968 |
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{
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"type": "table",
|
| 978 |
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"img_path": "images/dadbd052f80ebc40da5335c537abae5ee726446e1d387a7f4fc73961ba3ebea6.jpg",
|
| 979 |
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"table_caption": [
|
| 980 |
+
"Table 3: Compare with existing works. Our method improves network performance across all tasks. \\* denotes self-implementation results. † denotes data augmentation (Li et al., 2022). "
|
| 981 |
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],
|
| 982 |
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"table_footnote": [],
|
| 983 |
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"table_body": "<table><tr><td>Dataset</td><td>Model</td><td>Methods</td><td>Architecture</td><td>SimulationLength</td><td>Accuracy</td></tr><tr><td rowspan=\"10\">CIFAR10</td><td>Rathi et al. (2019)</td><td>Hybrid training Diet-SNN</td><td>ResNet-20</td><td>250</td><td>92.22</td></tr><tr><td>Rathi & Roy (2020)</td><td></td><td>ResNet-20</td><td>10</td><td>92.54</td></tr><tr><td>Wu et al. (2018)</td><td>STBP</td><td>CIFARNet</td><td>12</td><td>89.83</td></tr><tr><td>Wu et al. (2019)</td><td>STBP NeuNorm</td><td>CIFARNet</td><td>12</td><td>90.53</td></tr><tr><td>Zhang & Li (2020)</td><td>TSSL-BP</td><td>CIFARNet</td><td>5</td><td>91.41</td></tr><tr><td>Zheng et al. (2021)</td><td>STBP-tdBN</td><td>ResNet-19</td><td>6 4</td><td>93.16 92.92</td></tr><tr><td rowspan=\"3\">our model</td><td rowspan=\"3\">TET</td><td rowspan=\"3\"></td><td>2</td><td>92.34</td></tr><tr><td>6</td><td>94.50±0.07</td></tr><tr><td>4</td><td>94.44±0.08</td></tr><tr><td></td><td></td><td>ResNet-19</td><td>2</td><td>94.16±0.03</td></tr><tr><td rowspan=\"6\">CIFAR100</td><td>ANN*</td><td>ANN</td><td>ResNet-19</td><td>1</td><td>94.97</td></tr><tr><td>Rathi et al. (2019) Rathi & Roy (2020)</td><td>Hybrid training</td><td>VGG-11</td><td>125</td><td>67.87</td></tr><tr><td></td><td>Diet-SNN</td><td>ResNet-20</td><td>5</td><td>64.07 71.12±0.57</td></tr><tr><td rowspan=\"3\">Zheng et al. (2021)*</td><td rowspan=\"3\">STBP-tdBN</td><td rowspan=\"3\">ResNet-19</td><td>6</td><td>70.86±0.22</td></tr><tr><td>4 2</td><td>69.41±0.08</td></tr><tr><td>6</td><td>74.72±0.28</td></tr><tr><td rowspan=\"5\"></td><td>our model</td><td rowspan=\"2\">TET</td><td rowspan=\"2\">ResNet-19</td><td>4</td><td>74.47±0.15</td></tr><tr><td></td><td>2</td><td>72.87±0.10</td></tr><tr><td>ANN* Rathi etal. (2019)</td><td>ANN</td><td>ResNet-19</td><td>1</td><td>75.35</td></tr><tr><td></td><td>Hybrid training SPIKE-NORM</td><td>ResNet-34</td><td>250</td><td>61.48</td></tr><tr><td>Sengupta et al. (2018) Zheng et al. (2021)</td><td>STBP-tdBN</td><td>ResNet-34</td><td>2500</td><td>69.96</td></tr><tr><td rowspan=\"5\">ImageNet</td><td>Fang et al. (2021)</td><td>SEWResNet</td><td>Spiking-ResNet-34</td><td>6</td><td>63.72</td></tr><tr><td></td><td>TET</td><td>SEW-ResNet-34 Spiking-ResNet-34</td><td>4</td><td>67.04 64.79</td></tr><tr><td>our model</td><td>TET</td><td>SEW-ResNet-34</td><td>6 4</td><td>68.00</td></tr><tr><td>Zheng et al. (2021)</td><td>STBP-tdBN</td><td>ResNet-19</td><td>10</td><td>67.8</td></tr><tr><td>Kugele et al. (2020)</td><td>Streaming Rollout</td><td>DenseNet</td><td>10</td><td>66.8</td></tr><tr><td rowspan=\"5\">DVS-CIFAR10</td><td>Wu et al. (2021)</td><td>Conv3D</td><td>LIAF-Net</td><td></td><td>71.70</td></tr><tr><td>Wu et al. (2021)</td><td>LIAF</td><td>LIAF-Net</td><td>10 10</td><td>70.40</td></tr><tr><td rowspan=\"2\">our model</td><td>TET</td><td>VGGSNN</td><td>10</td><td>77.33±0.21</td></tr><tr><td>TETt</td><td>VGGSNN</td><td></td><td>83.17±0.15</td></tr><tr><td></td><td></td><td></td><td>10</td><td></td></tr></table>",
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"type": "text",
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"text": "ImageNet. The training set of ImageNet (Krizhevsky et al., 2012) provides $1 . 2 8 \\mathrm { k }$ training samples for each label. We choose the two most representative ResNet-34 to verify our algorithm on ImageNet with $\\lambda = 0 . 0 0 1$ . SEW-ResNet34 is not a typical SNN since it adopts the IF model and modifies the Residual structure. Although we only train our model for 120 epochs, the TET algorithm achieves a $1 . 0 7 \\%$ increment on Spiking-ResNet-34 and a $0 . 9 6 \\%$ increment on SEW-ResNet34. ",
|
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{
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"type": "text",
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| 1005 |
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"text": "DVS-CIFAR10. The neuromorphic datasets suffer much more noise than static datasets. Thus the well-trained SNN is easier to overfit on these datasets than static datasets. DVS-CIFAR10 (Li et al., 2017), which provides each label with $0 . 9 \\mathrm { k }$ training samples, is the most challenging mainstream neuromorphic dataset. Recent works prefer to deal with this dataset by complex architectures, which are more susceptible to overfitting and do not result in very high accuracy. Here, we adopt VGGSNN on the DVS-CIFAR10 dataset, set $\\lambda = 0 . 0 0 1$ , and report the mean and standard deviation of 3 runs under different random seeds. Along with data augmentation methods, VGGSNN can achieve an accuracy of $7 7 . 4 \\%$ . Then we apply the TET method to obtain a more generalizable optima. The accuracy rises to $8 3 . 1 7 \\%$ . Our TET method outperforms existing state-of-the-art by $1 1 . 4 7 \\%$ accuracy. Without data augmentation methods, VGGSNN obtains $7 \\bar { 3 } . 3 \\%$ accuracy by SDT and $7 7 . 3 \\%$ accuracy by TET. ",
|
| 1006 |
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"type": "text",
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"text": "6 CONCLUSION ",
|
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"text_level": 1,
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"type": "text",
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"text": "This paper focuses on the SNN generalization problem, which is described as the direct training SNN performs well on the training set but poor on the test set. We find this phenomenon is due to the incorrect SG that makes the SNN easily trapped into a local minimum with poor generalization. To solve this problem, we propose the temporal efficient training algorithm (TET). Extensive experiments verify that our proposed method consistently achieves better performance than the SDT process. Furthermore, TET significantly improves the time scalability robustness of SNN, which enables us to propose the time inheritance training (TIT) to significantly reduce the training time consumption by almost a half. ",
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"type": "text",
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"text": "",
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"type": "text",
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"text": "7 ACKNOWLEDGMENT ",
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| 1051 |
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"text_level": 1,
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},
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{
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"type": "text",
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| 1062 |
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"text": "This project is supported by NSFC 61876032 and JCYJ20210324140807019. Y. Li completed this work during his prior research assistantship in UESTC. ",
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"type": "text",
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"text": "REFERENCES ",
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| 1074 |
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"text_level": 1,
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},
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{
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"type": "text",
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"text": "Mike Davies, Narayan Srinivasa, Tsung-Han Lin, Gautham Chinya, Yongqiang Cao, Sri Harsha Choday, Georgios Dimou, Prasad Joshi, Nabil Imam, Shweta Jain, et al. Loihi: A neuromorphic manycore processor with on-chip learning. Ieee Micro, 38(1):82–99, 2018. ",
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},
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{
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"type": "text",
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"text": "Michael V DeBole, Brian Taba, Arnon Amir, Filipp Akopyan, Alexander Andreopoulos, William P Risk, Jeff Kusnitz, Carlos Ortega Otero, Tapan K Nayak, Rathinakumar Appuswamy, et al. Truenorth: Accelerating from zero to 64 million neurons in 10 years. Computer, 52(5):20–29, 2019. ",
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"type": "text",
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"type": "text",
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"text": "Yujie Wu, Lei Deng, Guoqi Li, Jun Zhu, and Luping Shi. Spatio-temporal backpropagation for training high-performance spiking neural networks. Frontiers in neuroscience, 12:331, 2018. ",
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"bbox": [
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821,
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+
310
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],
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+
"page_idx": 11
|
| 1489 |
+
},
|
| 1490 |
+
{
|
| 1491 |
+
"type": "text",
|
| 1492 |
+
"text": "Yujie Wu, Lei Deng, Guoqi Li, Jun Zhu, Yuan Xie, and Luping Shi. Direct training for spiking neural networks: Faster, larger, better. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 1311–1318, 2019. ",
|
| 1493 |
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"bbox": [
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176,
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+
319,
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+
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+
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],
|
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"page_idx": 11
|
| 1500 |
+
},
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| 1501 |
+
{
|
| 1502 |
+
"type": "text",
|
| 1503 |
+
"text": "Zhenzhi Wu, Hehui Zhang, Yihan Lin, Guoqi Li, Meng Wang, and Ye Tang. Liaf-net: Leaky integrate and analog fire network for lightweight and efficient spatiotemporal information processing. IEEE Transactions on Neural Networks and Learning Systems, 2021. ",
|
| 1504 |
+
"bbox": [
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| 1505 |
+
173,
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| 1506 |
+
371,
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| 1507 |
+
820,
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+
414
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],
|
| 1510 |
+
"page_idx": 11
|
| 1511 |
+
},
|
| 1512 |
+
{
|
| 1513 |
+
"type": "text",
|
| 1514 |
+
"text": "Yukun Yang, Wenrui Zhang, and Peng Li. Backpropagated neighborhood aggregation for accurate training of spiking neural networks. In International Conference on Machine Learning, pp. 11852–11862. PMLR, 2021. ",
|
| 1515 |
+
"bbox": [
|
| 1516 |
+
174,
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| 1517 |
+
422,
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| 1518 |
+
821,
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+
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],
|
| 1521 |
+
"page_idx": 11
|
| 1522 |
+
},
|
| 1523 |
+
{
|
| 1524 |
+
"type": "text",
|
| 1525 |
+
"text": "Wenrui Zhang and Peng Li. Temporal spike sequence learning via backpropagation for deep spiking neural networks. arXiv preprint arXiv:2002.10085, 2020. ",
|
| 1526 |
+
"bbox": [
|
| 1527 |
+
171,
|
| 1528 |
+
474,
|
| 1529 |
+
823,
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+
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],
|
| 1532 |
+
"page_idx": 11
|
| 1533 |
+
},
|
| 1534 |
+
{
|
| 1535 |
+
"type": "text",
|
| 1536 |
+
"text": "Hanle Zheng, Yujie Wu, Lei Deng, Yifan Hu, and Guoqi Li. Going deeper with directly-trained larger spiking neural networks. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pp. 11062–11070, 2021. ",
|
| 1537 |
+
"bbox": [
|
| 1538 |
+
174,
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| 1539 |
+
511,
|
| 1540 |
+
825,
|
| 1541 |
+
555
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],
|
| 1543 |
+
"page_idx": 11
|
| 1544 |
+
},
|
| 1545 |
+
{
|
| 1546 |
+
"type": "text",
|
| 1547 |
+
"text": "A APPENDIX ",
|
| 1548 |
+
"text_level": 1,
|
| 1549 |
+
"bbox": [
|
| 1550 |
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176,
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| 1551 |
+
102,
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| 1552 |
+
297,
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| 1553 |
+
117
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| 1554 |
+
],
|
| 1555 |
+
"page_idx": 12
|
| 1556 |
+
},
|
| 1557 |
+
{
|
| 1558 |
+
"type": "text",
|
| 1559 |
+
"text": "A.1 DATASET AND TRAINING DETAIL ",
|
| 1560 |
+
"text_level": 1,
|
| 1561 |
+
"bbox": [
|
| 1562 |
+
178,
|
| 1563 |
+
133,
|
| 1564 |
+
446,
|
| 1565 |
+
148
|
| 1566 |
+
],
|
| 1567 |
+
"page_idx": 12
|
| 1568 |
+
},
|
| 1569 |
+
{
|
| 1570 |
+
"type": "text",
|
| 1571 |
+
"text": "CIFAR. The CIFAR dataset (Krizhevsky et al., 2009) consists of 50k training images and 10k testing images with the size of $3 2 \\times 3 2$ . We use ResNet-19 for both CIFAR10 and CIFAR100. Moreover, random horizontal flip and crop are applied to the training images the augmentation. First, we use 300 epoch to train the SNN with the simulation length $T = 2$ . We use an Adam optimizer with a learning rate of 0.01 and cosine decay to 0. Next, following the TIT algorithm, we increase the simulation time (to 4 and 6) and continue training the SNN for only 50 epochs, with the learning rate changing to $1 e - 4$ . ",
|
| 1572 |
+
"bbox": [
|
| 1573 |
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173,
|
| 1574 |
+
160,
|
| 1575 |
+
825,
|
| 1576 |
+
257
|
| 1577 |
+
],
|
| 1578 |
+
"page_idx": 12
|
| 1579 |
+
},
|
| 1580 |
+
{
|
| 1581 |
+
"type": "text",
|
| 1582 |
+
"text": "ImageNet. ImageNet (Deng et al., 2009) contains more than $1 2 5 0 \\mathrm { k }$ training images and $5 0 \\mathrm { k }$ validation images. We crop the images to $2 2 4 \\times 2 2 4$ and using the standard augmentation for the training data. We use an SGD optimizer with 0.9 momentum and weight decay $4 e - 5$ . The learning rate is set to 0.1 and cosine decay to 0. We train the SEW-ResNet34 (Fang et al., 2021) with $T = 4$ for 120 epochs. As for the Spiking-ResNet34 (Zheng et al., 2021), we use TIT algorithm to train 90 epochs with $T = 4$ first, then change the simulation time to 6 and finetune the network for 30 epochs. We adopt an Adam optimizer on the finetune phase and change the learning rate to $1 e - 4$ . TIT algorithm significantly reduces the training time consumption since training the Spiking-ResNet34 is extremely slow. ",
|
| 1583 |
+
"bbox": [
|
| 1584 |
+
173,
|
| 1585 |
+
263,
|
| 1586 |
+
825,
|
| 1587 |
+
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|
| 1588 |
+
],
|
| 1589 |
+
"page_idx": 12
|
| 1590 |
+
},
|
| 1591 |
+
{
|
| 1592 |
+
"type": "text",
|
| 1593 |
+
"text": "DVS-CIFAR10. DVS-CIFAR10 (Li et al., 2017), the most challenging mainstream neuromorphic data set, is converted from CIFAR10. It has 10k images with the size $1 2 8 \\times 1 2 8$ . Following Samadzadeh et al. (2020), we divide the data stream into 10 blocks by time and accumulate the spikes in each block. Then, we split the dataset into $9 \\mathrm { k }$ training images and $1 \\mathrm { k }$ test images and reduce the spatial resolution to $4 8 \\times 4 8$ . Random horizontal flip and random roll within 5 pixels are taken as augmentation (Li et al., 2022). We adopt VGGSNN architecture with 300 epochs training on this classification task. And we use an Adam optimizer with the learning rate $1 e - 3$ and cosine decay to 0. As for the case that does not apply any augmentation, we add a weight decay of 5e-4 to the optimizer. ",
|
| 1594 |
+
"bbox": [
|
| 1595 |
+
173,
|
| 1596 |
+
396,
|
| 1597 |
+
825,
|
| 1598 |
+
522
|
| 1599 |
+
],
|
| 1600 |
+
"page_idx": 12
|
| 1601 |
+
},
|
| 1602 |
+
{
|
| 1603 |
+
"type": "text",
|
| 1604 |
+
"text": "A.2 LSDT LOSS LANDSCAPE OF RESNET-19 ",
|
| 1605 |
+
"text_level": 1,
|
| 1606 |
+
"bbox": [
|
| 1607 |
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176,
|
| 1608 |
+
540,
|
| 1609 |
+
486,
|
| 1610 |
+
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|
| 1611 |
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],
|
| 1612 |
+
"page_idx": 12
|
| 1613 |
+
},
|
| 1614 |
+
{
|
| 1615 |
+
"type": "text",
|
| 1616 |
+
"text": "Here we compare the classification loss $( \\mathcal { L } _ { \\mathrm { S D T } } )$ landscapes of ResNet-19 on CIFAR100. The position around the local minimal value found by the SDT $( \\mathcal { L } _ { \\mathrm { { S D T } } } )$ is very sharp. However, the area around the local minimum found by TET $( \\mathcal { L } _ { \\mathrm { T E T } } )$ is much smoother (Figure 5), which indicates that TET effectively improves the network generalization. Such improvements could be further utilized to other techniques like privacy-preserving data generalization (Kim et al., 2021) and neural architecture search (Kim et al., 2022). ",
|
| 1617 |
+
"bbox": [
|
| 1618 |
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173,
|
| 1619 |
+
565,
|
| 1620 |
+
825,
|
| 1621 |
+
648
|
| 1622 |
+
],
|
| 1623 |
+
"page_idx": 12
|
| 1624 |
+
},
|
| 1625 |
+
{
|
| 1626 |
+
"type": "image",
|
| 1627 |
+
"img_path": "images/ec3a5c919a88e624c8ee236df840321cb1292d402cae6ed2e4a7f134e697de42.jpg",
|
| 1628 |
+
"image_caption": [
|
| 1629 |
+
"Figure 5: STD loss landscape of ResNet-19 on CIFAR100 from different training approaches. "
|
| 1630 |
+
],
|
| 1631 |
+
"image_footnote": [],
|
| 1632 |
+
"bbox": [
|
| 1633 |
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274,
|
| 1634 |
+
665,
|
| 1635 |
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723,
|
| 1636 |
+
810
|
| 1637 |
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],
|
| 1638 |
+
"page_idx": 12
|
| 1639 |
+
},
|
| 1640 |
+
{
|
| 1641 |
+
"type": "text",
|
| 1642 |
+
"text": "A.3 EFFECT OF $\\mathcal { L } _ { \\mathrm { M S E } }$ ",
|
| 1643 |
+
"text_level": 1,
|
| 1644 |
+
"bbox": [
|
| 1645 |
+
176,
|
| 1646 |
+
868,
|
| 1647 |
+
334,
|
| 1648 |
+
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|
| 1649 |
+
],
|
| 1650 |
+
"page_idx": 12
|
| 1651 |
+
},
|
| 1652 |
+
{
|
| 1653 |
+
"type": "text",
|
| 1654 |
+
"text": "In this part, we examine the effect of the regular term $\\mathcal { L } _ { \\mathrm { M S E } }$ with 5 different levels of $\\lambda$ . Figure 6 Summarizes the final results. The regular term $\\mathcal { L } _ { \\mathrm { M S E } }$ effectively increases the performance of both ResNet-19 on CIFAR100 and VGGSNN on DVS-CIFAR10. The static dataset CIFAR100 is more suitable for larger $\\lambda$ , while smaller $\\lambda$ is suitable for DVS-CIFAR10. Theoretically, it is hard to obtain satisfying performance at the early simulation moment due to the sparseness of neuromorphic datasets. So too large regular term $\\mathcal { L } _ { \\mathrm { M S E } }$ is not suitable for the neuromorphic dataset. Furthermore, we find that a high $\\lambda$ may harm the early training phase on ImageNet, especially if zero-initialize (Goyal et al., 2017) is not performed. As a result, we set $\\lambda$ to $5 e - 2$ for CIFAR10 and CIFAR100, $1 e - 3$ for ImageNet and DVS-CIFAR10. ",
|
| 1655 |
+
"bbox": [
|
| 1656 |
+
174,
|
| 1657 |
+
895,
|
| 1658 |
+
825,
|
| 1659 |
+
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|
| 1660 |
+
],
|
| 1661 |
+
"page_idx": 12
|
| 1662 |
+
},
|
| 1663 |
+
{
|
| 1664 |
+
"type": "text",
|
| 1665 |
+
"text": "",
|
| 1666 |
+
"bbox": [
|
| 1667 |
+
173,
|
| 1668 |
+
103,
|
| 1669 |
+
826,
|
| 1670 |
+
200
|
| 1671 |
+
],
|
| 1672 |
+
"page_idx": 13
|
| 1673 |
+
},
|
| 1674 |
+
{
|
| 1675 |
+
"type": "image",
|
| 1676 |
+
"img_path": "images/1dd2e09ae0d1ba0fa6f9db557415a2e61436ffe4627041352f5dae8ffd64e9b0.jpg",
|
| 1677 |
+
"image_caption": [
|
| 1678 |
+
"Figure 6: The accuracy under different levels of $\\lambda$ . "
|
| 1679 |
+
],
|
| 1680 |
+
"image_footnote": [],
|
| 1681 |
+
"bbox": [
|
| 1682 |
+
282,
|
| 1683 |
+
218,
|
| 1684 |
+
710,
|
| 1685 |
+
357
|
| 1686 |
+
],
|
| 1687 |
+
"page_idx": 13
|
| 1688 |
+
},
|
| 1689 |
+
{
|
| 1690 |
+
"type": "text",
|
| 1691 |
+
"text": "A.4 STATISTICAL RESULTS ",
|
| 1692 |
+
"text_level": 1,
|
| 1693 |
+
"bbox": [
|
| 1694 |
+
176,
|
| 1695 |
+
417,
|
| 1696 |
+
372,
|
| 1697 |
+
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|
| 1698 |
+
],
|
| 1699 |
+
"page_idx": 13
|
| 1700 |
+
},
|
| 1701 |
+
{
|
| 1702 |
+
"type": "text",
|
| 1703 |
+
"text": "Here we provide statistical results (Figure 7) to prove that the total SNN accuracy is positively associated with every average of moment’s output test accuracy. We train CNN-5 on CIFAR10 for a total of 20 runs with SDT and 5 runs with TET. ",
|
| 1704 |
+
"bbox": [
|
| 1705 |
+
174,
|
| 1706 |
+
443,
|
| 1707 |
+
825,
|
| 1708 |
+
484
|
| 1709 |
+
],
|
| 1710 |
+
"page_idx": 13
|
| 1711 |
+
},
|
| 1712 |
+
{
|
| 1713 |
+
"type": "image",
|
| 1714 |
+
"img_path": "images/295735f1db530423a1bc9f14bdb244ee4d3157db65b06f1b197a62a8ce989d2a.jpg",
|
| 1715 |
+
"image_caption": [
|
| 1716 |
+
"Figure 7: Statistical results. The overall performance of SNN is highly positively associated with the average accuracy of each moment. The standard training obtains the green dots, while the red dots are trained by the TET method. "
|
| 1717 |
+
],
|
| 1718 |
+
"image_footnote": [],
|
| 1719 |
+
"bbox": [
|
| 1720 |
+
351,
|
| 1721 |
+
507,
|
| 1722 |
+
627,
|
| 1723 |
+
674
|
| 1724 |
+
],
|
| 1725 |
+
"page_idx": 13
|
| 1726 |
+
},
|
| 1727 |
+
{
|
| 1728 |
+
"type": "text",
|
| 1729 |
+
"text": "A.5 TIME SCALABILITY ROBUSTNESS OF SDT AND TET. ",
|
| 1730 |
+
"text_level": 1,
|
| 1731 |
+
"bbox": [
|
| 1732 |
+
174,
|
| 1733 |
+
765,
|
| 1734 |
+
581,
|
| 1735 |
+
779
|
| 1736 |
+
],
|
| 1737 |
+
"page_idx": 13
|
| 1738 |
+
},
|
| 1739 |
+
{
|
| 1740 |
+
"type": "text",
|
| 1741 |
+
"text": "Here we first show the test accuracy (ResNet19 on CIFAR100) of the membrane potential increment at each moment instead of the integrated membrane potential. We set the initial simulation length of the SNNs to 3 or 4 and trained them for a full 300 epochs. Then we expand their simulation length to 8. As shown in table 4, TET $( \\mathcal { L } _ { \\mathrm { T E T } } )$ makes the membrane potential increment at each moment have a higher classification ability than SDT $( \\mathcal { L } _ { \\mathrm { { S D T } } } )$ . And TET (1.41 and 0.08) also acquires a low accuracy variance than SDT (3.81 and 4.04). ",
|
| 1742 |
+
"bbox": [
|
| 1743 |
+
173,
|
| 1744 |
+
790,
|
| 1745 |
+
825,
|
| 1746 |
+
875
|
| 1747 |
+
],
|
| 1748 |
+
"page_idx": 13
|
| 1749 |
+
},
|
| 1750 |
+
{
|
| 1751 |
+
"type": "text",
|
| 1752 |
+
"text": "Then we compare the time scalability robustness between SDT $( \\mathcal { L } _ { \\mathrm { { S D T } } } )$ and TET $( \\mathcal { L } _ { \\mathrm { T E T } } )$ . We set the initial simulation length of ResNet19 SNNs to 2, 3, 4 and train with SDT or TET. Then we gradually increase SNN simulation length to 64 and record test accuracy of the integrated membrane potential. ",
|
| 1753 |
+
"bbox": [
|
| 1754 |
+
176,
|
| 1755 |
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|
| 1756 |
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|
| 1757 |
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|
| 1758 |
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],
|
| 1759 |
+
"page_idx": 13
|
| 1760 |
+
},
|
| 1761 |
+
{
|
| 1762 |
+
"type": "image",
|
| 1763 |
+
"img_path": "images/8be4907531399e22bedf40aaa0bdeff1ad93013af87033e52d12b9d582926cdd.jpg",
|
| 1764 |
+
"image_caption": [
|
| 1765 |
+
"Figure 8: The accuracy after increasing the simulation length. We first train the SNN with TET (only use $\\mathcal { L } _ { \\mathrm { T E T } } ,$ ) and SDT ${ ( \\mathcal { L } _ { \\mathrm { { S D T } } } ) }$ with simulation length (T) is 2, 3, or 4. Then, we increase the simulation to 64 without finetuning and record the test the classification accuracy (A) and the accuracy relative growth rate (B) of the total SNN output (integrate membrane potential) at each simulation time. "
|
| 1766 |
+
],
|
| 1767 |
+
"image_footnote": [],
|
| 1768 |
+
"bbox": [
|
| 1769 |
+
184,
|
| 1770 |
+
102,
|
| 1771 |
+
789,
|
| 1772 |
+
300
|
| 1773 |
+
],
|
| 1774 |
+
"page_idx": 14
|
| 1775 |
+
},
|
| 1776 |
+
{
|
| 1777 |
+
"type": "text",
|
| 1778 |
+
"text": "As we increase the simulation length, all the SNNs’ accuracy will first increase and then be stable in a certain area. Meanwhile, TET (1.80) has a small accuracy variance than the SDT (11.13) after increasing the simulation length. This phenomenon indicates that the initialization steps of TIT only need a small simulation length SNN for TET but a sufficiently large simulation (or enough epochs for finetuning step) for SDT. ",
|
| 1779 |
+
"bbox": [
|
| 1780 |
+
173,
|
| 1781 |
+
401,
|
| 1782 |
+
825,
|
| 1783 |
+
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|
| 1784 |
+
],
|
| 1785 |
+
"page_idx": 14
|
| 1786 |
+
},
|
| 1787 |
+
{
|
| 1788 |
+
"type": "table",
|
| 1789 |
+
"img_path": "images/52e3fc01f3ea8e2391bfd6f898f93f9ad9dfdc42e86e4f748550727f3448b45b.jpg",
|
| 1790 |
+
"table_caption": [
|
| 1791 |
+
"Table 4: Accuracy of each moment’s membrane potential increment. We use ${ \\mathcal { L } } _ { \\mathrm { S D T } }$ or ${ \\mathcal { L } } _ { \\mathrm { T E T } }$ to train the networks with simulation length 3 or 4. Then directly increase their simulation length to 8 and record each moment’s potential increment test accuracy. "
|
| 1792 |
+
],
|
| 1793 |
+
"table_footnote": [],
|
| 1794 |
+
"table_body": "<table><tr><td>Method</td><td>T=1</td><td>T=2</td><td>T=3</td><td>T=4</td><td>T=5</td><td>T=6</td><td>T=7</td><td>T=8</td></tr><tr><td>SDT (T=3)</td><td>55.61</td><td>57.95</td><td>56.87</td><td>55.09</td><td>57.56</td><td>53.54</td><td>57.72</td><td>54.04</td></tr><tr><td>SDT (T=4)</td><td>37.96</td><td>61.78</td><td>55.03</td><td>56.64</td><td>57.47</td><td>54.24</td><td>58.74</td><td>55.48</td></tr><tr><td>TET (T=3)</td><td>65.97</td><td>72.22</td><td>71.78</td><td>70.55</td><td>71.90</td><td>69.57</td><td>72.15</td><td>69.78</td></tr><tr><td>TET (T=4)</td><td>62.17</td><td>71.57</td><td>71.05</td><td>72.08</td><td>71.77</td><td>71.23</td><td>71.81</td><td>71.36</td></tr></table>",
|
| 1795 |
+
"bbox": [
|
| 1796 |
+
223,
|
| 1797 |
+
536,
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+
769,
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+
609
|
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+
],
|
| 1801 |
+
"page_idx": 14
|
| 1802 |
+
}
|
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+
]
|
parse/dev/_XNtisL32jv/_XNtisL32jv_middle.json
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parse/dev/lYNSvp51a7/lYNSvp51a7.md
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| 1 |
+
# Lift Yourself Up: Retrieval-augmented Text Generation with Self-Memory
|
| 2 |
+
|
| 3 |
+
Xin Cheng1 Di Luo2 Xiuying Chen3 Lemao Liu4 Dongyan Zhao1 Rui Yan2
|
| 4 |
+
|
| 5 |
+
1 Peking University 2 Remin University of China 3 KAUST 4 Tencent AI Lab chengxin1998@stu.pku.edu.cn
|
| 6 |
+
|
| 7 |
+
# Abstract
|
| 8 |
+
|
| 9 |
+
With direct access to human-written reference as memory, retrieval-augmented generation has achieved much progress in a wide range of text generation tasks. Since better memory would typically prompt better generation (we define this as primal problem). The traditional approach for memory retrieval involves selecting memory that exhibits the highest similarity to the input. However, this method is constrained by the quality of the fixed corpus from which memory is retrieved. In this paper, by exploring the duality of the primal problem: better generation also prompts better memory, we propose a novel framework, Selfmem, which addresses this limitation by iteratively employing a retrieval-augmented generator to create an unbounded memory pool and using a memory selector to choose one output as memory for the subsequent generation round. This enables the model to leverage its own output, referred to as self-memory, for improved generation. We evaluate the effectiveness of Selfmem on three distinct text generation tasks: neural machine translation, abstractive text summarization, and dialogue generation, under two generation paradigms: fine-tuned small model and few-shot LLM. Our approach achieves state-of-the-art results in four directions in JRC-Acquis translation dataset, 50.3 ROUGE-1 in XSum, and 62.9 ROUGE-1 in BigPatent, demonstrating the potential of self-memory in enhancing retrieval-augmented generation models. Furthermore, we conduct thorough analyses of each component in the Selfmem framework to identify current system bottlenecks and provide insights for future research1.
|
| 10 |
+
|
| 11 |
+
# 1 Introduction
|
| 12 |
+
|
| 13 |
+
In recent years, retrieval-augmented text generation has attracted growing interest across various fields, including neural machine translation[28, 17, 2], dialogue response generation[81, 6, 46], and language modeling[36, 77, 19]. This innovative generation paradigm initially equips a fine-tuned small model or a large language model (LLM) with access to an external database (typically the training corpus) using information retrieval techniques. Subsequently, the generation process is conducted based on both the input text and the retrieved memory.
|
| 14 |
+
|
| 15 |
+
In this paradigm, the guiding principle for memory retrieval is to find the memory that exhibits the highest similarity to the current input [36, 96, 49]. This aligns with the human intuition that a more similar demonstration sample typically offers more hints. As demonstrated in Figure 1, for a retrieval-augmented translation model, the memory similarity alone exhibits a strong correlation with the final translation quality, regardless of other factors that may influence translation quality (e.g., polysemy, morphology, and coreference). We define this as the primal problem: better memory prompts better generation. Consequently, numerous studies have focused on how to retrieve better memory, ranging from sparse retrieval to dense retrieval [10, 63], from a fixed retriever to a learnable retriever [41, 8], and from sentence-level memory to more fine-grained token-level memory [36, 35].
|
| 16 |
+
|
| 17 |
+
However, a fundamental limitation exists in all previous works: the memory is retrieved from a fixed corpus and is constrained by the corpus’s quality. Due to the finite retrieval space, bounded memory significantly restricts the potential of memory-augmented generation models [97]. In this paper, we explore the duality of the primal problem, which posits that better generation also prompts better memory. We propose a novel framework called Selfmem, which iteratively employs a retrieval-augmented generator to create an unbounded memory pool and uses a memory selector to choose one output as memory for the subsequent generation round. By combining the primal and dual problem, a retrievalaugmented generation model can elevate itself using its own output, referred to as self-memory. The key insight behind Selfmem is that the text more closely resembling the data distribution during inference is not the training data [87], but the model’s own output.
|
| 18 |
+
|
| 19 |
+
|
| 20 |
+
Figure 1: Relation between memory and hypothesis on JRC-Acquis E $_ { 1 \mathrm { D e } }$ dataset. The hypothesis is generated by a retrievalaugmented translator whose memory is retrieved from the training set. The $\mathbf { X }$ -axis represents the similarity between memory and the reference.
|
| 21 |
+
|
| 22 |
+
Selfmem consists of two complementary components:
|
| 23 |
+
|
| 24 |
+
a retrieval-augmented generator and a memory selector. The generator operates under two distinct paradigms: fine-tuning a small model or few-shot prompting an LLM. For the former, we train the generator with labeled data and retrieved memory, while for the latter, we employ a fixed black-box LLM exclusively for inference alongside retrieved in-context learning samples. We then use the generator’s output to train a memory selector based on a specific performance metric. By simply replacing the retrieved memory with unbounded generated memory, we achieve higher-quality generation output (primal problem), which subsequently serves as memory for the next round after being refined by the memory selector (dual problem).
|
| 25 |
+
|
| 26 |
+
To evaluate the efficacy of the Selfmem, we carry out comprehensive experiments in three distinct text generation tasks: neural machine translation, abstractive text summarization, and dialogue generation. We witness substantial enhancements over robust baselines, attaining state-of-the-art outcomes in JRC-Acquis (four directions), XSum (50.3 ROUGE-1), and BigPatent (62.9 ROUGE-1). To gain deeper insights into the Selfmem, we meticulously investigate each crucial component and pinpoint the existing system bottleneck to guide future research endeavors.
|
| 27 |
+
|
| 28 |
+
# 2 Related Work
|
| 29 |
+
|
| 30 |
+
# 2.1 Retrieval-augmented Text Generation
|
| 31 |
+
|
| 32 |
+
Since the world is not a snapshot once the training corpus is collected, we can never expect an ever-large model to capture everything in its parameters, even for LLMs like GPT-4 [62]. Therefore, it is crucial to equip these models with an external memory bank to store additional knowledge or useful demonstration examples for solving various NLP tasks[41, 78, 95].
|
| 33 |
+
|
| 34 |
+
In the translation domain, retrieval techniques have long been employed by the localization industry to enhance human translators’ productivity and consistency even before the advent of machine translation [94]. Early works on machine translation primarily focused on utilizing memory for statistical machine translation (SMT) systems [80, 50]. For neural machine translation (NMT), [28] were the first to use search engines to retrieve memory from the training set and incorporate it with an external memory network. Subsequent research explored various aspects of retrievalaugmented NMT, such as memory encoding methods [92, 93, 31], joint training of retrievers and generators with monolingual data [8], memory granularity [35], and memory diversity [17]. For few-shot LLM generation, strategies for in-context example selection have been proposed to improve translation quality [2]. Furthermore, in-context machine translation has been shown to be effective for on-the-fly adaptation [79]. For dialogue response generation tasks, employing exemplar/template retrieval as an intermediate step has proven advantageous for generating informative responses [89, 91, 6, 7]. In-context learning example retrieval also aids in controllable dialogue [46]. Other applications include abstractive summarization [64, 14, 18, 15], code generation [30], paraphrase generation [34, 83], language modeling [36, 105], counterfactual data generation [24], open domain question answering [12, 33] and semantic parsing [99].
|
| 35 |
+
|
| 36 |
+
# 2.2 Neural Text Reranking
|
| 37 |
+
|
| 38 |
+
By alleviating the discrepancy between training and inference (i.e., exposure bias) and directly optimizing desired metrics, two-stage reranking methods have facilitated significant progress in various text generation tasks. In machine translation, pioneering works by [75] and [61] introduced and popularized discriminative reranking for SMT. In the context of NMT, research has focused on two primary reranking approaches: generative reranking [56, 32, 88] and discriminative reranking [39, 71, 23]. For syntactic parsing, [21] were the first to employ a two-stage reranking method to select outputs from a base parser, while [11] introduced a maximum entropy reranker. In text summarization, RefSum [53] proposed a second-stage summarization framework to address train-test distribution mismatches. SimCLS [54] used pairwise Learning To Rank (LTR) to select candidates with the highest matching scores. SummaReranker [68] adopted a multi-task mixture-of-experts framework to leverage different metrics capturing various aspects of generated candidates. BRIO [55] reused the base model for a second round of fine-tuning with both cross-entropy loss and a candidate-level ranking loss. JGR [76] employed an alternate training paradigm to train the generator and reranker.
|
| 39 |
+
|
| 40 |
+
A key limitation of these reranking methods is that they only represent a one-way process, wherein the selected candidates become the system’s final output. In contrast, our framework innovatively utilizes the chosen candidates as memory for the subsequent generation round of a retrieval-augmented generator, which can produce better candidates with enhanced memory.
|
| 41 |
+
|
| 42 |
+
# 3 Methods
|
| 43 |
+
|
| 44 |
+
In this section, we begin with a motivating experiment on generation as memory $( \ S 3 . 1 )$ . Then, we introduce Selfmem, a framework comprising a retrieval-augmented generator $( \ S 3 . 2 )$ and a memory selector $( \ S \ 3 . 3 )$ . The complete framework and algorithm are illustrated in Figure 2 and Algorithm 1.
|
| 45 |
+
|
| 46 |
+
# 3.1 Generation as Memory
|
| 47 |
+
|
| 48 |
+
The primary motivation behind our framework stems from the observation that the memory, which is more similar in distribution to the data during inference, is not the training data (38.89 BLEU, as shown in the first row of Table 1). Instead, it is the model’s own output (58.58 BLEU) within the unbounded generation space. One interesting exploration involves directly utilizing the generated output as memory in relation to the primal problem: better memory prompts better generation.
|
| 49 |
+
|
| 50 |
+
We conduct experiments on the JRC-Acquis En De dataset. The first row in Table 1 represents conventional retrieval-augmented training with retrieved memory and achieves a 58.58 BLEU score. However, directly incorporating beam output of this trained model as memory (Beam) back into the generation model does not yield any improvements (row 2), despite its higher similarity to the reference compared to the retrieved ones. We hypothesize two potential reasons for this: (1) the retrieval-augmented generator may not generalize effectively in this context due to the
|
| 51 |
+
|
| 52 |
+
Table 1: Experiments on the relation between memory quality and the final hypothesis quality, measured by the BLEU score with ground truth translation. The retrieval-augmented translator keeps fixed while the memory is obtained from different sources.
|
| 53 |
+
|
| 54 |
+
<table><tr><td>Memory Source</td><td>Memory Quality</td><td>Hypothesis Quality</td></tr><tr><td>Retrieval</td><td>38.89</td><td>58.58</td></tr><tr><td>Beam</td><td>58.58</td><td>58.43</td></tr><tr><td>Reference</td><td>100</td><td>90.43</td></tr><tr><td>Random</td><td>1.14</td><td>49.08</td></tr></table>
|
| 55 |
+
|
| 56 |
+
memory distribution shift (from 38.89 to 58.58), and (2) the beam memory does not offer any information gain compared to the retrieved one, even it exhibits more overlap with the references.
|
| 57 |
+
|
| 58 |
+
To investigate the first hypothesis, we conduct experiments under the oracle and random scenarios by using the reference as memory (Reference) and randomly sampled sentences as memory (Random). The result is shown in Table 1 and it illustrates that a retrieval-augmented generator (trained with retrieved memory) has already learned to discriminate between different memories in both oracle and random scenarios, without updating the model weights.
|
| 59 |
+
|
| 60 |
+
|
| 61 |
+
Figure 2: Overall framework. There are two components in Selfmem, a retrieval-augmented generator (a) and a memory selector (b). For the primal problem, (a) takes source and memory as input to generate candidates for (b). For the dual problem, (b) takes as input source and generated candidates to select memory for (a).
|
| 62 |
+
|
| 63 |
+
To evaluate the second conjecture, we first define the token sets of the reference, retrieved memory, and beam memory as $\mathcal { R } , \mathcal { M }$ , and $\boldsymbol { B }$ , respectively. The overlap token set, denoted by $\mathcal { O }$ , is defined as the tokens that overlap with the references in the beam memory but not in the retrieved memory, which is represented as $\mathcal { R } \cap \mathcal { B } - \mathcal { R } \cap \mathcal { M } .$ $\mathcal { O }$ is considered as the additional information provided by the beam memory. Inspired by the confidence analysis of NMT model [58], we compute the set confidence score, $\psi ( \cdot )$ , as follows:
|
| 64 |
+
|
| 65 |
+
$$
|
| 66 |
+
\psi ( \cdot ) = { \frac { 1 } { | \cdot | } } \sum _ { y ^ { i } \in \cdot } p ( y _ { i } | x , y _ { < i } )
|
| 67 |
+
$$
|
| 68 |
+
|
| 69 |
+
where $p ( y _ { i } | x , y _ { < i } )$ is defined by the generation model. $\psi ( \cdot )$ measures the confidence with which the generation model generates the tokens. The value of $\psi ( \mathcal { R } )$ is 0.58, while that of $\mathcal { O }$ is 0.76, indicating that the generator is relatively confident in generating tokens in $\mathcal { O }$ , and therefore does not need to resort to external memory [38]. Beam search ranks generated candidates based on $p ( y | x )$ , where the selected memory falls within the confidence region of the generator and consequently provides no information gain. This observation motivates us to select memory according to metrics other than $p ( y | x )$ in the memory selector (§3.3).
|
| 70 |
+
|
| 71 |
+
# 3.2 Retrieval-augmented Generator
|
| 72 |
+
|
| 73 |
+
Given a text pair $( x , y )$ , where $x = \{ \mathbf { x } _ { 1 } , . . . , \mathbf { x } _ { | x | } \}$ is the source, $y = \{ \mathbf { y } _ { 1 } , . . . , \mathbf { y } _ { | y | } \}$ is the target. They could be (document, summary) in summarization, (context, response) in dialogue generation or (source, target) in machine translation. The retrieval-augmented generation would first use $x$ to retrieve memory $m$ from datastore $\mathbb { D }$ . Then the generator $G _ { \xi } ( x , m )$ , parameterized by $\xi$ , would take both $x$ and $m$ as input to generate the target sentence $y$ . In this paper, following standard practice, we choose the training set as $\mathbb { D } = \{ ( x ^ { i } , y ^ { i } ) \} _ { i = 1 } ^ { | \mathbb { D } | }$ . For LLM as $G _ { \xi }$ , we use the standard in-context learning format to give $( x , y )$ as demonstration example. For tunable generator $G _ { \xi }$ , we only keep the target side of top- $\mathbf { \xi } _ { l }$ retrieval results as memory and we consider two commonly used architectures: Joint-Encoder [29, 87, 41] and Dual-Encoder [92, 8, 17].
|
| 74 |
+
|
| 75 |
+
Joint-Encoder This architecture is the standard encoder-decoder-based model [3, 84]. The input is the concatenation of $x$ and $m$ . The encoder would first map the input into the hidden states $H$ :
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+
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+
$$
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H = { \mathrm { E n c o d e r } } ( x \ [ { \mathrm { S E P } } ] \ m )
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$$
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+
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And the decoder would incorporate $H$ by attention mechanism and generate tokens in an autoregressive manner:
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+
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$$
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h ^ { i } = \mathrm { D e c o d e r } ( \mathrm { C r o s s A t t n } ( H ) , y _ { < i } ) \quad P _ { G _ { \xi } } ( \cdot | x , y _ { < i } ) = \mathrm { S o f t m a x } ( h ^ { i } )
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+
$$
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+
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Dual-Encoder Instead of treating $x$ and $m$ as a long sequence, this architecture has two encoders, one for $x$ and the other for $m$ . Their outputs are sequentially attended by the decoder with dual cross attention as in [17]:
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+
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$$
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\begin{array} { c } { H _ { x } = \mathrm { S o u r c e E n c o d e r } ( x ) \quad H _ { m } = \mathrm { M e m o r y E n c o d e r } ( m ) } \\ { h ^ { i } = \mathrm { D e c o d e r } ( \mathrm { C r o s s A t t n } ( H _ { x } , H _ { m } ) , y _ { < i } ) } \end{array}
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$$
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We use Transformer [84] as the building block for both architectures and optimize $G _ { \xi }$ with NLL loss:
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$$
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\mathcal { L } _ { \mathrm { n l l } } = - \sum _ { t = 1 } ^ { | y | } \log P _ { G _ { \xi } } ( y _ { t } | x , m , y _ { < t } )
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$$
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# 3.3 Memory Selector
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The role of memory selector $S _ { \theta } ( x , c )$ , parameterized by $\theta$ , is to select one candidate $c$ from the candidate pool $\mathbb { C }$ generated by $G _ { \xi }$ based on a specific metric $\Delta ( \cdot , \cdot )$ . The chosen candidate $c$ is then utilized as memory $m$ for the subsequent generation round of $G _ { \xi }$ . As discussed in $\ S 3 . 1$ , using $p _ { G _ { \xi } } ( y | x )$ as the metric $\Delta ( \cdot , \cdot )$ would result in falling into the confidence region of $G _ { \xi }$ , leading to no information gain. Moreover, a larger value of $p _ { G _ { \xi } } ( y | x )$ does not necessarily guarantee improved generation quality [59]. Consequently, we define $\Delta ( \cdot , \cdot )$ as model-free metrics that are widely employed for assessing generation quality, such as BLEU for Neural Machine Translation (NMT) and ROUGE for Summarization. Our memory selector takes the concatenation of the source $x$ and candidate $c _ { i }$ as input, and produces a multinomial distribution $p _ { S _ { \theta } } ( \cdot | x )$ over $\mathbb { C }$ .
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In this paper, we focus on the role of the memory selector, $S _ { \theta } ( x , c )$ , which is parameterized by $\theta$ . The objective of this selector is to choose a single candidate $c$ from the candidate pool $\mathbb { C }$ , generated by $G _ { \xi }$ , based on a specific metric, $\Delta ( \cdot , \cdot )$ .
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$$
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p _ { S _ { \theta } } ( c _ { i } | x ) = \frac { \exp ( S _ { \theta } ( x \left[ \mathrm { S E P } \right] c _ { i } ) ) } { \sum _ { j = 1 } ^ { | \mathbb { C } | } \exp ( S _ { \theta } ( x \left[ \mathrm { S E P } \right] c _ { j } ) ) }
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$$
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In accordance with [39], the training goal for $S _ { \theta }$ is to minimize the discrepancy between the $S _ { \theta }$ ’s predictions and the scores determined by $\Delta ( \cdot , \cdot )$ . This divergence is quantified using the KullbackLeibler (KL) divergence.
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$$
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\mathcal { L } _ { \mathrm { k l } } = - \sum _ { i = 1 } ^ { | \mathbb { C } | } p _ { M } ( c _ { i } ) \mathrm { l o g } p _ { S _ { \theta } } ( c _ { i } | x ) \quad \mathrm { w h e r e } \quad p _ { M } ( c _ { i } ) = \frac { \exp ( \Delta ( c _ { i } , y ) / \tau ) } { \sum _ { j = 1 } ^ { | \mathbb { C } | } \exp ( \Delta ( c _ { j } , y ) / \tau ) }
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$$
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$\tau$ is the temperature to control the smoothness of the distribution. At inference, the output of the $S _ { \theta }$ is a $\operatorname { r g m a x } _ { c _ { i } \in \mathbb { C } } { \dot { p } } _ { S _ { \theta } } ( c _ { i } | x )$ .
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# 3.4 Combine Generator and Selector
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We define two generation modes for $G _ { \xi }$ . The first mode, referred to as the hypothesis mode, generates a single output for each input, which is utilized for system evaluation. The second mode, known as the candidate mode, produces $_ \mathrm { N }$ outputs for a given input, and is employed for training $S _ { \theta }$ as well as memory selection. By integrating two modes together, we present the complete framework of our proposed model, Selfmem, as illustrated in Algorithm 1.
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# 4 Experimental Setup
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# 4.1 Dataset
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We assess the performance of Selfmem on three generation tasks, utilizing a total of seven datasets. Translation. We evaluate our framework on JRC-Acquis datasets [82], a collection of parallel
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Require: a dataset $\mathbb { D }$ , a retriever $R$ , a memory selection metric $\Delta ( \cdot , \cdot )$ , a retrieval-augmented
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generator $G _ { \xi }$ , and a memory selector $S _ { \theta }$
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1: retrieve memory $\mathbb { M }$ in $\mathbb { D }$ with $R$
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2: train $G _ { \xi }$ with $\mathbb { D }$ and $\mathbb { M }$ (if not LLM)
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3: use $G _ { \xi }$ to generate candidate pool $\mathbb { C }$ with $\mathbb { M }$ in candidate mode
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4: train ${ \check { S } } _ { \theta }$ on $\mathbb { C }$ with $\Delta ( \cdot , \cdot )$
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5: while not converged in the validation set do
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6: $S _ { \theta }$ selects memory from $\mathbb { C }$ as $\mathbb { M }$
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7: $G _ { \xi }$ generates candidate pool $\mathbb { C }$ with $\mathbb { M }$ in candidate mode
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8: end while
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9: $G _ { \xi }$ generates the final hypothesis with $\mathbb { M }$ in hypothesis mode
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legislative text of European Union Law. It is the benchmark dataset used in translation memoryaugmented NMT task [28, 92, 8, 17]. We choose 4 translation directions, namely, Spanish English $( { \mathrm { E s } } { \mathrm { E n } } )$ , German English $( \mathrm { D e } \mathrm { E n } $ ). Summarization. We evaluate on 2 summarization datasets: 1) XSum [60], extreme summarization, a single-document summarization dataset with highly abstractive articles from British Broadcasting Corporation. 2) BigPatent [73], consisting of 1.3 million records of U.S. patent documents along with human-written abstractive summaries. Dialogue. We experiment on DailyDialog [44], which contains multi-turn dialogs on daily life topics and is used by [13, 4, 103]. The detailed statistics for these datasets can be found in the Appendix A.
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# 4.2 Implementation Details
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We utilize the BM25 algorithm [70] for retrieval purposes. For all tasks, the candidate generation method consists of beam search with a beam width of 50. The number of iterations is determined by the performance on the validation set. For translation, we follow the approach of [93, 8, 17], employing a randomly initialized Transformerbase architecture as $G _ { \xi }$ for trainable small model and XGLM [48] for LLM in-context learning. Evaluation metrics include BLEU, TER, and ${ \mathrm { c h r F } } + +$ obtained from SACREBLEU[66]. The memory selector $S _ { \theta }$ utilizes an XLM- ${ \bf R } _ { b a s e }$ [22] as backbone, with BLEU serving as $\Delta ( \cdot , \cdot )$ . For summarization, we initialize $G _ { \xi }$ with $\mathrm { B A R T _ { b a s e } } [ 4 0 ]$ for BigPatent and employ BRIO [55] for XSum. The evaluation metric comprises ROUGE (R1/2/L) [47]. For dialogue generation, $\mathbf { B A R T _ { b a s e } }$ serves as the backbone for $G _ { \xi }$ . Our dialogue system is evaluated using BLEU (B-1/2) and Distinct (D-1/2) scores [43]. For both dialogue and summarization tasks, we adhere to the methods of [54, 26], adopting $\mathrm { R o B E R T a _ { b a s e } }$ [52] as the backbone for $S _ { \theta }$ The linear combination of $_ { \mathrm { B - } 1 / 2 }$ is chosen as $\Delta ( \cdot , \cdot )$ for Dialogue Generation, while $\mathrm { \mathbf { R } } \mathrm { - } 1 / 2 / \mathrm { L }$ is used for Summarization, following [76]. For further implementation details, please refer to the Appendix B and Appendix C for evaluation metrics.
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# 5 Experimental Results
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# 5.1 Machine Translation
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We select four translation directions and experiment with two generation paradigms: trainable small models and few-shot prompted LLMs [85, 20]. For trainable models, we explore two architectures (joint and dual, as detailed in $\ S 3 . 2 \AA$ . The baselines comprise two types of translation systems: one being the vanilla sequence-to-sequence model [3, 84] without memory augmentation, and the other consisting of retrieval-augmented translation models focusing on memory encoding [28, 92], memory construction [101], memory retrieval [8], and memory diversity [17]. Based on the experimental results2 shown in Table 2, Selfmem significantly enhances the performance of $G _ { \xi }$ across four translation datasets and two different architectures. This is noteworthy, given that the parameters of the $G _ { \xi }$ remain fixed, with the only variable being the input memory. This finding is consistent with the primal problem which posits that improved memory typically leads to better generation results.
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Table 2: Results of translation task on JRC-Acquis measured by BLEU. Models denoted by the same symbol $\times$ and $\dagger .$ ) have the same parameters and only differ in memory as input. The bolded numbers show the SOTA performance and the underlined numbers show the second-best result. $^ *$ denotes the system is significantly better than baselines with $p$ -value $< 0 . 0 5$ tested by [37].
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<table><tr><td rowspan="2">System</td><td colspan="2">Es-→En</td><td colspan="2">En→Es</td><td colspan="2">De-→En</td><td colspan="2">En→De</td></tr><tr><td>Dev</td><td>Test</td><td>Dev</td><td>Test</td><td>Dev</td><td>Test</td><td>Dev</td><td>Test</td></tr><tr><td colspan="9">None Memory</td></tr><tr><td>RNNsearch [3]</td><td>55.02</td><td>59.34</td><td>50.54</td><td>50.48</td><td>50.20</td><td>49.74</td><td>44.94</td><td>43.98</td></tr><tr><td>Transformer [84]</td><td>64.08</td><td>64.63</td><td>62.02</td><td>61.80</td><td>60.18</td><td>60.16</td><td>54.65</td><td>55.43</td></tr><tr><td colspan="9">Retrieval Memory</td></tr><tr><td>SEG-NMT[28]</td><td>60.28</td><td>59.34</td><td>57.62</td><td>57.27</td><td>55.63</td><td>55.33</td><td>49.26</td><td>48.80</td></tr><tr><td>NMT-pieces [101]</td><td>63.97</td><td>64.30</td><td>61.50</td><td>61.56</td><td>60.10</td><td>60.26</td><td>55.54</td><td>55.14</td></tr><tr><td>G-TFM [92]</td><td>66.37</td><td>66.21</td><td>62.50</td><td>62.76</td><td>61.85</td><td>61.72</td><td>57.43</td><td>56.88</td></tr><tr><td>MonoNMT[8]</td><td>67.73</td><td>67.42</td><td>64.18</td><td>63.86</td><td>64.48</td><td>64.62</td><td>58.77</td><td>58.42</td></tr><tr><td>CMM[17]</td><td>67.48</td><td>67.76</td><td>63.84</td><td>64.04</td><td>64.22</td><td>64.33</td><td>58.94</td><td>58.69</td></tr><tr><td>Transformerdual*</td><td>66.87</td><td>67.12</td><td>63.14</td><td>63.54</td><td>64.09</td><td>63.36</td><td>58.69</td><td>58.06</td></tr><tr><td>Transformerunit</td><td>67.74</td><td>67.32</td><td>63.93</td><td>64.12</td><td>64.50</td><td>64.40</td><td>58.16</td><td>58.58</td></tr><tr><td colspan="9">Self-Memory</td></tr><tr><td>Transformerdual*</td><td>68.63*</td><td>69.20*</td><td>64.12*</td><td>64.67*</td><td>65.06*</td><td>64.98*</td><td>59.26*</td><td>59.49*</td></tr><tr><td>Transformerunit</td><td>68.26*</td><td>68.80*</td><td>66.07*</td><td>65.94*</td><td>65.32*</td><td>65.65*</td><td>59.88*</td><td>60.11*</td></tr></table>
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+
|
| 155 |
+
Table 3: Comparison between retrieval memory and self-memory. The quality of memory and hypothesis is measured by the n-gram overlap with reference (BLEU). All experiments are conducted with Transforme $\mathbf { \dot { j } } \mathbf { o } \mathbf { \dot { i } } \mathbf { n } \mathbf { t }$ on JRC-Acquis.
|
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+
|
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+
<table><tr><td rowspan="2"></td><td colspan="2">Retrieval</td><td colspan="2">Self</td></tr><tr><td>memory</td><td>hypothesis</td><td> memory</td><td>hypothesis</td></tr><tr><td rowspan="2">En-De</td><td>→</td><td>38.89</td><td>58.58</td><td>57.92</td><td>60.11</td></tr><tr><td>↑</td><td>42.56</td><td>64.40</td><td>64.32</td><td>65.65</td></tr><tr><td rowspan="2">En-Es</td><td>→</td><td>40.67</td><td>64.12</td><td>63.57</td><td>65.94</td></tr><tr><td>↑</td><td>43.05</td><td>67.32</td><td>67.78</td><td>68.80</td></tr></table>
|
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+
|
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The dual problem is revealed in Table 3. Self-memory, which essentially represents the model’s own output, exhibits greater similarity with the ground truth and serves as a more effective memory for generating the final output. This observation highlights a key distinction between Selfmem and previous reranking works [39, 68]. Reranking aims to select candidates of higher quality than the beam output, whereas in Selfmem, the chosen candidates serve as memory for the retrieval-augmented generator and do not necessarily need to surpass the quality of the beam hypotheses.
|
| 160 |
+
|
| 161 |
+
Table 4: Evaluation results of in-context learning with self-memory.
|
| 162 |
+
|
| 163 |
+
<table><tr><td rowspan="2" colspan="2"></td><td colspan="3">XGLM-1.7B</td><td colspan="3">XGLM-4.5B</td><td colspan="3">XGLM-7.5B</td></tr><tr><td>Random</td><td>kNN</td><td>Self</td><td>Random</td><td>kNN</td><td>Self</td><td>Random</td><td>kNN</td><td>Self</td></tr><tr><td rowspan="2">En-De</td><td>↑</td><td>11.51</td><td>37.87</td><td>40.94</td><td>17.51</td><td>37.60</td><td>38.25</td><td>18.48</td><td>47.82</td><td>48.32</td></tr><tr><td></td><td>27.42</td><td>51.00</td><td>51.88</td><td>30.62</td><td>48.12</td><td>48.36</td><td>33.03</td><td>55.65</td><td>55.12</td></tr><tr><td rowspan="2">En-Es</td><td>→</td><td>23.87</td><td>46.20</td><td>48.56</td><td>31.83</td><td>48.37</td><td>49.17</td><td>29.97</td><td>53.86</td><td>54.32</td></tr><tr><td>↑</td><td>25.29</td><td>51.55</td><td>53.13</td><td>32.16</td><td>48.55</td><td>49.22</td><td>35.22</td><td>57.25</td><td>57.56</td></tr></table>
|
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|
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+
In Table 4, we present the results of LLM with self-memory. We employ XGLM [48] as our backbone generator, with three different sizes ranging from 1.7B to 7.5B. We utilize the recommended prompt as described in [48]. We select three in-context learning examples and report the average scores from three separate runs, taking into account the sensitivity of example selection in ICL [49]. From the table, we first observe a general trend where few-shot translation performance improves as the size of the model increases. Furthermore, we find that more similar translation demonstrations significantly enhance performance across all model sizes (from random, kNN to Self). This suggests that demonstration examples in in-context learning not only act as triggers for model ability but also adhere to the primal problem, where better demonstration example leads to better generation. Also, by comparing the results in Table 2 and Table 4, we can conclude that the cross-lingual LLM with designed examples still falls short of the supervised baselines in this task.
|
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|
| 167 |
+
# 5.2 Summarization
|
| 168 |
+
|
| 169 |
+
In this paper, we compare the performance of our trainable model with those of REINA [87], PEGASUS [100], and BART [40]. The results are presented in Table5. Initially, it can be observed that memory has varying impacts on different datasets. The enhancement brought by memory in the BigPatent dataset is significantly larger than that in the XSum dataset. This can be attributed to the inherent characteristics of the BigPatent dataset, which consists of official patent documents that exhibit considerable similarity. Consequently, this greatly improves the summarization quality in accordance with the primal problem. Furthermore, we discovered that self-memory substantially enhances the performance of both BRIO $( + 1 . 2 { \ R } 1 )$ and BART $( + 1 8 . 5 \mathrm { R } 1 ) $ ), achieving state-of-the-art results on both datasets. We selected these baselines for a fair comparison, as they share the same base generator. Due to space constraints, additional comparisons and the confidence region of the SOTA model can be found in the Appendix E.
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+
Table 5: Results of summarization task on XSum and BigPatent measured by ROUGE.
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<table><tr><td>System</td><td>Memory</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td></td><td>XSum</td><td></td><td></td><td></td></tr><tr><td>PEGASUS</td><td>None</td><td>47.2</td><td>24.6</td><td>39.3</td></tr><tr><td>BRIO</td><td>None</td><td>49.1</td><td>25.6</td><td>40.4</td></tr><tr><td>REINA (PG)</td><td>Retrieval</td><td>48.2</td><td>26.0</td><td>40.2</td></tr><tr><td>REINA (B)</td><td>Retrieval</td><td>43.2</td><td>21.0</td><td>35.5</td></tr><tr><td>REINA (L)</td><td>Retrieval</td><td>46.5</td><td>24.1</td><td>38.6</td></tr><tr><td>BRIOdual*</td><td>Retrieval</td><td>48.6</td><td>26.1</td><td>40.6</td></tr><tr><td>BRIOjoint</td><td>Retrieval</td><td>49.5</td><td>26.5</td><td>41.2</td></tr><tr><td>BRIOdual*</td><td>Self</td><td>49.2</td><td>26.2</td><td>40.8</td></tr><tr><td>BRIOjointt</td><td>Self</td><td>50.3</td><td>26.7</td><td>41.6</td></tr></table>
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<table><tr><td>System</td><td>Memory</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td></td><td>BigPatent</td><td></td><td></td><td></td></tr><tr><td>PEGASUS</td><td>None</td><td>53.6</td><td>33.2</td><td>43.2</td></tr><tr><td>BART</td><td>None</td><td>44.4</td><td>21.3</td><td>31.0</td></tr><tr><td>REINA (B)</td><td>Retrieval</td><td>59.5</td><td>42.6</td><td>50.6</td></tr><tr><td>REINA (L)</td><td>Retrieval</td><td>60.7</td><td>43.3</td><td>51.3</td></tr><tr><td>REINA (PG)</td><td>Retrieval</td><td>44.6</td><td>21.5</td><td>33.3</td></tr><tr><td>BARTdual*</td><td>Retrieval</td><td>57.4</td><td>43.3</td><td>49.7</td></tr><tr><td>BARTjointt</td><td>Retrieval</td><td>59.6</td><td>43.4</td><td>51.0</td></tr><tr><td>BARTdual*</td><td>Self</td><td>61.2</td><td>44.6</td><td>52.3</td></tr><tr><td>BARTjoint</td><td>Self</td><td>62.9</td><td>48.1</td><td>59.6</td></tr></table>
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+
# 5.3 Dialogue Generation
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| 178 |
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As demonstrated in Table 6, the self-memory significantly enhances the performance of the retrievalaugmented generator for dialogue generation tasks. By optimizing memory using BLEU as $\Delta ( \cdot , \cdot )$ , the self-memory improves the B-1,2 score over retrieved memory by $3 . 0 8 \ \mathrm { B } \cdot 1$ and $0 . 6 \ \mathbf { B } { - } 2$ on $\mathbf { B A R T _ { j o i n t } }$ . Intriguingly, although Selfmem surpasses the baselines in terms of $_ { \mathrm { B - } 1 / 2 }$ , it falls behind in D-1 and D-2, which can be attributed to the trade-off between BLEU score and Distinct score when evaluating a dialogue system [104]. To address this issue, we opt for D-1,2 as $\Delta ( \cdot , \cdot )$ when optimizing $S _ { \theta }$ , denoted as $\mathbf { B A R T } _ { \mathrm { j o i n t } } \dagger ( \mathbf { D } )$ . The results in Table 6 highlight the remarkable flexibility of Selfmem by directly optimizing memory to achieve the desired attributes for diverse and informative dialogue.
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+
# 6 Further Analysis
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| 183 |
+
To gain a deeper insight into Selfmem, we first examine the impact of each key component, namely $G _ { \xi }$ and $S _ { \theta }$ . Subsequently, we perform a detailed token-level analysis of the generated output concerning their frequency in the training set. Experiments are conducted on the JRC-Acquis En De dataset. We also include latency analysis and human evaluation on Appendix F and G.
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+
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Tuning $S _ { \theta }$ We explored various $S _ { \theta }$ by direct selection from the candidate pool based on gold rankings. As shown in Figure 3a, both architectures with enhanced $S _ { \theta }$ significantly outperform the current SOTA performance (60.11 BLEU). Moreover, we assessed the candidate pool quality during this iterative process using an oracle $S _ { \theta }$ , as displayed in Figure 3b. A clear pattern emerges in this boxplot, revealing improvements in the oracle, quartile, average, and minimum scores of the candidate pool. These two experiments jointly clarify the Selfmem’s underlying intuition: a retrieval-augmented generator profits from superior memory, which can be chosen from its own unbounded output, and subsequently, the generator with improved memory produces a higher-quality candidate pool for the next selection round. Consequently, the model lift itself up.
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Table 6: Results of dialogue generation task on DailyDialog measured by B-1/2 and D-1/2. $\mathbf { B A R T _ { j o i n t } }$ (D) denotes the metric $\Delta ( \cdot , \cdot )$ for $S _ { \theta }$ is the average of D-1 and D-2.
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<table><tr><td>System</td><td>Memory</td><td>B-1</td><td>B-2</td><td>D-1</td><td>D-2</td></tr><tr><td>NCM [86]</td><td>None</td><td>33.60</td><td>26.80</td><td>3.00</td><td>12.80</td></tr><tr><td>iVAE [25]</td><td>None</td><td>30.90</td><td>24.90</td><td>2.90</td><td>25.00</td></tr><tr><td>PLATO-2 [5]</td><td>None</td><td>34.80</td><td>25.12</td><td>3.54</td><td>25.11</td></tr><tr><td>DialoFlow [45]</td><td>None</td><td>36.17</td><td>27.67</td><td>4.56</td><td>27.12</td></tr><tr><td>BART</td><td>None</td><td>20.72</td><td>11.36</td><td>3.92</td><td>19.44</td></tr><tr><td>BARTdual*</td><td>Retrieval</td><td>29.50</td><td>21.89</td><td>4.74</td><td>26.01</td></tr><tr><td>BARTjointt</td><td>Retrieval</td><td>36.72</td><td>31.55</td><td>6.13</td><td>35.65</td></tr><tr><td>BARTdual*</td><td>Self</td><td>33.43</td><td>22.85</td><td>4.66</td><td>26.16</td></tr><tr><td>BARTjoint</td><td>Self</td><td>39.80</td><td>32.15</td><td>5.84</td><td>32.16</td></tr><tr><td>BARTjoint † (D)</td><td>Self</td><td>36.92</td><td>32.09</td><td>9.12</td><td>37.05</td></tr></table>
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Figure 3: (a) shows generation quality in the iteration process with different $S _ { \theta }$ in both trainable generator architectures. (b) shows candidates quality in the iteration process with an oracle $S _ { \theta }$ .
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Tuning $G _ { \xi }$ As discussed in $\ S 3 . 1$ , we demonstrated that a trained retrieval-augmented generator, with fixed parameters, possesses the ability to distinguish between "good" and "bad" memory. This observation not only justifies our decision to maintain a fixed generator within our framework but also implies that the $G _ { \xi }$ is not the current bottleneck of the Selfmem.
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Figure 4: 1-gram F1 score sorted by training corpus frequency.
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Frequency Analysis We conduct a comprehensive tokenlevel analysis by computing the 1-gram F1 scores for generated translations and subsequently categorizing the tokens based on their frequency in the training set. The results are depicted in Figure 4. A noticeable pattern emerges, suggesting that the more frequently a model encounters a token during training, the higher the accuracy of the generated output [102]. Moreover, our findings indicate that retrievalaugmented models, particularly those incorporating self-memory augmentation, exhibit superio performance in handling long-tail inputs which are challenges for parametric models [67, 57].
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# 7 Conclusion
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For the first time, we investigate the fundamental limitation of bounded memory in the current retrieval-augmented literature. We combine the primal and dual problems together and propose Selfmem, a general framework for retrieval-augmented text generation by uplifting generation model with its own output. We conduct comprehensive experiments across various text generation tasks and different generation paradigms, including trainable small model and few-shot prompted LLM. We surpass strong baselines and improve the state-of-the-art performance in serval datasets. We also meticulously investigate each crucial component and pinpoint the existing system bottleneck to guide future research endeavors.
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# Limitations
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We discuss the limitations of our framework as follows:
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(1) Although Selfmem greatly improves the generation quality compared with other retrievalaugmented generation models, it requires more computational resources with respect to the memory selection process. For large dataset with long context (e.g., BigPatent), it would become a more crucial problem considering the quadratic time complexity of transformer architecture.
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(2) This paper proposes a general idea for the retrieval-augmented generation. But we only experiment with transformer-based architecture for both generator and memory selector and the architecture of generator and memory selector keeps the same across all text generation tasks. We believe the task-specific design for the model architecture, training objective and generation methods in different text generation scenarios would further improve the performance.
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# Acknowledgement
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This work was supported by the National Key Research and Development Program of China (No.2021YFC3340304) and National Natural Science Foundation of China (NSFC Grant No.62122089). We appreciate the anonymous reviewers for their helpful comments. Dongyan Zhao and Rui Yan are the corresponding authors.
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[96] Dani Yogatama, Cyprien de Masson d’Autume, and Lingpeng Kong. Adaptive semiparametric language models. Trans. Assoc. Comput. Linguistics, 2021.
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+
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[97] Wenhao Yu, Dan Iter, Shuohang Wang, Yichong Xu, Mingxuan Ju, Soumya Sanyal, Chenguang Zhu, Michael Zeng, and Meng Jiang. Generate rather than retrieve: Large language models are strong context generators, 2023.
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[98] Manzil Zaheer, Guru Guruganesh, Kumar Avinava Dubey, Joshua Ainslie, Chris Alberti, Santiago Ontanon, Philip Pham, Anirudh Ravula, Qifan Wang, Li Yang, and Amr Ahmed. Big bird: Transformers for longer sequences. In Proc. of NeurIPS, 2020.
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+
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[99] Yury Zemlyanskiy, Michiel de Jong, Joshua Ainslie, Panupong Pasupat, Peter Shaw, Linlu Qiu, Sumit Sanghai, and Fei Sha. Generate-and-retrieve: Use your predictions to improve retrieval for semantic parsing. In Proceedings of the 29th International Conference on Computational Linguistics, pages 4946–4951, Gyeongju, Republic of Korea, October 2022. International Committee on Computational Linguistics.
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+
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[100] Jingqing Zhang, Yao Zhao, Mohammad Saleh, and Peter J. Liu. PEGASUS: pre-training with extracted gap-sentences for abstractive summarization. In Proc. of ICML, 2020.
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+
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[101] Jingyi Zhang, Masao Utiyama, Eiichiro Sumita, Graham Neubig, and Satoshi Nakamura. Guiding neural machine translation with retrieved translation pieces. In Proc. of NAACL, 2018.
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[102] Tong Zhang, Wei Ye, Baosong Yang, Long Zhang, Xingzhang Ren, Dayiheng Liu, Jinan Sun, Shikun Zhang, Haibo Zhang, and Wen Zhao. Frequency-aware contrastive learning for neural machine translation. In Proc. of AAAI, 2022.
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+
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[103] Xueliang Zhao, Lemao Liu, Tingchen Fu, Shuming Shi, Dongyan Zhao, and Rui Yan. Towards efficient dialogue pre-training with transferable and interpretable latent structure. CoRR, 2022.
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+
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[104] Yinhe Zheng, Zikai Chen, Rongsheng Zhang, Shilei Huang, Xiaoxi Mao, and Minlie Huang. Stylized dialogue response generation using stylized unpaired texts. In Proc. of AAAI, 2021.
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+
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[105] Zexuan Zhong, Tao Lei, and Danqi Chen. Training language models with memory augmentation. CoRR, 2022.
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+
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+
# A Dataset Details
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+
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+
Table 7: Dataset statistics for three tasks.
|
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+
|
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+
<table><tr><td>Task</td><td>Dataset</td><td>#Train</td><td>#Dev</td><td>#Test</td></tr><tr><td rowspan="2">Translation</td><td>JRC (en ←→ de)</td><td>663,487</td><td>2,454</td><td>2,483</td></tr><tr><td>JRC (en ←→ es)</td><td>653,127</td><td>2,533</td><td>2,596</td></tr><tr><td rowspan="2">Summarization</td><td>BigPatent</td><td>1,207,222</td><td>67,068</td><td>67,072</td></tr><tr><td>XSum</td><td>204,045</td><td>11,332</td><td>11,334</td></tr><tr><td>Dialogue</td><td>DailyDialog</td><td>87,170</td><td>8,069</td><td>7,740</td></tr></table>
|
| 358 |
+
|
| 359 |
+
# B Self Memory Details
|
| 360 |
+
|
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+
For machine translation tasks, following [93, 8, 17] we use randomly initialize Transformerbase architecture [84] as $G _ { \xi }$ . We use the joint-bpe algorithm [72] and share the parameters between the memory encoder and source encoder for dual encoder architecture. The hyper-parameter setting follows [17] with dropout 0.1, label smoothing 0.1, gradient clipping 1.0, Adafactor [74], warm-up steps 4000, maximum learning rate $4 . 4 \mathrm { e } { - 2 }$ and training epochs 30 for total. The evaluation metrics are BLEU, TER and ${ \mathrm { c h r F } } + +$ from SACREBLEU [66]. The backbone of memory selector $S _ { \theta }$ is XLM- $. { \bf R } _ { b a s e }$ [22] with BLEU as $\Delta ( \cdot , \cdot )$ . The hyper-parameter setting for $S _ { \theta }$ follows [39] with $\tau 0 . 5$ , minmax normalization for candidates ranking, Adam optimizer with max learning rate 5e-5 and polynomial decay scheduler, and classifier dropout 0.2.
|
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+
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+
For Summarization, we init the $G _ { \xi }$ with $\mathbf { B A R T _ { b a s e } }$ [40] for BigPatent following [87] and state-of-theart BRIO [55] for XSum. Optimization is based on Adafactor with a maximum learning rate of 5e-3, warm-up steps 10000 and gradient clipping value 1.0. The maximum input length is 512 for XSum and 1024 for BigPatent. The evaluation metric is Rouge (R-1/2/L) [47].
|
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+
|
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+
For Dialogue Generation, we use $\mathbf { B A R T _ { b a s e } }$ as the backbone for $G _ { \xi }$ on DailyDialog. We tune the hyper-parameters from learning rate $\{ 5 \mathrm { e } { - } 3 , 1 \mathrm { e } { - } 3 , 4 \mathrm { e } { - } 4 \}$ and set dropout 0.1, batch size 64, label smoothing factor 0.1, maximum input length 120 for DailyDialog. Following [4, 13], we evaluate our dialogue system with BLEU (B-1/2) and Distinct (D-1,2) [43]. For both Summarization and Dialogue Generation task, we follow [54, 26] and adopt $\mathrm { R o B E R T a _ { b a s e } }$ [52] as the backbone for $S _ { \theta }$ . We choose the linear combination of B-1/2 as $\Delta ( \cdot , \cdot )$ for Dialogue Generation and R-1/2/L for Summarization following [76]. We tune the hyper-parameters $\tau$ from $\{ 0 . 0 8 , 0 . 2 , 0 . 5 , 0 . 8 \}$ , learning rate from {5e-5,7e-5,2e-4}. The maximum input length for $S _ { \theta }$ is 512 and we truncate tokens from the longer input of source and candidate.
|
| 366 |
+
|
| 367 |
+
# C Evaluation Details
|
| 368 |
+
|
| 369 |
+
Machine Translation We evaluate our MT system with BLEU, TER and ${ \mathrm { c h r F } } + +$ from SACREBLEU3 [66]. The signatures for BLEU, TER and ${ \mathrm { c h r F } } + +$ are shown in Table 8.
|
| 370 |
+
|
| 371 |
+
Table 8: Signature from SACREBLEU.
|
| 372 |
+
|
| 373 |
+
<table><tr><td>[c]Signature</td></tr><tr><td>nrefs:1lcase:mixedleff:noltok:13alsmooth:explversion:2.0.0</td></tr><tr><td>nrefs:1lcase:lcltok:tercomlnorm:nolpunct:yeslasian:nolversion:2.0.0</td></tr><tr><td>nrefs:1lcase:mixedleff:yeslnc:6lnw:2lspace:nolversion:2.0.0</td></tr></table>
|
| 374 |
+
|
| 375 |
+
Summarization We evaluate our Summarization system with standard ROUGE [47] Perl package4 for evaluation. Following [55], we use PTB tokenizer5 for tokenization. And the parameters for ROUGE are " $\mathsf { \Pi } _ { - \mathrm { c } } ^ { \prime } 9 5 \mathsf { \Pi } _ { - \mathrm { r } } 1 0 0 0 \mathsf { \Pi } _ { - \mathrm { n } } 2 \mathsf { \Pi } _ { - \mathrm { m } } \mathsf { " }$ .
|
| 376 |
+
|
| 377 |
+
Dialogue Generation Following [27], we evaluate our dialogue system with NLTK BLEU 6 with space as tokenizer and smoothing method1. The Distinction score is from [42].
|
| 378 |
+
|
| 379 |
+
# D More results on translation tasks
|
| 380 |
+
|
| 381 |
+
Table 9: Evaluation results on JRC-Acquis En De measured by BLEU, TER and ${ \mathrm { c h r F } } + +$
|
| 382 |
+
|
| 383 |
+
<table><tr><td>System</td><td>Memory</td><td>BLEU 个</td><td>chrF++ 个</td><td>TER</td></tr><tr><td>Transformer</td><td>None</td><td>55.43</td><td>70.31</td><td>36.35</td></tr><tr><td>Transformerdual</td><td>Retrieval</td><td>58.06</td><td>71.58</td><td>35.41</td></tr><tr><td>Transformerjoint</td><td>Retrieval</td><td>58.58</td><td>72.22</td><td>34.39</td></tr><tr><td>Transformerdual</td><td>Self</td><td>59.49</td><td>72.62</td><td>34.04</td></tr><tr><td>Transformerjoint</td><td>Self</td><td>60.11</td><td>73.25</td><td>32.62</td></tr></table>
|
| 384 |
+
|
| 385 |
+
# E More Summarization Baselines
|
| 386 |
+
|
| 387 |
+
In this Table 10, we include more baselines on the benchmark dataset XSum and BigPatent. We also report the confidence region of SOTA model for XSum and BigPatent as shown in Table 11.
|
| 388 |
+
|
| 389 |
+
Table 10: More baselines on XSum and BigPatent.
|
| 390 |
+
|
| 391 |
+
<table><tr><td>System</td><td>R-1</td><td>R-2</td><td>R-L</td></tr><tr><td></td><td>XSum</td><td></td><td></td></tr><tr><td>[51]</td><td>38.8</td><td>16.5</td><td>31.3 37.3</td></tr><tr><td>[40]</td><td>45.1</td><td>22.3</td><td>39.3</td></tr><tr><td>[100]</td><td>47.2</td><td>24.6</td><td>39.4</td></tr><tr><td>[54] [55]</td><td>47.6 49.1</td><td>24.6</td><td>40.4</td></tr><tr><td>[87](PG)</td><td>48.2</td><td>25.6</td><td>40.2</td></tr><tr><td>[87](B)</td><td>43.1</td><td>26.0</td><td>35.5</td></tr><tr><td></td><td></td><td>21.0</td><td>38.6</td></tr><tr><td>[87](L)</td><td>46.5</td><td>24.1</td><td>40.0</td></tr><tr><td>[68]</td><td>48.1</td><td>25.0</td><td>38.8</td></tr><tr><td>[69]</td><td>47.1</td><td>24.1</td><td></td></tr><tr><td>[16]</td><td>47.8</td><td>25.0</td><td>39.7</td></tr><tr><td>Selfmem</td><td>50.3</td><td>26.7</td><td>41.6</td></tr></table>
|
| 392 |
+
|
| 393 |
+
<table><tr><td> System</td><td>R-1 R-2</td><td>R-L</td></tr><tr><td></td><td>BigPatent</td><td></td></tr><tr><td>[100]</td><td>53.6 33.1</td><td>42.3</td></tr><tr><td>[40] 44.4</td><td>21.3</td><td>31.0</td></tr><tr><td>[98] 60.6</td><td>42.5</td><td>50.0</td></tr><tr><td>[65]</td><td>38.7 12.3</td><td>34.1</td></tr><tr><td>[90] 45.0</td><td>20.3</td><td>39.2</td></tr><tr><td>[1] 52.3</td><td>33.5</td><td>42.8</td></tr><tr><td>[87] (B) 59.5</td><td>42.6</td><td>50.6</td></tr><tr><td>[87] (L) 60.7</td><td>43.3</td><td>51.3</td></tr><tr><td>[87] (PG) 44.6</td><td>21.5</td><td>33.3</td></tr><tr><td>Selfmem</td><td>62.9 48.1</td><td>59.6</td></tr></table>
|
| 394 |
+
|
| 395 |
+
# F Empirical analysis of latency
|
| 396 |
+
|
| 397 |
+
In Table 12, we present empirical results of Selfmem latency, measured in seconds. We compare Selfmem with a retrieval-augmented baseline model across various datasets and computational platforms, including CPU and CUDA. The number of iterations for Selfmem is set to one. All experiments are conducted on the same device, equipped with one NVIDIA A100 GPU and one AMD EPYC 7V13 64-Core Processor.
|
| 398 |
+
|
| 399 |
+
Table 11: Confidence region for SOTA model in XSum and BigPatent.
|
| 400 |
+
|
| 401 |
+
<table><tr><td> System</td><td>ROUGE-1/2/L</td><td>95 % -conf.int</td></tr><tr><td></td><td>XSum</td><td></td></tr><tr><td rowspan="4">BRIOjoint</td><td>50.3</td><td>0.49986 - 0.50602</td></tr><tr><td>26.7</td><td>0.26300 - 0.26989</td></tr><tr><td>41.6</td><td>0.41231 - 0.41900</td></tr><tr><td>BigPatent</td><td></td></tr><tr><td rowspan="3">BARTjoint</td><td>62.9</td><td>0.62664 - 0.63080</td></tr><tr><td>48.1</td><td>0.47783 - 0.48333</td></tr><tr><td>59.6</td><td>0.59401 - 0.59847</td></tr></table>
|
| 402 |
+
|
| 403 |
+
Table 12: Generation Latency analysis.
|
| 404 |
+
|
| 405 |
+
<table><tr><td colspan="2"></td><td>NMT</td><td> XSum</td><td>BigPatent</td><td>DailyDialog</td></tr><tr><td colspan="2">Average Input Length</td><td>87</td><td>512</td><td>1024</td><td>71</td></tr><tr><td colspan="2">Average ：Output Length</td><td>44</td><td>75</td><td>127</td><td>16</td></tr><tr><td colspan="2">Retrieval-augmented Baseline</td><td>CPU 0.97</td><td>1.79</td><td>3.16</td><td>0.32</td></tr><tr><td rowspan="5">Selfmem</td><td>Candidate Generation Memory</td><td>3.20</td><td>7.50</td><td>15.00</td><td>1.02</td></tr><tr><td>Selection</td><td>0.50</td><td>0.52</td><td>0.95</td><td>0.14</td></tr><tr><td>Hypothesis Generation</td><td>0.97</td><td>1.79</td><td>3.00</td><td>0.32</td></tr><tr><td>×4.80</td><td></td><td>×5.47</td><td>×6.04</td><td>×4.63</td></tr><tr><td colspan="2">CUDA</td><td></td><td></td><td></td></tr><tr><td colspan="2">Retrieval-augmented Baseline</td><td>0.29</td><td>0.44</td><td>0.75</td><td>0.10</td></tr><tr><td rowspan="3">Selfmem</td><td>Candidate Generation Memory Hypothesis Generation</td><td>0.51</td><td>1.00</td><td>1.72</td><td>0.18</td></tr><tr><td>Selection</td><td>0.01</td><td>0.01</td><td>0.01</td><td>0.01</td></tr><tr><td>0.29 ×2.76</td><td></td><td>0.44 ×2.99</td><td>0.75 ×3.35</td><td>0.10 ×2.91</td></tr></table>
|
| 406 |
+
|
| 407 |
+
# G Human and GPT-4 Evaluation
|
| 408 |
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|
| 409 |
+
We employ both human annotators and GPT-4 (gpt-4-0314) annotators to perform pairwise ranking of the output generated by Selfmem and baseline systems. For GPT-4 annotators, we utilize the prompt from Alpaca Eval 7. We randomly select 50 samples for translation tasks and 20 samples for summarization and dialogue tasks. The win rate of Selfmem versus retrieval-augmented baselines is depicted in Figure 1.
|
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+
Figure 5: Human and GPT-4 evaluation results.
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