Daily Papers

Low-Rank Adaptation (LoRA) is a widely adopted parameter-efficient method for fine-tuning Large Langauge Models. It updates the weight matrix as W=W_0+sBA, where W_0 is the original frozen weight, s is a scaling factor and A,B are trainable low-rank matrices. Despite its robust empirical effectiveness, the theoretical foundations of LoRA remain insufficiently understood, particularly with respect to feature learning stability. In this paper, we first establish that, LoRA can, in principle, naturally achieve and sustain stable feature learning (i.e., be self-stabilized) under appropriate hyper-parameters and initializations of A and B. However, we also uncover a fundamental limitation that the necessary non-zero initialization of A compromises self-stability, leading to suboptimal performances. To address this challenge, we propose Stable-LoRA, a weight-shrinkage optimization strategy that dynamically enhances stability of LoRA feature learning. By progressively shrinking A during the earliest training steps, Stable-LoRA is both theoretically and empirically validated to effectively eliminate instability of LoRA feature learning while preserving the benefits of the non-zero start. Experiments show that Stable-LoRA consistently outperforms other baselines across diverse models and tasks, with no additional memory usage and only negligible computation overheads. The code is available at https://github.com/Yize-Wu/Stable-LoRA.

A primary goal of class-incremental learning is to strike a balance between stability and plasticity, where models should be both stable enough to retain knowledge learned from previously seen classes, and plastic enough to learn concepts from new classes. While previous works demonstrate strong performance on class-incremental benchmarks, it is not clear whether their success comes from the models being stable, plastic, or a mixture of both. This paper aims to shed light on how effectively recent class-incremental learning algorithms address the stability-plasticity trade-off. We establish analytical tools that measure the stability and plasticity of feature representations, and employ such tools to investigate models trained with various algorithms on large-scale class-incremental benchmarks. Surprisingly, we find that the majority of class-incremental learning algorithms heavily favor stability over plasticity, to the extent that the feature extractor of a model trained on the initial set of classes is no less effective than that of the final incremental model. Our observations not only inspire two simple algorithms that highlight the importance of feature representation analysis, but also suggest that class-incremental learning approaches, in general, should strive for better feature representation learning.

Current diffusion-based face animation methods generally adopt a ReferenceNet (a copy of U-Net) and a large amount of curated self-acquired data to learn appearance features, as robust appearance features are vital for ensuring temporal stability. However, when trained on public datasets, the results often exhibit a noticeable performance gap in image quality and temporal consistency. To address this issue, we meticulously examine the essential appearance features in the facial animation tasks, which include motion-agnostic (e.g., clothing, background) and motion-related (e.g., facial details) texture components, along with high-level discriminative identity features. Drawing from this analysis, we introduce a Motion-Identity Modulated Appearance Learning Module (MIA) that modulates CLIP features at both motion and identity levels. Additionally, to tackle the semantic/ color discontinuities between clips, we design an Inter-clip Affinity Learning Module (ICA) to model temporal relationships across clips. Our method achieves precise facial motion control (i.e., expressions and gaze), faithful identity preservation, and generates animation videos that maintain both intra/inter-clip temporal consistency. Moreover, it easily adapts to various modalities of driving sources. Extensive experiments demonstrate the superiority of our method.

Optimal configuration of the learning rate (LR) is a fundamental yet formidable challenge in large-scale pre-training. Given the stringent trade-off between training costs and model performance, the pivotal question is whether the optimal LR can be accurately extrapolated from low-cost experiments. In this paper, we formalize this investigation into two distinct research paradigms: Fitting and Transfer. Within the Fitting Paradigm, we innovatively introduce a Scaling Law for search factor, effectively reducing the search complexity from O(n^3) to O(n*C_D*C_η) via predictive modeling. Within the Transfer Paradigm, we extend the principles of μTransfer to the Mixture of Experts (MoE) architecture, broadening its applicability to encompass model depth, weight decay, and token horizons. By pushing the boundaries of existing hyperparameter research in terms of scale, we conduct a comprehensive comparison between these two paradigms. Our empirical results challenge the scalability of the widely adopted μ Transfer in large-scale pre-training scenarios. Furthermore, we provide a rigorous analysis through the dual lenses of training stability and feature learning to elucidate the underlying reasons why module-wise parameter tuning underperforms in large-scale settings. This work offers systematic practical guidelines and a fresh theoretical perspective for optimizing industrial-level pre-training.

Recent work shows that flow matching can be effective for scalar Q-value function estimation in reinforcement learning (RL), but it remains unclear why or how this approach differs from standard critics. Contrary to conventional belief, we show that their success is not explained by distributional RL, as explicitly modeling return distributions can reduce performance. Instead, we argue that the use of integration for reading out values and dense velocity supervision at each step of this integration process for training improves TD learning via two mechanisms. First, it enables robust value prediction through test-time recovery, whereby iterative computation through integration dampens errors in early value estimates as more integration steps are performed. This recovery mechanism is absent in monolithic critics. Second, supervising the velocity field at multiple interpolant values induces more plastic feature learning within the network, allowing critics to represent non-stationary TD targets without discarding previously learned features or overfitting to individual TD targets encountered during training. We formalize these effects and validate them empirically, showing that flow-matching critics substantially outperform monolithic critics (2times in final performance and around 5times in sample efficiency) in settings where loss of plasticity poses a challenge e.g., in high-UTD online RL problems, while remaining stable during learning.

Deep learning (DL) algorithms have been widely applied to short-term voltage stability (STVS) assessment in power systems. However, transferring the knowledge learned in one power grid to other power grids with topology changes is still a challenging task. This paper proposed a transferable DL-based model for STVS assessment by constructing the topology-aware voltage dynamic features from raw PMU data. Since the reactive power flow and grid topology are essential to voltage stability, the topology-aware and physics-informed voltage dynamic features are utilized to effectively represent the topological and temporal patterns from post-disturbance system dynamic trajectories. The proposed DL-based STVS assessment model is tested under random operating conditions on the New England 39-bus system. It has 99.99\% classification accuracy of the short-term voltage stability status using the topology-aware and physics-informed voltage dynamic features. In addition to high accuracy, the experiments show good adaptability to PMU errors. Moreover, The proposed STVS assessment method has outstanding performance on new grid topologies after fine-tuning. In particular, the highest accuracy reaches 99.68\% in evaluation, which demonstrates a good knowledge transfer ability of the proposed model for power grid topology change.

Exemplar-free class-incremental learning is very challenging due to the negative effect of catastrophic forgetting. A balance between stability and plasticity of the incremental process is needed in order to obtain good accuracy for past as well as new classes. Existing exemplar-free class-incremental methods focus either on successive fine tuning of the model, thus favoring plasticity, or on using a feature extractor fixed after the initial incremental state, thus favoring stability. We introduce a method which combines a fixed feature extractor and a pseudo-features generator to improve the stability-plasticity balance. The generator uses a simple yet effective geometric translation of new class features to create representations of past classes, made of pseudo-features. The translation of features only requires the storage of the centroid representations of past classes to produce their pseudo-features. Actual features of new classes and pseudo-features of past classes are fed into a linear classifier which is trained incrementally to discriminate between all classes. The incremental process is much faster with the proposed method compared to mainstream ones which update the entire deep model. Experiments are performed with three challenging datasets, and different incremental settings. A comparison with ten existing methods shows that our method outperforms the others in most cases.

Catastrophic forgetting has been a major challenge in continual learning, where the model needs to learn new tasks with limited or no access to data from previously seen tasks. To tackle this challenge, methods based on knowledge distillation in feature space have been proposed and shown to reduce forgetting. However, most feature distillation methods directly constrain the new features to match the old ones, overlooking the need for plasticity. To achieve a better stability-plasticity trade-off, we propose Backward Feature Projection (BFP), a method for continual learning that allows the new features to change up to a learnable linear transformation of the old features. BFP preserves the linear separability of the old classes while allowing the emergence of new feature directions to accommodate new classes. BFP can be integrated with existing experience replay methods and boost performance by a significant margin. We also demonstrate that BFP helps learn a better representation space, in which linear separability is well preserved during continual learning and linear probing achieves high classification accuracy. The code can be found at https://github.com/rvl-lab-utoronto/BFP

Pixel-wise predictions are required in a wide variety of tasks such as image restoration, image segmentation, or disparity estimation. Common models involve several stages of data resampling, in which the resolution of feature maps is first reduced to aggregate information and then increased to generate a high-resolution output. Previous works have shown that resampling operations are subject to artifacts such as aliasing. During downsampling, aliases have been shown to compromise the prediction stability of image classifiers. During upsampling, they have been leveraged to detect generated content. Yet, the effect of aliases during upsampling has not yet been discussed w.r.t. the stability and robustness of pixel-wise predictions. While falling under the same term (aliasing), the challenges for correct upsampling in neural networks differ significantly from those during downsampling: when downsampling, some high frequencies can not be correctly represented and have to be removed to avoid aliases. However, when upsampling for pixel-wise predictions, we actually require the model to restore such high frequencies that can not be encoded in lower resolutions. The application of findings from signal processing is therefore a necessary but not a sufficient condition to achieve the desirable output. In contrast, we find that the availability of large spatial context during upsampling allows to provide stable, high-quality pixel-wise predictions, even when fully learning all filter weights.

In the setting of continual learning, a network is trained on a sequence of tasks, and suffers from catastrophic forgetting. To balance plasticity and stability of network in continual learning, in this paper, we propose a novel network training algorithm called Adam-NSCL, which sequentially optimizes network parameters in the null space of previous tasks. We first propose two mathematical conditions respectively for achieving network stability and plasticity in continual learning. Based on them, the network training for sequential tasks can be simply achieved by projecting the candidate parameter update into the approximate null space of all previous tasks in the network training process, where the candidate parameter update can be generated by Adam. The approximate null space can be derived by applying singular value decomposition to the uncentered covariance matrix of all input features of previous tasks for each linear layer. For efficiency, the uncentered covariance matrix can be incrementally computed after learning each task. We also empirically verify the rationality of the approximate null space at each linear layer. We apply our approach to training networks for continual learning on benchmark datasets of CIFAR-100 and TinyImageNet, and the results suggest that the proposed approach outperforms or matches the state-ot-the-art continual learning approaches.

Federated Learning (FL) is popular for its privacy-preserving and collaborative learning capabilities. Recently, personalized FL (pFL) has received attention for its ability to address statistical heterogeneity and achieve personalization in FL. However, from the perspective of feature extraction, most existing pFL methods only focus on extracting global or personalized feature information during local training, which fails to meet the collaborative learning and personalization goals of pFL. To address this, we propose a new pFL method, named GPFL, to simultaneously learn global and personalized feature information on each client. We conduct extensive experiments on six datasets in three statistically heterogeneous settings and show the superiority of GPFL over ten state-of-the-art methods regarding effectiveness, scalability, fairness, stability, and privacy. Besides, GPFL mitigates overfitting and outperforms the baselines by up to 8.99% in accuracy.

The ability to learn new concepts continually is necessary in this ever-changing world. However, deep neural networks suffer from catastrophic forgetting when learning new categories. Many works have been proposed to alleviate this phenomenon, whereas most of them either fall into the stability-plasticity dilemma or take too much computation or storage overhead. Inspired by the gradient boosting algorithm to gradually fit the residuals between the target model and the previous ensemble model, we propose a novel two-stage learning paradigm FOSTER, empowering the model to learn new categories adaptively. Specifically, we first dynamically expand new modules to fit the residuals between the target and the output of the original model. Next, we remove redundant parameters and feature dimensions through an effective distillation strategy to maintain the single backbone model. We validate our method FOSTER on CIFAR-100 and ImageNet-100/1000 under different settings. Experimental results show that our method achieves state-of-the-art performance. Code is available at: https://github.com/G-U-N/ECCV22-FOSTER.

Reinforcement learning (RL) is a core approach for robot control when expert demonstrations are unavailable. On-policy methods such as Proximal Policy Optimization (PPO) are widely used for their stability, but their reliance on narrowly distributed on-policy data limits accurate policy evaluation in high-dimensional state and action spaces. Off-policy methods can overcome this limitation by learning from a broader state-action distribution, yet suffer from slow convergence and instability, as fitting a value function over diverse data requires many gradient updates, causing critic errors to accumulate through bootstrapping. We present FlashSAC, a fast and stable off-policy RL algorithm built on Soft Actor-Critic. Motivated by scaling laws observed in supervised learning, FlashSAC sharply reduces gradient updates while compensating with larger models and higher data throughput. To maintain stability at increased scale, FlashSAC explicitly bounds weight, feature, and gradient norms, curbing critic error accumulation. Across over 60 tasks in 10 simulators, FlashSAC consistently outperforms PPO and strong off-policy baselines in both final performance and training efficiency, with the largest gains on high-dimensional tasks such as dexterous manipulation. In sim-to-real humanoid locomotion, FlashSAC reduces training time from hours to minutes, demonstrating the promise of off-policy RL for sim-to-real transfer.

Despite strong results on recognition and segmentation, current 3D visual pre-training methods often underperform on robotic manipulation. We attribute this gap to two factors: the lack of state-action-state dynamics modeling and the unnecessary redundancy of explicit geometric reconstruction. We introduce AFRO, a self-supervised framework that learns dynamics-aware 3D representations without action or reconstruction supervision. AFRO casts state prediction as a generative diffusion process and jointly models forward and inverse dynamics in a shared latent space to capture causal transition structure. To prevent feature leakage in action learning, we employ feature differencing and inverse-consistency supervision, improving the quality and stability of visual features. When combined with Diffusion Policy, AFRO substantially increases manipulation success rates across 16 simulated and 4 real-world tasks, outperforming existing pre-training approaches. The framework also scales favorably with data volume and task complexity. Qualitative visualizations indicate that AFRO learns semantically rich, discriminative features, offering an effective pre-training solution for 3D representation learning in robotics. Project page: https://kolakivy.github.io/AFRO/

Continual learning, especially class-incremental learning (CIL), on the basis of a pre-trained model (PTM) has garnered substantial research interest in recent years. However, how to effectively learn both discriminative and comprehensive feature representations while maintaining stability and plasticity over very long task sequences remains an open problem. We propose CaRE, a scalable {C}ontinual Le{a}rner with efficient Bi-Level {R}outing Mixture-of-{E}xperts (BR-MoE). The core idea of BR-MoE is a bi-level routing mechanism: a router selection stage that dynamically activates relevant task-specific routers, followed by an expert routing phase that dynamically activates and aggregates experts, aiming to inject discriminative and comprehensive representations into every intermediate network layer. On the other hand, we introduce a challenging dataset, OmniBenchmark-1K, for CIL performance evaluation on very long task sequences with hundreds of tasks. Extensive experiments show that CaRE demonstrates leading performance across a variety of datasets and task settings, including commonly used CIL datasets with classical CIL settings (e.g., 5-20 tasks). To the best of our knowledge, CaRE is the first continual learner that scales to very long task sequences (ranging from 100 to over 300 non-overlapping tasks), while outperforming all baselines by a large margin on such task sequences. We hope that this work will inspire further research into continual learning over extremely long task sequences. Code and dataset are publicly released at https://github.com/LMMMEng/CaRE.

Despite recent progress in 3D self-supervised learning, collecting large-scale 3D scene scans remains expensive and labor-intensive. In this work, we investigate whether 3D representations can be learned from unlabeled videos recorded without any real 3D sensors. We present Laplacian-Aware Multi-level 3D Clustering with Sinkhorn-Knopp (LAM3C), a self-supervised framework that learns from video-generated point clouds from unlabeled videos. We first introduce RoomTours, a video-generated point cloud dataset constructed by collecting room-walkthrough videos from the web (e.g., real-estate tours) and generating 49,219 scenes using an off-the-shelf feed-forward reconstruction model. We also propose a noise-regularized loss that stabilizes representation learning by enforcing local geometric smoothness and ensuring feature stability under noisy point clouds. Remarkably, without using any real 3D scans, LAM3C achieves higher performance than the previous self-supervised methods on indoor semantic and instance segmentation. These results suggest that unlabeled videos represent an abundant source of data for 3D self-supervised learning.

Self-distillation (SD) offers a promising path for adapting large language models (LLMs) without relying on stronger external teachers. However, SD in autoregressive LLMs remains challenging because self-generated trajectories are free-form, correctness is task-dependent, and plausible rationales can still provide unstable or unreliable supervision. Existing methods mainly examine isolated design choices, leaving their effectiveness, roles, and interactions unclear. In this paper, we propose UniSD, a unified framework to systematically study self-distillation. UniSD integrates complementary mechanisms that address supervision reliability, representation alignment, and training stability, including multi-teacher agreement, EMA teacher stabilization, token-level contrastive learning, feature matching, and divergence clipping. Across six benchmarks and six models from three model families, UniSD reveals when self-distillation improves over static imitation, which components drive the gains, and how these components interact across tasks. Guided by these insights, we construct UniSDfull, an integrated pipeline that combines complementary components and achieves the strongest overall performance, improving over the base model by +5.4 points and the strongest baseline by +2.8 points. Extensive evaluation highlights self-distillation as a practical and steerable approach for efficient LLM adaptation without stronger external teachers.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Scaling limits, such as infinite-width limits, serve as promising theoretical tools to study large-scale models. However, it is widely believed that existing infinite-width theory does not faithfully explain the behavior of practical networks, especially those trained in standard parameterization (SP) meaning He initialization with a global learning rate. For instance, existing theory for SP predicts instability at large learning rates and vanishing feature learning at stable ones. In practice, however, optimal learning rates decay slower than theoretically predicted and networks exhibit both stable training and non-trivial feature learning, even at very large widths. Here, we show that this discrepancy is not fully explained by finite-width phenomena. Instead, we find a resolution through a finer-grained analysis of the regime previously considered unstable and therefore uninteresting. In particular, we show that, under cross-entropy (CE) loss, the unstable regime comprises two distinct sub-regimes: a catastrophically unstable regime and a more benign controlled divergence regime, where logits diverge but gradients and activations remain stable. Moreover, under large learning rates at the edge of the controlled divergence regime, there exists a well-defined infinite width limit where features continue to evolve in all the hidden layers. In experiments across optimizers, architectures, and data modalities, we validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss. Our empirical evidence suggests that width-scaling considerations are surprisingly useful for predicting empirically maximal stable learning rate exponents which provide useful guidance on optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scaling for standard initialization.

Analysis of learned representations has a blind spot: it focuses on similarity, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce geometric stability, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present Shesha, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated (ρapprox 0.01) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2times more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability (ρ= 0.89-0.96); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying how reliably systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.

We characterize the pre-softmax attention matrix QK^top in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).

We present a bag of tricks framework for few-shot class-incremental learning (FSCIL), which is a challenging form of continual learning that involves continuous adaptation to new tasks with limited samples. FSCIL requires both stability and adaptability, i.e., preserving proficiency in previously learned tasks while learning new ones. Our proposed bag of tricks brings together eight key and highly influential techniques that improve stability, adaptability, and overall performance under a unified framework for FSCIL. We organize these tricks into three categories: stability tricks, adaptability tricks, and training tricks. Stability tricks aim to mitigate the forgetting of previously learned classes by enhancing the separation between the embeddings of learned classes and minimizing interference when learning new ones. On the other hand, adaptability tricks focus on the effective learning of new classes. Finally, training tricks improve the overall performance without compromising stability or adaptability. We perform extensive experiments on three benchmark datasets, CIFAR-100, CUB-200, and miniIMageNet, to evaluate the impact of our proposed framework. Our detailed analysis shows that our approach substantially improves both stability and adaptability, establishing a new state-of-the-art by outperforming prior works in the area. We believe our method provides a go-to solution and establishes a robust baseline for future research in this area.

Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on the properties of the base algorithm, or on the dimensionality of the covariates. Our guarantee applies to many variants of bagging and is optimal up to a constant. Empirical results validate our findings, showing that bagging successfully stabilizes even highly unstable base algorithms.

Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the field of continual learning to overcome this forgetting, we show that a set of common state-of-the-art methods still suffers from substantial forgetting upon starting to learn new tasks, except that this forgetting is temporary and followed by a phase of performance recovery. We refer to this intriguing but potentially problematic phenomenon as the stability gap. The stability gap had likely remained under the radar due to standard practice in the field of evaluating continual learning models only after each task. Instead, we establish a framework for continual evaluation that uses per-iteration evaluation and we define a new set of metrics to quantify worst-case performance. Empirically we show that experience replay, constraint-based replay, knowledge-distillation, and parameter regularization methods are all prone to the stability gap; and that the stability gap can be observed in class-, task-, and domain-incremental learning benchmarks. Additionally, a controlled experiment shows that the stability gap increases when tasks are more dissimilar. Finally, by disentangling gradients into plasticity and stability components, we propose a conceptual explanation for the stability gap.

Adapting pre-trained models to specialized tasks often leads to catastrophic forgetting, where new knowledge overwrites foundational capabilities. Existing methods either compromise performance on the new task or struggle to balance training stability with efficient reuse of pre-trained knowledge. We introduce a novel function-preserving expansion method that resolves this dilemma. Our technique expands model capacity by replicating pre-trained parameters within transformer submodules and applying a scaling correction that guarantees the expanded model is mathematically identical to the original at initialization, enabling stable training while exploiting existing knowledge. Empirically, our method eliminates the trade-off between plasticity and stability, matching the performance of full fine-tuning on downstream tasks without any degradation of the model's original capabilities. Furthermore, we demonstrate the modularity of our approach, showing that by selectively expanding a small subset of layers we can achieve the same performance as full fine-tuning at a fraction of the computational cost.

This paper does not describe a novel method. Instead, it studies a straightforward, incremental, yet must-know baseline given the recent progress in computer vision: self-supervised learning for Vision Transformers (ViT). While the training recipes for standard convolutional networks have been highly mature and robust, the recipes for ViT are yet to be built, especially in the self-supervised scenarios where training becomes more challenging. In this work, we go back to basics and investigate the effects of several fundamental components for training self-supervised ViT. We observe that instability is a major issue that degrades accuracy, and it can be hidden by apparently good results. We reveal that these results are indeed partial failure, and they can be improved when training is made more stable. We benchmark ViT results in MoCo v3 and several other self-supervised frameworks, with ablations in various aspects. We discuss the currently positive evidence as well as challenges and open questions. We hope that this work will provide useful data points and experience for future research.

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (ρ= 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial ρ= 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (ρapprox 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2times greater geometric change than CKA during post-training alignment (up to 5.23times in Llama) while providing earlier warning in 73\% of models and maintaining a 6times lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

Continual learning in visual understanding aims to deal with catastrophic forgetting in Multimodal Large Language Models (MLLMs). MLLMs deployed on devices have to continuously adapt to dynamic scenarios in downstream tasks, such as variations in background and perspective, to effectively perform complex visual tasks. To this end, we construct a multimodal visual understanding dataset (MSVQA) encompassing four different scenarios and perspectives including high altitude, underwater, low altitude and indoor, to investigate the catastrophic forgetting in MLLMs under the dynamics of scenario shifts in real-world data streams. Furthermore, we propose mUltimodal coNtInual learning with MLLMs From multi-scenarIo pERspectives (UNIFIER) to address visual discrepancies while learning different scenarios. Specifically, it decouples the visual information from different scenarios into distinct branches within each vision block and projects them into the same feature space. A consistency constraint is imposed on the features of each branch to maintain the stability of visual representations across scenarios. Extensive experiments on the MSVQA dataset demonstrate that UNIFIER effectively alleviates forgetting of cross-scenario tasks and achieves knowledge accumulation within the same scenario.

We study how features emerge, disappear, and persist across models fine-tuned on different domains of text. More specifically, we start from a base one-layer Transformer language model that is trained on a combination of the BabyLM corpus, and a collection of Python code from The Stack. This base model is adapted to two new domains of text: TinyStories, and the Lua programming language, respectively; and then these two models are merged using these two models using spherical linear interpolation. Our exploration aims to provide deeper insights into the stability and transformation of features across typical transfer-learning scenarios using small-scale models and sparse auto-encoders.

Accurate defect segmentation is critical for industrial inspection, yet dense pixel-level annotations are rarely available. A common workaround is to convert inexpensive bounding boxes into pseudo-masks using foundation segmentation models such as the Segment Anything Model (SAM). However, these pseudo-labels are systematically noisy on industrial surfaces, often hallucinating background structure while missing sparse defects. To address this limitation, a noise-robust box-to-pixel distillation framework, Boxes2Pixels, is proposed that treats SAM as a noisy teacher rather than a source of ground-truth supervision. Bounding boxes are converted into pseudo-masks offline by SAM, and a compact student is trained with (i) a hierarchical decoder over frozen DINOv2 features for semantic stability, (ii) an auxiliary binary localization head to decouple sparse foreground discovery from class prediction, and (iii) a one-sided online self-correction mechanism that relaxes background supervision when the student is confident, targeting teacher false negatives. On a manually annotated wind turbine inspection benchmark, the proposed Boxes2Pixels improves anomaly mIoU by +6.97 and binary IoU by +9.71 over the strongest baseline trained under identical weak supervision. Moreover, online self-correction increases the binary recall by +18.56, while the model employs 80\% fewer trainable parameters. Code is available at https://github.com/CLendering/Boxes2Pixels.

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties of orthogonal convolutional layers.We establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. The conditions prove that orthogonal convolutional transforms exist for almost all architectures used in practice for 'circular' padding.We also exhibit limitations with 'valid' boundary conditions and 'same' boundary conditions with zero-padding.Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed, and impressive empirical results have been obtained in different applications (Wang et al. 2020).The second motivation of the present paper is to specify the theory behind this.We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and that, in the presence of small errors and when the size of the signal/image is large, the convolutional layers remain close to isometric.The theoretical results are confirmed with experiments and the landscape of the regularization term is studied. Experiments on real data sets show that when orthogonality is used to enforce robustness, the parameter multiplying the regularization termcan be used to tune a tradeoff between accuracy and orthogonality, for the benefit of both accuracy and robustness.Altogether, the study guarantees that the regularization proposed in Wang et al. (2020) is an efficient, flexible and stable numerical strategy to learn orthogonal convolutional layers.

Deep neural policies have recently been installed in a diverse range of settings, from biotechnology to automated financial systems. However, the utilization of deep neural networks to approximate the value function leads to concerns on the decision boundary stability, in particular, with regard to the sensitivity of policy decision making to indiscernible, non-robust features due to highly non-convex and complex deep neural manifolds. These concerns constitute an obstruction to understanding the reasoning made by deep neural policies, and their foundational limitations. Hence, it is crucial to develop techniques that aim to understand the sensitivities in the learnt representations of neural network policies. To achieve this we introduce a theoretically founded method that provides a systematic analysis of the unstable directions in the deep neural policy decision boundary across both time and space. Through experiments in the Arcade Learning Environment (ALE), we demonstrate the effectiveness of our technique for identifying correlated directions of instability, and for measuring how sample shifts remold the set of sensitive directions in the neural policy landscape. Most importantly, we demonstrate that state-of-the-art robust training techniques yield learning of disjoint unstable directions, with dramatically larger oscillations over time, when compared to standard training. We believe our results reveal the fundamental properties of the decision process made by reinforcement learning policies, and can help in constructing reliable and robust deep neural policies.

The feasibility of making profitable trades on a single asset on stock exchanges based on patterns identification has long attracted researchers. Reinforcement Learning (RL) and Natural Language Processing have gained notoriety in these single-asset trading tasks, but only a few works have explored their combination. Moreover, some issues are still not addressed, such as extracting market sentiment momentum through the explicit capture of sentiment features that reflect the market condition over time and assessing the consistency and stability of RL results in different situations. Filling this gap, we propose the Sentiment-Aware RL (SentARL) intelligent trading system that improves profit stability by leveraging market mood through an adaptive amount of past sentiment features drawn from textual news. We evaluated SentARL across twenty assets, two transaction costs, and five different periods and initializations to show its consistent effectiveness against baselines. Subsequently, this thorough assessment allowed us to identify the boundary between news coverage and market sentiment regarding the correlation of price-time series above which SentARL's effectiveness is outstanding.

The reliability with Machine Learning (ML) techniques in novel materials discovery often depend on the quality of the dataset, in addition to the relevant features used in describing the material. In this regard, the current study presents and validates a newly processed materials dataset that can be utilized for benchmark ML analysis, as it relates to the prediction and classification of deterministic target properties. Originally, the dataset was extracted from the Open Quantum Materials Database (OQMD) and contains a robust 16,323 samples of ABX3 inorganic perovskite structures. The dataset is tabular in form and is preprocessed to include sixty-one generalized input features that broadly describes the physicochemical, stability/geometrical, and Density Functional Theory (DFT) target properties associated with the elemental ionic sites in a three-dimensional ABX3 polyhedral. For validation, four different ML models are employed to predict three distinctive target properties, namely: formation energy, energy band gap, and crystal system. On experimentation, the best accuracy measurements are reported at 0.013 eV/atom MAE, 0.216 eV MAE, and 85% F1, corresponding to the formation energy prediction, band gap prediction and crystal system multi-classification, respectively. Moreover, the realized results are compared with previous literature and as such, affirms the resourcefulness of the current dataset for future benchmark materials analysis via ML techniques. The preprocessed dataset and source codes are openly available to download from github.com/chenebuah/ML_abx3_dataset.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

We propose an empirical measure of the approximate accuracy of feature importance estimates in deep neural networks. Our results across several large-scale image classification datasets show that many popular interpretability methods produce estimates of feature importance that are not better than a random designation of feature importance. Only certain ensemble based approaches---VarGrad and SmoothGrad-Squared---outperform such a random assignment of importance. The manner of ensembling remains critical, we show that some approaches do no better then the underlying method but carry a far higher computational burden.

Online continual learning aims to get closer to a live learning experience by learning directly on a stream of data with temporally shifting distribution and by storing a minimum amount of data from that stream. In this empirical evaluation, we evaluate various methods from the literature that tackle online continual learning. More specifically, we focus on the class-incremental setting in the context of image classification, where the learner must learn new classes incrementally from a stream of data. We compare these methods on the Split-CIFAR100 and Split-TinyImagenet benchmarks, and measure their average accuracy, forgetting, stability, and quality of the representations, to evaluate various aspects of the algorithm at the end but also during the whole training period. We find that most methods suffer from stability and underfitting issues. However, the learned representations are comparable to i.i.d. training under the same computational budget. No clear winner emerges from the results and basic experience replay, when properly tuned and implemented, is a very strong baseline. We release our modular and extensible codebase at https://github.com/AlbinSou/ocl_survey based on the avalanche framework to reproduce our results and encourage future research.

In this work, we show that Latent Flow-Matching (LFM) models are robust to different types of perturbations, including data reduction and model capacity shrinkage. We characterize this stability by their tendency to generate similar outputs under identical noise seeds. We provide a perspective relating this phenomenon to flow matching theory, which indicates that this stability is inherent to the FM objective. We further exploit this stability to derive practical algorithms for more efficient training and inference. Concretely, first, we show that by training LFM models on significantly reduced datasets, the performance does not degrade perceptually or quantitatively. This yields multiple advantages, such as reducing training time by converging faster under limited compute budget, and alleviating annotation effort when training conditional models. Second, LFM stability under architectural shrinkage gives rise to a two-model coarse-to-fine approach, one using a light-weight architecture for the first phase of the FM trajectory, and one with higher capacity for the second, thereby reducing the inference cost substantially. To determine which samples are informative, we introduce three sample-scoring criteria and evaluate them under standard metrics for generative models. Our results are thoroughly evaluated on multiple datasets, demonstrating the practical advantage of this stability, including data saving and a more than two-fold inference speedup while generating comparable outputs.

Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time on long video sequences. To address this issue, we (1) introduce a diagnostic tool which produces input sequences optimized to trigger instabilities and that can be interpreted as visualizations of temporal receptive fields, and (2) propose two approaches to enforce the stability of a model during training: constraining the spectral norm or constraining the stable rank of its convolutional layers. We then introduce Stable Rank Normalization for Convolutional layers (SRN-C), a new algorithm that enforces these constraints. Our experimental results suggest that SRN-C successfully enforces stability in recurrent video processing models without a significant performance loss.

Continual learning aims to equip models with the ability to retain previously learned knowledge like a human. Recent work incorporating Parameter-Efficient Fine-Tuning has revitalized the field by introducing lightweight extension modules. However, existing methods usually overlook the issue of information leakage caused by the fact that the experiment data have been used in pre-trained models. Once these duplicate data are removed in the pre-training phase, their performance can be severely affected. In this paper, we propose a new LoRA-based rehearsal-free method named DESIRE. Our method avoids imposing additional constraints during training to mitigate catastrophic forgetting, thereby maximizing the learning of new classes. To integrate knowledge from old and new tasks, we propose two efficient post-processing modules. On the one hand, we retain only two sets of LoRA parameters for merging and propose dynamic representation consolidation to calibrate the merged feature representation. On the other hand, we propose decision boundary refinement to address classifier bias when training solely on new class data. Extensive experiments demonstrate that our method achieves state-of-the-art performance on multiple datasets and strikes an effective balance between stability and plasticity. Our code will be publicly available.

Recent years have seen considerable progress in the continual training of deep neural networks, predominantly thanks to approaches that add replay or regularization terms to the loss function to approximate the joint loss over all tasks so far. However, we show that even with a perfect approximation to the joint loss, these approaches still suffer from temporary but substantial forgetting when starting to train on a new task. Motivated by this 'stability gap', we propose that continual learning strategies should focus not only on the optimization objective, but also on the way this objective is optimized. While there is some continual learning work that alters the optimization trajectory (e.g., using gradient projection techniques), this line of research is positioned as alternative to improving the optimization objective, while we argue it should be complementary. To evaluate the merits of our proposition, we plan to combine replay-approximated joint objectives with gradient projection-based optimization routines to test whether the addition of the latter provides benefits in terms of (1) alleviating the stability gap, (2) increasing the learning efficiency and (3) improving the final learning outcome.

We introduce a novel and general loss function, called Symmetric Contrastive (Sy-CON) loss, for effective continual self-supervised learning (CSSL). We first argue that the conventional loss form of continual learning which consists of single task-specific loss (for plasticity) and a regularizer (for stability) may not be ideal for contrastive loss based CSSL that focus on representation learning. Our reasoning is that, in contrastive learning based methods, the task-specific loss would suffer from decreasing diversity of negative samples and the regularizer may hinder learning new distinctive representations. To that end, we propose Sy-CON that consists of two losses (one for plasticity and the other for stability) with symmetric dependence on current and past models' negative sample embeddings. We argue our model can naturally find good trade-off between the plasticity and stability without any explicit hyperparameter tuning. We validate the effectiveness of our approach through extensive experiments, demonstrating that MoCo-based implementation of Sy-CON loss achieves superior performance compared to other state-of-the-art CSSL methods.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development of CTR models, feature representation learning has become a trending topic and has been extensively studied by both industrial and academic researchers in recent years. This survey aims at summarizing the feature representation learning in a broader picture and pave the way for future research. To achieve such a goal, we first present a taxonomy of current research methods on feature representation learning following two main issues: (i) which feature to represent and (ii) how to represent these features. Then we give a detailed description of each method regarding these two issues. Finally, the review concludes with a discussion on the future directions of this field.

Learning features from data is one of the defining characteristics of deep learning, but our theoretical understanding of the role features play in deep learning is still rudimentary. To address this gap, we introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. With the interaction tensor, we make several key observations about how features are distributed in data and how models with different random seeds learn different features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form. We demonstrate that the proposed framework can explain empirically observed phenomena, including the recently discovered Generalization Disagreement Equality (GDE) that allows for estimating the generalization error with only unlabeled data. Further, our theory also provides explicit construction of natural data distributions that break the GDE. Thus, we believe this work provides valuable new insight into our understanding of feature learning.

Current LLM unlearning methods face a critical security vulnerability that undermines their fundamental purpose: while they appear to successfully remove sensitive or harmful knowledge, this ``forgotten" information remains precariously recoverable through relearning attacks. We identify that the root cause is that conventional methods optimizing the forgetting loss at individual data points will drive model parameters toward sharp minima in the loss landscape. In these unstable regions, even minimal parameter perturbations can drastically alter the model's behaviors. Consequently, relearning attacks exploit this vulnerability by using just a few fine-tuning samples to navigate the steep gradients surrounding these unstable regions, thereby rapidly recovering knowledge that was supposedly erased. This exposes a critical robustness gap between apparent unlearning and actual knowledge removal. To address this issue, we propose StableUN, a bi-level feedback-guided optimization framework that explicitly seeks more stable parameter regions via neighborhood-aware optimization. It integrates forgetting feedback, which uses adversarial perturbations to probe parameter neighborhoods, with remembering feedback to preserve model utility, aligning the two objectives through gradient projection. Experiments on WMDP and MUSE benchmarks demonstrate that our method is significantly more robust against both relearning and jailbreaking attacks while maintaining competitive utility performance.

Teams that have trained large Transformer-based models have reported training instabilities at large scale that did not appear when training with the same hyperparameters at smaller scales. Although the causes of such instabilities are of scientific interest, the amount of resources required to reproduce them has made investigation difficult. In this work, we seek ways to reproduce and study training stability and instability at smaller scales. First, we focus on two sources of training instability described in previous work: the growth of logits in attention layers (Dehghani et al., 2023) and divergence of the output logits from the log probabilities (Chowdhery et al., 2022). By measuring the relationship between learning rate and loss across scales, we show that these instabilities also appear in small models when training at high learning rates, and that mitigations previously employed at large scales are equally effective in this regime. This prompts us to investigate the extent to which other known optimizer and model interventions influence the sensitivity of the final loss to changes in the learning rate. To this end, we study methods such as warm-up, weight decay, and the muParam (Yang et al., 2022), and combine techniques to train small models that achieve similar losses across orders of magnitude of learning rate variation. Finally, to conclude our exploration we study two cases where instabilities can be predicted before they emerge by examining the scaling behavior of model activation and gradient norms.

Neural networks are very effective when trained on large datasets for a large number of iterations. However, when they are trained on non-stationary streams of data and in an online fashion, their performance is reduced (1) by the online setup, which limits the availability of data, (2) due to catastrophic forgetting because of the non-stationary nature of the data. Furthermore, several recent works (Caccia et al., 2022; Lange et al., 2023) arXiv:2205.13452 showed that replay methods used in continual learning suffer from the stability gap, encountered when evaluating the model continually (rather than only on task boundaries). In this article, we study the effect of model ensembling as a way to improve performance and stability in online continual learning. We notice that naively ensembling models coming from a variety of training tasks increases the performance in online continual learning considerably. Starting from this observation, and drawing inspirations from semi-supervised learning ensembling methods, we use a lightweight temporal ensemble that computes the exponential moving average of the weights (EMA) at test time, and show that it can drastically increase the performance and stability when used in combination with several methods from the literature.

Neural network training is inherently sensitive to initialization and the randomness induced by stochastic gradient descent. However, it is unclear to what extent such effects lead to meaningfully different networks, either in terms of the models' weights or the underlying functions that were learned. In this work, we show that during the initial "chaotic" phase of training, even extremely small perturbations reliably causes otherwise identical training trajectories to diverge-an effect that diminishes rapidly over training time. We quantify this divergence through (i) L^2 distance between parameters, (ii) the loss barrier when interpolating between networks, (iii) L^2 and barrier between parameters after permutation alignment, and (iv) representational similarity between intermediate activations; revealing how perturbations across different hyperparameter or fine-tuning settings drive training trajectories toward distinct loss minima. Our findings provide insights into neural network training stability, with practical implications for fine-tuning, model merging, and diversity of model ensembles.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.

In this paper, we propose a method to partially mimic natural intelligence for the problem of lifelong learning representations that are compatible. We take the perspective of a learning agent that is interested in recognizing object instances in an open dynamic universe in a way in which any update to its internal feature representation does not render the features in the gallery unusable for visual search. We refer to this learning problem as Compatible Lifelong Learning Representations (CL2R) as it considers compatible representation learning within the lifelong learning paradigm. We identify stationarity as the property that the feature representation is required to hold to achieve compatibility and propose a novel training procedure that encourages local and global stationarity on the learned representation. Due to stationarity, the statistical properties of the learned features do not change over time, making them interoperable with previously learned features. Extensive experiments on standard benchmark datasets show that our CL2R training procedure outperforms alternative baselines and state-of-the-art methods. We also provide novel metrics to specifically evaluate compatible representation learning under catastrophic forgetting in various sequential learning tasks. Code at https://github.com/NiccoBiondi/CompatibleLifelongRepresentation.

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In this work, we seek to understand the fundamental difficulty of out-of-distribution generalization with deep neural networks. We first empirically show that perhaps surprisingly, even allowing a neural network to explicitly fit the representations obtained from a teacher network that can generalize out-of-distribution is insufficient for the generalization of the student network. Then, by a theoretical study of two-layer ReLU networks optimized by stochastic gradient descent (SGD) under a structured feature model, we identify a fundamental yet unexplored feature learning proclivity of neural networks, feature contamination: neural networks can learn uncorrelated features together with predictive features, resulting in generalization failure under distribution shifts. Notably, this mechanism essentially differs from the prevailing narrative in the literature that attributes the generalization failure to spurious correlations. Overall, our results offer new insights into the non-linear feature learning dynamics of neural networks and highlight the necessity of considering inductive biases in out-of-distribution generalization.

Language models obtain extensive capabilities through pre-training. However, the pre-training process remains a black box. In this work, we track linear interpretable feature evolution across pre-training snapshots using a sparse dictionary learning method called crosscoders. We find that most features begin to form around a specific point, while more complex patterns emerge in later training stages. Feature attribution analyses reveal causal connections between feature evolution and downstream performance. Our feature-level observations are highly consistent with previous findings on Transformer's two-stage learning process, which we term a statistical learning phase and a feature learning phase. Our work opens up the possibility to track fine-grained representation progress during language model learning dynamics.

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

With the success of pretraining techniques in representation learning, a number of continual learning methods based on pretrained models have been proposed. Some of these methods design continual learning mechanisms on the pre-trained representations and only allow minimum updates or even no updates of the backbone models during the training of continual learning. In this paper, we question whether the complexity of these models is needed to achieve good performance by comparing them to a simple baseline that we designed. We argue that the pretrained feature extractor itself can be strong enough to achieve a competitive or even better continual learning performance on Split-CIFAR100 and CoRe 50 benchmarks. To validate this, we conduct a very simple baseline that 1) use the frozen pretrained model to extract image features for every class encountered during the continual learning stage and compute their corresponding mean features on training data, and 2) predict the class of the input based on the nearest neighbor distance between test samples and mean features of the classes; i.e., Nearest Mean Classifier (NMC). This baseline is single-headed, exemplar-free, and can be task-free (by updating the means continually). This baseline achieved 88.53% on 10-Split-CIFAR-100, surpassing most state-of-the-art continual learning methods that are all initialized using the same pretrained transformer model. We hope our baseline may encourage future progress in designing learning systems that can continually add quality to the learning representations even if they started from some pretrained weights.

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often result in difficult optimization procedures that remain hard to scale to larger networks. Through a comprehensive analysis, we show how a simple bounding technique, interval bound propagation (IBP), can be exploited to train large provably robust neural networks that beat the state-of-the-art in verified accuracy. While the upper bound computed by IBP can be quite weak for general networks, we demonstrate that an appropriate loss and clever hyper-parameter schedule allow the network to adapt such that the IBP bound is tight. This results in a fast and stable learning algorithm that outperforms more sophisticated methods and achieves state-of-the-art results on MNIST, CIFAR-10 and SVHN. It also allows us to train the largest model to be verified beyond vacuous bounds on a downscaled version of ImageNet.

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which recently received a lot of attention is described by the notion of invariance. In this work we provide a causal perspective and new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization, where we are able to significantly boost the score of existing models.

We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

This work examines the challenges of training neural networks using vector quantization using straight-through estimation. We find that a primary cause of training instability is the discrepancy between the model embedding and the code-vector distribution. We identify the factors that contribute to this issue, including the codebook gradient sparsity and the asymmetric nature of the commitment loss, which leads to misaligned code-vector assignments. We propose to address this issue via affine re-parameterization of the code vectors. Additionally, we introduce an alternating optimization to reduce the gradient error introduced by the straight-through estimation. Moreover, we propose an improvement to the commitment loss to ensure better alignment between the codebook representation and the model embedding. These optimization methods improve the mathematical approximation of the straight-through estimation and, ultimately, the model performance. We demonstrate the effectiveness of our methods on several common model architectures, such as AlexNet, ResNet, and ViT, across various tasks, including image classification and generative modeling.

In recent years, discriminative self-supervised methods have made significant strides in advancing various visual tasks. The central idea of learning a data encoder that is robust to data distortions/augmentations is straightforward yet highly effective. Although many studies have demonstrated the empirical success of various learning methods, the resulting learned representations can exhibit instability and hinder downstream performance. In this study, we analyze discriminative self-supervised methods from a causal perspective to explain these unstable behaviors and propose solutions to overcome them. Our approach draws inspiration from prior works that empirically demonstrate the ability of discriminative self-supervised methods to demix ground truth causal sources to some extent. Unlike previous work on causality-empowered representation learning, we do not apply our solutions during the training process but rather during the inference process to improve time efficiency. Through experiments on both controlled image datasets and realistic image datasets, we show that our proposed solutions, which involve tempering a linear transformation with controlled synthetic data, are effective in addressing these issues.

We address the problem of class incremental learning, which is a core step towards achieving adaptive vision intelligence. In particular, we consider the task setting of incremental learning with limited memory and aim to achieve better stability-plasticity trade-off. To this end, we propose a novel two-stage learning approach that utilizes a dynamically expandable representation for more effective incremental concept modeling. Specifically, at each incremental step, we freeze the previously learned representation and augment it with additional feature dimensions from a new learnable feature extractor. This enables us to integrate new visual concepts with retaining learned knowledge. We dynamically expand the representation according to the complexity of novel concepts by introducing a channel-level mask-based pruning strategy. Moreover, we introduce an auxiliary loss to encourage the model to learn diverse and discriminate features for novel concepts. We conduct extensive experiments on the three class incremental learning benchmarks and our method consistently outperforms other methods with a large margin.

Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and developing different practical strategies to enforce certain Lipschitz properties, we aim to thoroughly examine and characterise the Lipschitz behaviour of Neural Networks. Thus, we carry out an empirical investigation in a range of different settings (namely, architectures, datasets, label noise, and more) by exhausting the limits of the simplest and the most general lower and upper bounds. As a highlight of this investigation, we showcase a remarkable fidelity of the lower Lipschitz bound, identify a striking Double Descent trend in both upper and lower bounds to the Lipschitz and explain the intriguing effects of label noise on function smoothness and generalisation.

Fine-tuning over large pretrained language models (PLMs) has established many state-of-the-art results. Despite its superior performance, such fine-tuning can be unstable, resulting in significant variance in performance and potential risks for practical applications. Previous works have attributed such instability to the catastrophic forgetting problem in the top layers of PLMs, which indicates iteratively that fine-tuning layers in a top-down manner is a promising solution. In this paper, we first point out that this method does not always work out due to the different convergence speeds of different layers/modules. Inspired by this observation, we propose a simple component-wise gradient norm clipping method to adjust the convergence speed for different components. Experiment results demonstrate that our method achieves consistent improvements in terms of generalization performance, convergence speed, and training stability. The codebase can be found at https://github.com/yangalan123/FineTuningStability.

Neural networks are often trained with empirical risk minimization; however, it has been shown that a shift between training and testing distributions can cause unpredictable performance degradation. On this issue, a research direction, invariant learning, has been proposed to extract invariant features insensitive to the distributional changes. This work proposes EDNIL, an invariant learning framework containing a multi-head neural network to absorb data biases. We show that this framework does not require prior knowledge about environments or strong assumptions about the pre-trained model. We also reveal that the proposed algorithm has theoretical connections to recent studies discussing properties of variant and invariant features. Finally, we demonstrate that models trained with EDNIL are empirically more robust against distributional shifts.

The intrinsic difficulty in adapting deep learning models to non-stationary environments limits the applicability of neural networks to real-world tasks. This issue is critical in practical supervised learning settings, such as the ones in which a pre-trained model computes projections toward a latent space where different task predictors are sequentially learned over time. As a matter of fact, incrementally fine-tuning the whole model to better adapt to new tasks usually results in catastrophic forgetting, with decreasing performance over the past experiences and losing valuable knowledge from the pre-training stage. In this paper, we propose a novel strategy to make the fine-tuning procedure more effective, by avoiding to update the pre-trained part of the network and learning not only the usual classification head, but also a set of newly-introduced learnable parameters that are responsible for transforming the input data. This process allows the network to effectively leverage the pre-training knowledge and find a good trade-off between plasticity and stability with modest computational efforts, thus especially suitable for on-the-edge settings. Our experiments on four image classification problems in a continual learning setting confirm the quality of the proposed approach when compared to several fine-tuning procedures and to popular continual learning methods.

Robots capable of learning from demonstration (LfD) must exhibit stability while executing learned motion skills. To be effective in the real world, they should also remember multiple skills over time -- a capability lacking in current stable-LfD methods. We propose an approach to stable, continual LfD, and highlight the role of stability in improving continual learning. Our proposed hypernetwork generates the parameters of two neural networks: a trajectory learning dynamics model, and a trajectory-stabilizing Lyapunov function. These generated networks form a clock-augmented stable neural ODE solver (sNODE), a stable dynamics model that offers a superior stability-accuracy trade-off compared to the state-of-the-art. We further propose stochastic hypernetwork regularization with a single, uniformly-sampled task embedding, reducing the cumulative training time for N tasks from O(N^2) to O(N) without degrading performance on real-world tasks. We introduce high-dimensional variants of the popular LASA dataset to assess scalability and extend a dataset of robotic LfD tasks to assess real-world performance. We empirically evaluate our approach on multiple LfD datasets of varying complexity, including sequences of 7--26 tasks, trajectories of 2--32 dimensions, and real-world tasks involving position and orientation. Our thorough evaluation on multiple LfD datasets demonstrates that our approach sequentially learns and retains multiple motion skills without retraining on past demonstrations, and outperforms other relevant baselines in terms of trajectory errors, continual learning scores, and stability metrics. Notably, we show that stability greatly enhances continual learning performance, particularly in size-efficient chunked hypernetworks. Our code is available at https://github.com/sayantanauddy/clfd-snode.

Most papers caution against using predictive models for disease stratification based on unselected radiomic features, as these features are affected by contouring variability. Instead, they advocate for the use of the Intraclass Correlation Coefficient (ICC) as a measure of stability for feature selection. However, the direct effect of segmentation variability on the predictive models is rarely studied. This study investigates the impact of segmentation variability on feature stability and predictive performance in radiomics-based prediction of Triple-Negative Breast Cancer (TNBC) subtype using Magnetic Resonance Imaging. A total of 244 images from the Duke dataset were used, with segmentation variability introduced through modifications of manual segmentations. For each mask, explainable radiomic features were selected using the Shapley Additive exPlanations method and used to train logistic regression models. Feature stability across segmentations was assessed via ICC, Pearson's correlation, and reliability scores quantifying the relationship between feature stability and segmentation variability. Results indicate that segmentation accuracy does not significantly impact predictive performance. While incorporating peritumoral information may reduce feature reproducibility, it does not diminish feature predictive capability. Moreover, feature selection in predictive models is not inherently tied to feature stability with respect to segmentation, suggesting that an overreliance on ICC or reliability scores for feature selection might exclude valuable predictive features.

The stability of language model pre-training and its effects on downstream performance are still understudied. Prior work shows that the training process can yield significantly different results in response to slight variations in initial conditions, e.g., the random seed. Crucially, the research community still lacks sufficient resources and tools to systematically investigate pre-training stability, particularly for decoder-only language models. We introduce the PolyPythias, a set of 45 new training runs for the Pythia model suite: 9 new seeds across 5 model sizes, from 14M to 410M parameters, resulting in about 7k new checkpoints that we release. Using these new 45 training runs, in addition to the 5 already available, we study the effects of different initial conditions determined by the seed -- i.e., parameters' initialisation and data order -- on (i) downstream performance, (ii) learned linguistic representations, and (iii) emergence of training phases. In addition to common scaling behaviours, our analyses generally reveal highly consistent training dynamics across both model sizes and initial conditions. Further, the new seeds for each model allow us to identify outlier training runs and delineate their characteristics. Our findings show the potential of using these methods to predict training stability.

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in high-stakes contexts, such as medical diagnosis and finance. We show that this inconsistent behavior extends beyond predictions to feature attributions, which may likewise have negative implications for the intelligibility of a model, and one's ability to find recourse for subjects. We then introduce selective ensembles to mitigate such inconsistencies by applying hypothesis testing to the predictions of a set of models trained using randomly-selected starting conditions; importantly, selective ensembles can abstain in cases where a consistent outcome cannot be achieved up to a specified confidence level. We prove that that prediction disagreement between selective ensembles is bounded, and empirically demonstrate that selective ensembles achieve consistent predictions and feature attributions while maintaining low abstention rates. On several benchmark datasets, selective ensembles reach zero inconsistently predicted points, with abstention rates as low 1.5%.

In many real-world applications, deep neural networks are retrained from scratch as a dataset grows in size. Given the computational expense for retraining networks, it has been argued that continual learning could make updating networks more efficient. An obstacle to achieving this goal is the stability gap, which refers to an observation that when updating on new data, performance on previously learned data degrades before recovering. Addressing this problem would enable learning new data with fewer network updates, resulting in increased computational efficiency. We study how to mitigate the stability gap. We test a variety of hypotheses to understand why the stability gap occurs. This leads us to discover a method that vastly reduces this gap. In large-scale class incremental learning experiments, we are able to significantly reduce the number of network updates needed for continual learning. Our work has the potential to advance the state-of-the-art in continual learning for real-world applications along with reducing the carbon footprint required to maintain updated neural networks.

Click-through prediction (CTR) models transform features into latent vectors and enumerate possible feature interactions to improve performance based on the input feature set. Therefore, when selecting an optimal feature set, we should consider the influence of both feature and its interaction. However, most previous works focus on either feature field selection or only select feature interaction based on the fixed feature set to produce the feature set. The former restricts search space to the feature field, which is too coarse to determine subtle features. They also do not filter useless feature interactions, leading to higher computation costs and degraded model performance. The latter identifies useful feature interaction from all available features, resulting in many redundant features in the feature set. In this paper, we propose a novel method named OptFS to address these problems. To unify the selection of feature and its interaction, we decompose the selection of each feature interaction into the selection of two correlated features. Such a decomposition makes the model end-to-end trainable given various feature interaction operations. By adopting feature-level search space, we set a learnable gate to determine whether each feature should be within the feature set. Because of the large-scale search space, we develop a learning-by-continuation training scheme to learn such gates. Hence, OptFS generates the feature set only containing features which improve the final prediction results. Experimentally, we evaluate OptFS on three public datasets, demonstrating OptFS can optimize feature sets which enhance the model performance and further reduce both the storage and computational cost.

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jacobian regularization that increases classification margins of neural networks. The stabilizing effect of the Jacobian regularizer leads to significant improvements in robustness, as measured against both random and adversarial input perturbations, without severely degrading generalization properties on clean data.

Within the field of causal inference, we consider the problem of estimating heterogeneous treatment effects from data. We propose and validate a novel approach for learning feature representations to aid the estimation of the conditional average treatment effect or CATE. Our method focuses on an intermediate layer in a neural network trained to predict the outcome from the features. In contrast to previous approaches that encourage the distribution of representations to be treatment-invariant, we leverage a genetic algorithm that optimizes over representations useful for predicting the outcome to select those less useful for predicting the treatment. This allows us to retain information within the features useful for predicting outcome even if that information may be related to treatment assignment. We validate our method on synthetic examples and illustrate its use on a real life dataset.

Neural multivariate regression underpins a wide range of domains such as control, robotics, and finance, yet the geometry of its learned representations remains poorly characterized. While neural collapse has been shown to benefit generalization in classification, we find that analogous collapse in regression consistently degrades performance. To explain this contrast, we analyze models through the lens of intrinsic dimension. Across control tasks and synthetic datasets, we estimate the intrinsic dimension of last-layer features (ID_H) and compare it with that of the regression targets (ID_Y). Collapsed models exhibit ID_H < ID_Y, leading to over-compression and poor generalization, whereas non-collapsed models typically maintain ID_H > ID_Y. For the non-collapsed models, performance with respect to ID_H depends on the data quantity and noise levels. From these observations, we identify two regimes (over-compressed and under-compressed) that determine when expanding or reducing feature dimensionality improves performance. Our results provide new geometric insights into neural regression and suggest practical strategies for enhancing generalization.

Large language models trained on natural language exhibit pronounced anisotropy: a small number of directions concentrate disproportionate energy, while the remaining dimensions form a broad semantic tail. In low-bit training regimes, this geometry becomes numerically unstable. Because blockwise quantization scales are determined by extreme elementwise magnitudes, dominant directions stretch the dynamic range, compressing long-tail semantic variation into narrow numerical bins. We show that this instability is primarily driven by a coherent rank-one mean bias, which constitutes the dominant component of spectral anisotropy in LLM representations. This mean component emerges systematically across layers and training stages and accounts for the majority of extreme activation magnitudes, making it the principal driver of dynamic-range inflation under low precision. Crucially, because the dominant instability is rank-one, it can be eliminated through a simple source-level mean-subtraction operation. This bias-centric conditioning recovers most of the stability benefits of SVD-based spectral methods while requiring only reduction operations and standard quantization kernels. Empirical results on FP4 (W4A4G4) training show that mean removal substantially narrows the loss gap to BF16 and restores downstream performance, providing a hardware-efficient path to stable low-bit LLM training.

In this paper, we study the implicit regularization of stochastic gradient descent (SGD) through the lens of {\em dynamical stability} (Wu et al., 2018). We start by revising existing stability analyses of SGD, showing how the Frobenius norm and trace of Hessian relate to different notions of stability. Notably, if a global minimum is linearly stable for SGD, then the trace of Hessian must be less than or equal to 2/eta, where eta denotes the learning rate. By contrast, for gradient descent (GD), the stability imposes a similar constraint but only on the largest eigenvalue of Hessian. We then turn to analyze the generalization properties of these stable minima, focusing specifically on two-layer ReLU networks and diagonal linear networks. Notably, we establish the {\em equivalence} between these metrics of sharpness and certain parameter norms for the two models, which allows us to show that the stable minima of SGD provably generalize well. By contrast, the stability-induced regularization of GD is provably too weak to ensure satisfactory generalization. This discrepancy provides an explanation of why SGD often generalizes better than GD. Note that the learning rate (LR) plays a pivotal role in the strength of stability-induced regularization. As the LR increases, the regularization effect becomes more pronounced, elucidating why SGD with a larger LR consistently demonstrates superior generalization capabilities. Additionally, numerical experiments are provided to support our theoretical findings.

Deep generative models have made tremendous progress in modeling complex data, often exhibiting generation quality that surpasses a typical human's ability to discern the authenticity of samples. Undeniably, a key driver of this success is enabled by the massive amounts of web-scale data consumed by these models. Due to these models' striking performance and ease of availability, the web will inevitably be increasingly populated with synthetic content. Such a fact directly implies that future iterations of generative models must contend with the reality that their training is curated from both clean data and artificially generated data from past models. In this paper, we develop a framework to rigorously study the impact of training generative models on mixed datasets (of real and synthetic data) on their stability. We first prove the stability of iterative training under the condition that the initial generative models approximate the data distribution well enough and the proportion of clean training data (w.r.t. synthetic data) is large enough. We empirically validate our theory on both synthetic and natural images by iteratively training normalizing flows and state-of-the-art diffusion models on CIFAR10 and FFHQ.

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training sophisticated deep networks on large numbers of relatively unprocessed inputs (so-called automated feature engineering), for many tasks in physics, sets of theoretically well-motivated and well-understood features already exist. Working with such features can bring many benefits, including greater interpretability, reduced training and run time, and enhanced stability and robustness. We develop a new feature selection method based on Distance Correlation (DisCo), and demonstrate its effectiveness on the tasks of boosted top- and W-tagging. Using our method to select features from a set of over 7,000 energy flow polynomials, we show that we can match the performance of much deeper architectures, by using only ten features and two orders-of-magnitude fewer model parameters.

Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained deep learning model, so as to better differentiate between in-distribution (ID) and OOD samples. However, existing feature-shaping methods usually employ rules manually designed for specific model architectures and OOD datasets, which consequently limit their generalization ability. To address this gap, we first formulate an abstract optimization framework for studying feature-shaping methods. We then propose a concrete reduction of the framework with a simple piecewise constant shaping function and show that existing feature-shaping methods approximate the optimal solution to the concrete optimization problem. Further, assuming that OOD data is inaccessible, we propose a formulation that yields a closed-form solution for the piecewise constant shaping function, utilizing solely the ID data. Through extensive experiments, we show that the feature-shaping function optimized by our method improves the generalization ability of OOD detection across a large variety of datasets and model architectures.

State-of-the-art deep neural networks have achieved impressive results on many image classification tasks. However, these same architectures have been shown to be unstable to small, well sought, perturbations of the images. Despite the importance of this phenomenon, no effective methods have been proposed to accurately compute the robustness of state-of-the-art deep classifiers to such perturbations on large-scale datasets. In this paper, we fill this gap and propose the DeepFool algorithm to efficiently compute perturbations that fool deep networks, and thus reliably quantify the robustness of these classifiers. Extensive experimental results show that our approach outperforms recent methods in the task of computing adversarial perturbations and making classifiers more robust.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

Machine learning models, such as neural networks, decision trees, random forests, and gradient boosting machines, accept a feature vector, and provide a prediction. These models learn in a supervised fashion where we provide feature vectors mapped to the expected output. It is common practice to engineer new features from the provided feature set. Such engineered features will either augment or replace portions of the existing feature vector. These engineered features are essentially calculated fields based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different kinds of engineered features. This paper reports empirical research to demonstrate what kinds of engineered features are best suited to various machine learning model types. We provide this recommendation by generating several datasets that we designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model can synthesize the needed feature on its own. If a model can synthesize a planned feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.

Many recent methods for unsupervised or self-supervised representation learning train feature extractors by maximizing an estimate of the mutual information (MI) between different views of the data. This comes with several immediate problems: For example, MI is notoriously hard to estimate, and using it as an objective for representation learning may lead to highly entangled representations due to its invariance under arbitrary invertible transformations. Nevertheless, these methods have been repeatedly shown to excel in practice. In this paper we argue, and provide empirical evidence, that the success of these methods cannot be attributed to the properties of MI alone, and that they strongly depend on the inductive bias in both the choice of feature extractor architectures and the parametrization of the employed MI estimators. Finally, we establish a connection to deep metric learning and argue that this interpretation may be a plausible explanation for the success of the recently introduced methods.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

In this work, we provide a characterization of the feature-learning process in two-layer ReLU networks trained by gradient descent on the logistic loss following random initialization. We consider data with binary labels that are generated by an XOR-like function of the input features. We permit a constant fraction of the training labels to be corrupted by an adversary. We show that, although linear classifiers are no better than random guessing for the distribution we consider, two-layer ReLU networks trained by gradient descent achieve generalization error close to the label noise rate. We develop a novel proof technique that shows that at initialization, the vast majority of neurons function as random features that are only weakly correlated with useful features, and the gradient descent dynamics 'amplify' these weak, random features to strong, useful features.

Adversarial text attacks remain a persistent threat to transformer models, yet existing defenses are typically attack-specific or require costly model retraining. We introduce Representation Stability (RS), a model-agnostic detection framework that identifies adversarial examples by measuring how embedding representations change when important words are masked. RS first ranks words using importance heuristics, then measures embedding sensitivity to masking top-k critical words, and processes the resulting patterns with a BiLSTM detector. Experiments show that adversarially perturbed words exhibit disproportionately high masking sensitivity compared to naturally important words. Across three datasets, three attack types, and two victim models, RS achieves over 88% detection accuracy and demonstrates competitive performance compared to existing state-of-the-art methods, often at lower computational cost. Using Normalized Discounted Cumulative Gain (NDCG) to measure perturbation identification quality, we reveal that gradient-based ranking outperforms attention and random selection approaches, with identification quality correlating with detection performance for word-level attacks. RS also generalizes well to unseen datasets, attacks, and models without retraining, providing a practical solution for adversarial text detection.

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

Visual Language Models (VLMs) have achieved remarkable progress, yet their reliability under small, meaning-preserving input changes remains poorly understood. We present the first large-scale, systematic study of VLM robustness to benign visual and textual perturbations: pixel-level shifts, light geometric transformations, padded rescaling, paraphrasing, and multilingual rewrites that do not alter the underlying semantics of an image-question pair. Across a broad set of models and datasets, we find that modern VLMs are highly sensitive to such minor perturbations: a substantial fraction of samples change their predicted answer under at least one visual or textual modification. We characterize how this instability varies across perturbation types, question categories, and models, revealing that even state-of-the-art systems (e.g., GPT-4o, Gemini 2.0 Flash) frequently fail under shifts as small as a few pixels or harmless rephrasings. We further show that sample-level stability serves as a strong indicator of correctness: stable samples are consistently far more likely to be answered correctly. Leveraging this, we demonstrate that the stability patterns of small, accessible open-source models can be used to predict the correctness of much larger closed-source models with high precision. Our findings expose a fundamental fragility in current VLMs and highlight the need for robustness evaluations that go beyond adversarial perturbations, focusing instead on invariances that models should reliably uphold.

This paper is a study of fine-tuning of BERT contextual representations, with focus on commonly observed instabilities in few-sample scenarios. We identify several factors that cause this instability: the common use of a non-standard optimization method with biased gradient estimation; the limited applicability of significant parts of the BERT network for down-stream tasks; and the prevalent practice of using a pre-determined, and small number of training iterations. We empirically test the impact of these factors, and identify alternative practices that resolve the commonly observed instability of the process. In light of these observations, we re-visit recently proposed methods to improve few-sample fine-tuning with BERT and re-evaluate their effectiveness. Generally, we observe the impact of these methods diminishes significantly with our modified process.

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.

The ability of deep learning models to learn continuously is essential for adapting to new data categories and evolving data distributions. In recent years, approaches leveraging frozen feature extractors after an initial learning phase have been extensively studied. Many of these methods estimate per-class covariance matrices and prototypes based on backbone-derived feature representations. Within this paradigm, we introduce FeNeC (Feature Neighborhood Classifier) and FeNeC-Log, its variant based on the log-likelihood function. Our approach generalizes the existing concept by incorporating data clustering to capture greater intra-class variability. Utilizing the Mahalanobis distance, our models classify samples either through a nearest neighbor approach or trainable logit values assigned to consecutive classes. Our proposition may be reduced to the existing approaches in a special case while extending them with the ability of more flexible adaptation to data. We demonstrate that two FeNeC variants achieve competitive performance in scenarios where task identities are unknown and establish state-of-the-art results on several benchmarks.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

We address hallucination detection in Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) by framing the problem through the lens of dynamical systems stability theory. Rather than treating hallucination as a straightforward classification task, we conceptualize (M)LLMs as dynamical systems, where factual knowledge is represented by stable equilibrium points within the representation space. Our main insight is that hallucinations tend to arise at the boundaries of knowledge-transition regions separating stable and unstable zones. To capture this phenomenon, we propose Lyapunov Probes: lightweight networks trained with derivative-based stability constraints that enforce a monotonic decay in confidence under input perturbations. By performing systematic perturbation analysis and applying a two-stage training process, these probes reliably distinguish between stable factual regions and unstable, hallucination-prone regions. Experiments on diverse datasets and models demonstrate consistent improvements over existing baselines.

Compatible features enable the direct comparison of old and new learned features allowing to use them interchangeably over time. In visual search systems, this eliminates the need to extract new features from the gallery-set when the representation model is upgraded with novel data. This has a big value in real applications as re-indexing the gallery-set can be computationally expensive when the gallery-set is large, or even infeasible due to privacy or other concerns of the application. In this paper, we propose CoReS, a new training procedure to learn representations that are compatible with those previously learned, grounding on the stationarity of the features as provided by fixed classifiers based on polytopes. With this solution, classes are maximally separated in the representation space and maintain their spatial configuration stationary as new classes are added, so that there is no need to learn any mappings between representations nor to impose pairwise training with the previously learned model. We demonstrate that our training procedure largely outperforms the current state of the art and is particularly effective in the case of multiple upgrades of the training-set, which is the typical case in real applications.

We introduce new methods for 1) accelerating and 2) stabilizing training for large language-vision models. 1) For acceleration, we introduce SwitchBack, a linear layer for int8 quantized training which provides a speed-up of 13-25% while matching the performance of bfloat16 training within 0.1 percentage points for the 1B parameter CLIP ViT-Huge -- the largest int8 training to date. Our main focus is int8 as GPU support for float8 is rare, though we also analyze float8 training through simulation. While SwitchBack proves effective for float8, we show that standard techniques are also successful if the network is trained and initialized so that large feature magnitudes are discouraged, which we accomplish via layer-scale initialized with zeros. 2) For stability, we analyze loss spikes and find they consistently occur 1-8 iterations after the squared gradients become under-estimated by their AdamW second moment estimator. As a result, we recommend an AdamW-Adafactor hybrid which avoids loss spikes when training a CLIP ViT-Huge model and outperforms gradient clipping at the scales we test.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

Loss of plasticity is a phenomenon where neural networks become more difficult to train during the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good predictive performance while maintaining network trainability. We develop new techniques for improving continual learning by first reconsidering how initialization can ensure trainability during early phases of learning. From this perspective, we derive new regularization strategies for continual learning that ensure beneficial initialization properties are better maintained throughout training. In particular, we investigate two new regularization techniques for continual learning: (i) Wasserstein regularization toward the initial weight distribution, which is less restrictive than regularizing toward initial weights; and (ii) regularizing weight matrix singular values, which directly ensures gradient diversity is maintained throughout training. We present an experimental analysis that shows these alternative regularizers can improve continual learning performance across a range of supervised learning tasks and model architectures. The alternative regularizers prove to be less sensitive to hyperparameters while demonstrating better training in individual tasks, sustaining trainability as new tasks arrive, and achieving better generalization performance.

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all widths, a process known as feature learning. Here, we show that feature learning is achieved by scaling the spectral norm of weight matrices and their updates like texttt{fan-out/fan-in}, in contrast to widely used but heuristic scalings based on Frobenius norm and entry size. Our spectral scaling analysis also leads to an elementary derivation of maximal update parametrization. All in all, we aim to provide the reader with a solid conceptual understanding of feature learning in neural networks.

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

We propose a simple, yet powerful regularization technique that can be used to significantly improve both the pairwise and triplet losses in learning local feature descriptors. The idea is that in order to fully utilize the expressive power of the descriptor space, good local feature descriptors should be sufficiently "spread-out" over the space. In this work, we propose a regularization term to maximize the spread in feature descriptor inspired by the property of uniform distribution. We show that the proposed regularization with triplet loss outperforms existing Euclidean distance based descriptor learning techniques by a large margin. As an extension, the proposed regularization technique can also be used to improve image-level deep feature embedding.

Parameter-efficient finetuning (PEFT) has become the standard approach for adapting large language models, yet evaluations largely emphasize downstream accuracy while overlooking the retention of pretrained capabilities. We argue that PEFT should be assessed through the stability-plasticity dilemma: the trade-off between target-task adaptation and resistance to forgetting. We introduce PEFT-Arena, a benchmark that jointly measures downstream performance and general capability retention. Across methods, we find distinct stability-plasticity profiles; under comparable parameter budgets, orthogonal finetuning achieves the most favorable Pareto frontier. To explain these differences, we analyze PEFT updates from two geometric perspectives. In weight space, spectral analysis reveals how parameterizations interact with the pretrained singular-value structure. In activation space, retention metrics show whether finetuning preserves or distorts general-capability representations, with forgetting linked to non-isometric representation distortion. Finally, an analysis shows that final SFT checkpoints often overshoot a better target-retention operating point. Inspired by this, we present case studies of a post-hoc improvement with path-wise rewinding.

Machine learning models will often fail when deployed in an environment with a data distribution that is different than the training distribution. When multiple environments are available during training, many methods exist that learn representations which are invariant across the different distributions, with the hope that these representations will be transportable to unseen domains. In this work, we present a nonparametric strategy for learning invariant representations based on the recently-proposed Nadaraya-Watson (NW) head. The NW head makes a prediction by comparing the learned representations of the query to the elements of a support set that consists of labeled data. We demonstrate that by manipulating the support set, one can encode different causal assumptions. In particular, restricting the support set to a single environment encourages the model to learn invariant features that do not depend on the environment. We present a causally-motivated setup for our modeling and training strategy and validate on three challenging real-world domain generalization tasks in computer vision.

Inducing and leveraging sparse activations during training and inference is a promising avenue for improving the computational efficiency of deep networks, which is increasingly important as network sizes continue to grow and their application becomes more widespread. Here we use the large width Gaussian process limit to analyze the behaviour, at random initialization, of nonlinear activations that induce sparsity in the hidden outputs. A previously unreported form of training instability is proven for arguably two of the most natural candidates for hidden layer sparsification; those being a shifted ReLU (phi(x)=max(0, x-tau) for tauge 0) and soft thresholding (phi(x)=0 for |x|letau and x-sign(x)tau for |x|>tau). We show that this instability is overcome by clipping the nonlinear activation magnitude, at a level prescribed by the shape of the associated Gaussian process variance map. Numerical experiments verify the theory and show that the proposed magnitude clipped sparsifying activations can be trained with training and test fractional sparsity as high as 85\% while retaining close to full accuracy.

In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of (input, output) examples and performs inference on-the-fly. In this work, we formalize in-context learning as an algorithm learning problem where a transformer model implicitly constructs a hypothesis function at inference-time. We first explore the statistical aspects of this abstraction through the lens of multitask learning: We obtain generalization bounds for ICL when the input prompt is (1) a sequence of i.i.d. (input, label) pairs or (2) a trajectory arising from a dynamical system. The crux of our analysis is relating the excess risk to the stability of the algorithm implemented by the transformer. We characterize when transformer/attention architecture provably obeys the stability condition and also provide empirical verification. For generalization on unseen tasks, we identify an inductive bias phenomenon in which the transfer learning risk is governed by the task complexity and the number of MTL tasks in a highly predictable manner. Finally, we provide numerical evaluations that (1) demonstrate transformers can indeed implement near-optimal algorithms on classical regression problems with i.i.d. and dynamic data, (2) provide insights on stability, and (3) verify our theoretical predictions.

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. In this paper we provide an explanation for this behavior based on the recently observed phenomenon that the features learned by overparameterized classification networks show an interesting clustering property, called neural collapse. We demonstrate both theoretically and empirically that neural collapse generalizes to new samples from the training classes, and -- more importantly -- to new classes as well, allowing foundation models to provide feature maps that work well in transfer learning and, specifically, in the few-shot setting.

Recent unlearning methods for LLMs are vulnerable to relearning attacks: knowledge believed-to-be-unlearned re-emerges by fine-tuning on a small set of (even seemingly-unrelated) examples. We study this phenomenon in a controlled setting for example-level unlearning in vision classifiers. We make the surprising discovery that forget-set accuracy can recover from around 50% post-unlearning to nearly 100% with fine-tuning on just the retain set -- i.e., zero examples of the forget set. We observe this effect across a wide variety of unlearning methods, whereas for a model retrained from scratch excluding the forget set (gold standard), the accuracy remains at 50%. We observe that resistance to relearning attacks can be predicted by weight-space properties, specifically, L_2-distance and linear mode connectivity between the original and the unlearned model. Leveraging this insight, we propose a new class of methods that achieve state-of-the-art resistance to relearning attacks.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based on deep learning overwhelm the more traditional model-based approaches in performance, but they typically suffer from instability with respect to data perturbation. In this paper, we theoretically analyze the trade-off between stability and accuracy of neural networks, when used to solve linear imaging inverse problems for not under-determined cases. Moreover, we propose different supervised and unsupervised solutions to increase the network stability and maintain a good accuracy, by means of regularization properties inherited from a model-based iterative scheme during the network training and pre-processing stabilizing operator in the neural networks. Extensive numerical experiments on image deblurring confirm the theoretical results and the effectiveness of the proposed deep learning-based approaches to handle noise on the data.

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small ell_2-norm and appear in each data point; (ii) strong features which have a larger ell_2-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".

Offline-to-online reinforcement learning (RL) has emerged as a practical paradigm that leverages offline datasets for pretraining and online interactions for fine-tuning. However, its empirical behavior is highly inconsistent: design choices of online-fine tuning that work well in one setting can fail completely in another. We propose a stability--plasticity principle that can explain this inconsistency: we should preserve the knowledge of pretrained policy or offline dataset during online fine-tuning, whichever is better, while maintaining sufficient plasticity. This perspective identifies three regimes of online fine-tuning, each requiring distinct stability properties. We validate this framework through a large-scale empirical study, finding that the results strongly align with its predictions in 45 of 63 cases. This work provides a principled framework for guiding design choices in offline-to-online RL based on the relative performance of the offline dataset and the pretrained policy.