Daily Papers

Catastrophic forgetting is a problem faced by many machine learning models and algorithms. When trained on one task, then trained on a second task, many machine learning models "forget" how to perform the first task. This is widely believed to be a serious problem for neural networks. Here, we investigate the extent to which the catastrophic forgetting problem occurs for modern neural networks, comparing both established and recent gradient-based training algorithms and activation functions. We also examine the effect of the relationship between the first task and the second task on catastrophic forgetting. We find that it is always best to train using the dropout algorithm--the dropout algorithm is consistently best at adapting to the new task, remembering the old task, and has the best tradeoff curve between these two extremes. We find that different tasks and relationships between tasks result in very different rankings of activation function performance. This suggests the choice of activation function should always be cross-validated.

The incredible success of transformers on sequence modeling tasks can be largely attributed to the self-attention mechanism, which allows information to be transferred between different parts of a sequence. Self-attention allows transformers to encode causal structure which makes them particularly suitable for sequence modeling. However, the process by which transformers learn such causal structure via gradient-based training algorithms remains poorly understood. To better understand this process, we introduce an in-context learning task that requires learning latent causal structure. We prove that gradient descent on a simplified two-layer transformer learns to solve this task by encoding the latent causal graph in the first attention layer. The key insight of our proof is that the gradient of the attention matrix encodes the mutual information between tokens. As a consequence of the data processing inequality, the largest entries of this gradient correspond to edges in the latent causal graph. As a special case, when the sequences are generated from in-context Markov chains, we prove that transformers learn an induction head (Olsson et al., 2022). We confirm our theoretical findings by showing that transformers trained on our in-context learning task are able to recover a wide variety of causal structures.

Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning geometrical and invariant temporal properties of the system in question (like attractors). However, training reconstruction algorithms like recurrent neural networks (RNNs) on such systems by gradient-descent based techniques faces severe challenges. This is mainly due to exploding gradients caused by the exponential divergence of trajectories in chaotic systems. Moreover, for (scientific) interpretability we wish to have as low dimensional reconstructions as possible, preferably in a model which is mathematically tractable. Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system. We show on several DS that with these amendments we can reconstruct DS better than current SOTA algorithms, in much lower dimensions. Performance differences were particularly compelling on real world data with which most other methods severely struggled. This work thus led to a simple yet powerful DS reconstruction algorithm which is highly interpretable at the same time.

Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of neuroevolution techniques that improve performance. We demonstrate the latter by showing that combining DNNs with novelty search, which encourages exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g.\ DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA is faster than ES, A3C, and DQN (it can train Atari in {raise.17ex\scriptstyle\sim}4 hours on one desktop or {raise.17ex\scriptstyle\sim}1 hour distributed on 720 cores), and enables a state-of-the-art, up to 10,000-fold compact encoding technique.

We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms. We reformulate training as a large-scale feasibility problem: finding network parameters and states that satisfy local constraints derived from its elementary operations. Training then involves projecting onto these constraints, a local operation that can be parallelized across the network. We introduce PJAX, a JAX-based software framework that enables this paradigm. PJAX composes projection operators for elementary operations, automatically deriving the solution operators for the feasibility problems (akin to autodiff for derivatives). It inherently supports GPU/TPU acceleration, provides a familiar NumPy-like API, and is extensible. We train diverse architectures (MLPs, CNNs, RNNs) on standard benchmarks using PJAX, demonstrating its functionality and generality. Our results show that this approach is as a compelling alternative to gradient-based training, with clear advantages in parallelism and the ability to handle non-differentiable operations.

In recent years, large language models (LLMs) have made remarkable progress, with model optimization primarily relying on gradient-based optimizers such as Adam. However, these gradient-based methods impose stringent hardware requirements, demanding high-concurrency, high-memory GPUs. Moreover, they require all neural network operations to be differentiable, thereby excluding many promising non-differentiable architectures from practical use. To address these limitations, we propose EA4LLM, an evolutionary algorithm for optimizing LLMs, and, for the first time, empirically verify full-parameter optimization from the pretraining stage across model sizes ranging from 0.5B to 32B. We conduct extensive experiments and provide key insights into how evolutionary algorithms can effectively optimize neural networks. Our work challenges the prevailing assumption that gradient-based optimization is the only viable approach for training neural networks. It also holds significant potential to reduce the computational cost of training large language models, thereby enabling groups with limited computational resources to participate in deep learning research.

Gradient-based algorithms are a cornerstone of artificial neural network training, yet it remains unclear whether biological neural networks use similar gradient-based strategies during learning. Experiments often discover a diversity of synaptic plasticity rules, but whether these amount to an approximation to gradient descent is unclear. Here we investigate a previously overlooked possibility: that learning dynamics may include fundamentally non-gradient "curl"-like components while still being able to effectively optimize a loss function. Curl terms naturally emerge in networks with inhibitory-excitatory connectivity or Hebbian/anti-Hebbian plasticity, resulting in learning dynamics that cannot be framed as gradient descent on any objective. To investigate the impact of these curl terms, we analyze feedforward networks within an analytically tractable student-teacher framework, systematically introducing non-gradient dynamics through neurons exhibiting rule-flipped plasticity. Small curl terms preserve the stability of the original solution manifold, resulting in learning dynamics similar to gradient descent. Beyond a critical value, strong curl terms destabilize the solution manifold. Depending on the network architecture, this loss of stability can lead to chaotic learning dynamics that destroy performance. In other cases, the curl terms can counterintuitively speed learning compared to gradient descent by allowing the weight dynamics to escape saddles by temporarily ascending the loss. Our results identify specific architectures capable of supporting robust learning via diverse learning rules, providing an important counterpoint to normative theories of gradient-based learning in neural networks.

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which classical analysis applies only if the loss is either convex or smooth. We show that a very small modification to SGDM closes this gap: simply scale the update at each time point by an exponentially distributed random scalar. The resulting algorithm achieves optimal convergence guarantees. Intriguingly, this result is not derived by a specific analysis of SGDM: instead, it falls naturally out of a more general framework for converting online convex optimization algorithms to non-convex optimization algorithms.

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations both scale well with increasing resolution, are continuous, and can be many-times differentiable. However, given a dataset of signals that we would like to represent, having to optimize a separate neural field for each signal is inefficient, and cannot capitalize on shared information or structures among signals. Existing generalization methods view this as a meta-learning problem and employ gradient-based meta-learning to learn an initialization which is then fine-tuned with test-time optimization, or learn hypernetworks to produce the weights of a neural field. We instead propose a new paradigm that views the large-scale training of neural representations as a part of a partially-observed neural process framework, and leverage neural process algorithms to solve this task. We demonstrate that this approach outperforms both state-of-the-art gradient-based meta-learning approaches and hypernetwork approaches.

Diffusion models have shown remarkable performance in image synthesis, but they demand extensive computational and memory resources for training, fine-tuning and inference. Although advanced quantization techniques have successfully minimized memory usage for inference, training and fine-tuning these quantized models still require large memory possibly due to dequantization for accurate computation of gradients and/or backpropagation for gradient-based algorithms. However, memory-efficient fine-tuning is particularly desirable for applications such as personalization that often must be run on edge devices like mobile phones with private data. In this work, we address this challenge by quantizing a diffusion model with personalization via Textual Inversion and by leveraging a zeroth-order optimization on personalization tokens without dequantization so that it does not require gradient and activation storage for backpropagation that consumes considerable memory. Since a gradient estimation using zeroth-order optimization is quite noisy for a single or a few images in personalization, we propose to denoise the estimated gradient by projecting it onto a subspace that is constructed with the past history of the tokens, dubbed Subspace Gradient. In addition, we investigated the influence of text embedding in image generation, leading to our proposed time steps sampling, dubbed Partial Uniform Timestep Sampling for sampling with effective diffusion timesteps. Our method achieves comparable performance to prior methods in image and text alignment scores for personalizing Stable Diffusion with only forward passes while reducing training memory demand up to 8.2times.

Morphological neural networks, or layers, can be a powerful tool to boost the progress in mathematical morphology, either on theoretical aspects such as the representation of complete lattice operators, or in the development of image processing pipelines. However, these architectures turn out to be difficult to train when they count more than a few morphological layers, at least within popular machine learning frameworks which use gradient descent based optimization algorithms. In this paper we investigate the potential and limitations of differentiation based approaches and back-propagation applied to morphological networks, in light of the non-smooth optimization concept of Bouligand derivative. We provide insights and first theoretical guidelines, in particular regarding initialization and learning rates.

Existing reinforcement learning (RL)-based post-training methods for large language models have advanced rapidly, yet their design has largely been guided by heuristics rather than systematic theoretical principles. This gap limits our understanding of the properties of the gradient estimators and the associated optimization algorithms, thereby constraining opportunities to improve training stability and overall performance. In this work, we provide a unified theoretical framework that characterizes the statistical properties of commonly used policy-gradient estimators under mild assumptions. Our analysis establishes unbiasedness, derives exact variance expressions, and yields an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of gradients. We further show that the variance-optimal baseline is a gradient-weighted estimator, offering a new principle for variance reduction and naturally enhancing stability beyond existing methods. These insights motivate Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO), an algorithm that jointly adapts learning rates and baselines in a theoretically grounded manner. Experiments on Qwen3-4B-Base and Qwen3-8B-Base demonstrate consistent gains over existing policy optimization methods, validating that our theoretical contributions translate into practical improvements in large-scale post-training.

LLMs have been found to memorize training textual sequences and regurgitate verbatim said sequences during text generation time. This fact is known to be the cause of privacy and related (e.g., copyright) problems. Unlearning in LLMs then takes the form of devising new algorithms that will properly deal with these side-effects of memorized data, while not hurting the model's utility. We offer a fresh perspective towards this goal, namely, that each textual sequence to be forgotten should be treated differently when being unlearned based on its degree of memorization within the LLM. We contribute a new metric for measuring unlearning quality, an adversarial attack showing that SOTA algorithms lacking this perspective fail for privacy, and two new unlearning methods based on Gradient Ascent and Task Arithmetic, respectively. A comprehensive performance evaluation across an extensive suite of NLP tasks then mapped the solution space, identifying the best solutions under different scales in model capacities and forget set sizes and quantified the gains of the new approaches.

Reinforcement Learning from Human Feedback (RLHF) has become the predominant approach for language model (LM) alignment. At its core, RLHF uses a margin-based loss for preference optimization, specifying ideal LM behavior only by the difference between preferred and dispreferred responses. In this paper, we identify a common pitfall of margin-based methods -- the under-specification of ideal LM behavior on preferred and dispreferred responses individually, which leads to two unintended consequences as the margin increases: (1) The probability of dispreferred (e.g., unsafe) responses may increase, resulting in potential safety alignment failures. (2) The probability of preferred responses may decrease, even when those responses are ideal. We demystify the reasons behind these problematic behaviors: margin-based losses couple the change in the preferred probability to the gradient of the dispreferred one, and vice versa, often preventing the preferred probability from increasing while the dispreferred one decreases, and thus causing a synchronized increase or decrease in both probabilities. We term this effect, inherent in margin-based objectives, gradient entanglement. Formally, we derive conditions for general margin-based alignment objectives under which gradient entanglement becomes concerning: the inner product of the gradients of preferred and dispreferred log-probabilities is large relative to the individual gradient norms. We theoretically investigate why such inner products can be large when aligning language models and empirically validate our findings. Empirical implications of our framework extend to explaining important differences in the training dynamics of various preference optimization algorithms, and suggesting potential algorithm designs to mitigate the under-specification issue of margin-based methods and thereby improving language model alignment.

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty value. These training methods are particularly relevant for active learning and data subset selection problems. For SGD with a constant step size update, we present convergence results for linear classifiers and linearly separable datasets using squared hinge loss and similar training loss functions. Additionally, we extend our analysis to more general classifiers and datasets, considering a wide range of loss-based sampling strategies and smooth convex training loss functions. We propose a novel algorithm called Adaptive-Weight Sampling (AWS) that utilizes SGD with an adaptive step size that achieves stochastic Polyak's step size in expectation. We establish convergence rate results for AWS for smooth convex training loss functions. Our numerical experiments demonstrate the efficiency of AWS on various datasets by using either exact or estimated loss values.

Abstract Language Models (LMs) achieve substantial language capabilities when finetuned using Reinforcement Learning with Human Feedback (RLHF). However, RLHF is an unstable and data-hungry process that continually requires new high-quality LM-generated data for finetuning. We introduce Advantage-Leftover Lunch RL (A-LoL), a new class of offline policy gradient algorithms that enable RL training on any pre-existing data. By assuming the entire LM output sequence as a single action, A-LoL allows incorporating sequence-level classifiers or human-designed scoring functions as rewards. Subsequently, by using LM's internal sequence-level value estimate, A-LoL filters negative advantage (low-quality) data points during training, making it resilient to noise. Overall, A-LoL is an easy-to-implement LM training recipe that is sample-efficient and stable. We demonstrate the effectiveness of A-LoL and its variants with a set of four different language generation tasks. We compare against both online RL (PPO) and recent preference-based (DPO, PRO) and reward-based (GOLD) offline RL baselines. On the commonly-used RLHF benchmark, Helpful and Harmless Assistant (HHA), LMs trained with A-LoL methods achieve the highest diversity while also being rated more safe and helpful than baselines according to humans. Additionally, in the remaining three tasks, A-LoL could optimize multiple distinct reward functions even when using noisy or suboptimal training data. We also release our experimental code. https://github.com/abaheti95/LoL-RL

Text retrieval plays a crucial role in incorporating factual knowledge for decision making into language processing pipelines, ranging from chat-based web search to question answering systems. Current state-of-the-art text retrieval models leverage pre-trained large language models (LLMs) to achieve competitive performance, but training LLM-based retrievers via typical contrastive losses requires intricate heuristics, including selecting hard negatives and using additional supervision as learning signals. This reliance on heuristics stems from the fact that the contrastive loss itself is heuristic and does not directly optimize the downstream metrics of decision quality at the end of the processing pipeline. To address this issue, we introduce Neural PG-RANK, a novel training algorithm that learns to rank by instantiating a LLM as a Plackett-Luce ranking policy. Neural PG-RANK provides a principled method for end-to-end training of retrieval models as part of larger decision systems via policy gradient, with little reliance on complex heuristics, and it effectively unifies the training objective with downstream decision-making quality. We conduct extensive experiments on various text retrieval benchmarks. The results demonstrate that when the training objective aligns with the evaluation setup, Neural PG-RANK yields remarkable in-domain performance improvement, with substantial out-of-domain generalization to some critical datasets employed in downstream question answering tasks.

Many modern deep learning applications require balancing multiple objectives that are often conflicting. Examples include multi-task learning, fairness-aware learning, and the alignment of Large Language Models (LLMs). This leads to multi-objective deep learning, which tries to find optimal trade-offs or Pareto-optimal solutions by adapting mathematical principles from the field of Multi-Objective Optimization (MOO). However, directly applying gradient-based MOO techniques to deep neural networks presents unique challenges, including high computational costs, optimization instability, and the difficulty of effectively incorporating user preferences. This paper provides a comprehensive survey of gradient-based techniques for multi-objective deep learning. We systematically categorize existing algorithms based on their outputs: (i) methods that find a single, well-balanced solution, (ii) methods that generate a finite set of diverse Pareto-optimal solutions, and (iii) methods that learn a continuous Pareto set of solutions. In addition to this taxonomy, the survey covers theoretical analyses, key applications, practical resources, and highlights open challenges and promising directions for future research. A comprehensive list of multi-objective deep learning algorithms is available at https://github.com/Baijiong-Lin/Awesome-Multi-Objective-Deep-Learning.

A fine-grained data recipe is crucial for pre-training large language models, as it can significantly enhance training efficiency and model performance. One important ingredient in the recipe is to select samples based on scores produced by defined rules, LLM judgment, or statistical information in embeddings, which can be roughly categorized into quality and diversity metrics. Due to the high computational cost when applied to trillion-scale token pre-training datasets such as FineWeb and DCLM, these two or more types of metrics are rarely considered jointly in a single selection process. However, in our empirical study, selecting samples based on quality metrics exhibit severe diminishing returns during long-term pre-training, while selecting on diversity metrics removes too many valuable high-quality samples, both of which limit pre-trained LLMs' capabilities. Therefore, we introduce DATAMASK, a novel and efficient joint learning framework designed for large-scale pre-training data selection that can simultaneously optimize multiple types of metrics in a unified process, with this study focusing specifically on quality and diversity metrics. DATAMASK approaches the selection process as a mask learning problem, involving iterative sampling of data masks, computation of policy gradients based on predefined objectives with sampled masks, and updating of mask sampling logits. Through policy gradient-based optimization and various acceleration enhancements, it significantly reduces selection time by 98.9% compared to greedy algorithm, enabling our study to explore joint learning within trillion-scale tokens. With DATAMASK, we select a subset of about 10% from the 15 trillion-token FineWeb dataset, termed FineWeb-Mask. Evaluated across 12 diverse tasks, we achieves significant improvements of 3.2% on a 1.5B dense model and 1.9% on a 7B MoE model.

Detecting plagiarism involves finding similar items in two different sources. In this article, we propose a novel method for detecting plagiarism that is based on attention mechanism-based long short-term memory (LSTM) and bidirectional encoder representations from transformers (BERT) word embedding, enhanced with optimized differential evolution (DE) method for pre-training and a focal loss function for training. BERT could be included in a downstream task and fine-tuned as a task-specific BERT can be included in a downstream task and fine-tuned as a task-specific structure, while the trained BERT model is capable of detecting various linguistic characteristics. Unbalanced classification is one of the primary issues with plagiarism detection. We suggest a focal loss-based training technique that carefully learns minority class instances to solve this. Another issue that we tackle is the training phase itself, which typically employs gradient-based methods like back-propagation for the learning process and thus suffers from some drawbacks, including sensitivity to initialization. To initiate the BP process, we suggest a novel DE algorithm that makes use of a clustering-based mutation operator. Here, a winning cluster is identified for the current DE population, and a fresh updating method is used to produce potential answers. We evaluate our proposed approach on three benchmark datasets ( MSRP, SNLI, and SemEval2014) and demonstrate that it performs well when compared to both conventional and population-based methods.

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

Test-time training (TTT) methods explicitly update the weights of a model to adapt to the specific test instance, and they have found success in a variety of settings, including most recently language modeling and reasoning. To demystify this success, we investigate a gradient-based TTT algorithm for in-context learning, where we train a transformer model on the in-context demonstrations provided in the test prompt. Specifically, we provide a comprehensive theoretical characterization of linear transformers when the update rule is a single gradient step. Our theory (i) delineates the role of alignment between pretraining distribution and target task, (ii) demystifies how TTT can alleviate distribution shift, and (iii) quantifies the sample complexity of TTT including how it can significantly reduce the eventual sample size required for in-context learning. As our empirical contribution, we study the benefits of TTT for TabPFN, a tabular foundation model. In line with our theory, we demonstrate that TTT significantly reduces the required sample size for tabular classification (3 to 5 times fewer) unlocking substantial inference efficiency with a negligible training cost.

We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and leverages its underlying structure making the gradients sequentially predictable. By exploiting the predictability and ideas from optimistic online learning, the proposed algorithm can accelerate the convergence and increase sample efficiency. After establishing a tighter upper bound under some convexity conditions on the regret, we offer a complimentary view of our algorithm which generalizes the offline and stochastic version of nonconvex optimization. In the nonconvex case, we establish a non-asymptotic convergence bound independently of the initialization. We illustrate the practical speedup on several deep learning models via numerical experiments.

Neural networks are a group of neurons stacked together in multiple layers to mimic the biological neurons in a human brain. Neural networks have been trained using the backpropagation algorithm based on gradient descent strategy for several decades. Several variants have been developed to improve the backpropagation algorithm. The loss function for the neural network is optimized through backpropagation, but several local minima exist in the manifold of the constructed neural network. We obtain several solutions matching the minima. The gradient descent strategy cannot avoid the problem of local minima and gets stuck in the minima due to the initialization. Particle swarm optimization (PSO) was proposed to select the best local minima among the search space of the loss function. The search space is limited to the instantiated particles in the PSO algorithm, and sometimes it cannot select the best solution. In the proposed approach, we overcome the problem of gradient descent and the limitation of the PSO algorithm by training individual neurons separately, capable of collectively solving the problem as a group of neurons forming a network. Our code and data are available at https://github.com/dipkmr/train-nn-wobp/

Large language models (LLMs) are commonly trained on multi-domain datasets, where domain sampling strategies significantly impact model performance due to varying domain importance across downstream tasks. Existing approaches for optimizing domain-level sampling strategies struggle with maintaining intra-domain consistency and accurately measuring domain impact. In this paper, we present Domain Impact-aware Data Sampling (DIDS). To ensure intra-domain consistency, a gradient clustering algorithm is proposed to group training data based on their learning effects, where a proxy language model and dimensionality reduction are employed to reduce computational overhead. To accurately measure domain impact, we develop a Fisher Information Matrix (FIM) guided metric that quantifies how domain-specific parameter updates affect the model's output distributions on downstream tasks, with theoretical guarantees. Furthermore, to determine optimal sampling ratios, DIDS combines both the FIM-guided domain impact assessment and loss learning trajectories that indicate domain-specific potential, while accounting for diminishing marginal returns. Extensive experiments demonstrate that DIDS achieves 3.4% higher average performance while maintaining comparable training efficiency.

Recent reinforcement learning (RL) methods have achieved success in various domains. However, multi-agent RL (MARL) remains a challenge in terms of decentralization, partial observability and scalability to many agents. Meanwhile, collective behavior requires resolution of the aforementioned challenges, and remains of importance to many state-of-the-art applications such as active matter physics, self-organizing systems, opinion dynamics, and biological or robotic swarms. Here, MARL via mean field control (MFC) offers a potential solution to scalability, but fails to consider decentralized and partially observable systems. In this paper, we enable decentralized behavior of agents under partial information by proposing novel models for decentralized partially observable MFC (Dec-POMFC), a broad class of problems with permutation-invariant agents allowing for reduction to tractable single-agent Markov decision processes (MDP) with single-agent RL solution. We provide rigorous theoretical results, including a dynamic programming principle, together with optimality guarantees for Dec-POMFC solutions applied to finite swarms of interest. Algorithmically, we propose Dec-POMFC-based policy gradient methods for MARL via centralized training and decentralized execution, together with policy gradient approximation guarantees. In addition, we improve upon state-of-the-art histogram-based MFC by kernel methods, which is of separate interest also for fully observable MFC. We evaluate numerically on representative collective behavior tasks such as adapted Kuramoto and Vicsek swarming models, being on par with state-of-the-art MARL. Overall, our framework takes a step towards RL-based engineering of artificial collective behavior via MFC.

Quantization is a key method for reducing the GPU memory requirement of training large language models (LLMs). Yet, current approaches are ineffective for 4-bit activations and 8-bit gradients, which would easily cause slow convergence or accuracy loss. To address this, we introduce AGoQ, incorporating two new techniques: 1) a layer-aware activation quantization algorithm that allocates appropriate bit-widths for activations of various layers based on their types and pipeline stages to achieve near 4-bit activation storage, and 2) a gradient quantization algorithm that reduces memory usage and shortens communication time by employing 8-bit gradient storage and precision-preserving 8-bit All-Reduce communication. We conduct extensive experiments using different sizes of LLMs on two GPU clusters (up to 64 GPUs), and the experimental results show that our AGoQ reduces the memory by up to 52\% and achieves up to 1.34times improvement of training speed compared to state-of-the-art training systems Megatron-LM (w/ or w/o ZeRO), COAT and DeepSpeed with 8B to 32B LLaMA models, while achieving convergence loss on pretraining and comparable accuracy on downstream tasks with LLaMA architectures.

The increasing complexity of large language models (LLMs) necessitates efficient training strategies to mitigate the high computational costs associated with distributed training. A significant bottleneck in this process is gradient synchronization across multiple GPUs, particularly in the zero-redundancy parallelism mode. In this paper, we introduce Transformer-Aware Gradient Compression (TAGC), an optimized gradient compression algorithm designed specifically for transformer-based models. TAGC extends the lossless homomorphic compression method by adapting it for sharded models and incorporating transformer-specific optimizations, such as layer-selective compression and dynamic sparsification. Our experimental results demonstrate that TAGC accelerates training by up to 15% compared to the standard Fully Sharded Data Parallel (FSDP) approach, with minimal impact on model quality. We integrate TAGC into the PyTorch FSDP framework, the implementation is publicly available at https://github.com/ipolyakov/TAGC.

Training large language models (LLMs) presents numerous challenges, including gradient instability and loss spikes. These phenomena can lead to catastrophic divergence, requiring costly checkpoint restoration and data batch skipping. Traditional gradient clipping techniques, such as constant or norm-based methods, fail to address these issues effectively due to their reliance on fixed thresholds or heuristics, leading to inefficient learning and requiring frequent manual intervention. In this work, we propose ZClip, an adaptive gradient clipping algorithm that dynamically adjusts the clipping threshold based on statistical properties of gradient norms over time. Unlike prior reactive strategies, ZClip proactively adapts to training dynamics without making any prior assumptions on the scale and the temporal evolution of gradient norms. At its core, it leverages z-score-based anomaly detection to identify and mitigate large gradient spikes, preventing malignant loss spikes while not interfering with convergence otherwise. Our code is available at: https://github.com/bluorion-com/ZClip.

Transformers trained via Reinforcement Learning (RL) with outcome-based supervision can spontaneously develop the ability to generate intermediate reasoning steps (Chain-of-Thought). Yet the mechanism by which sparse rewards drive policy gradient to discover such systematic reasoning remains poorly understood. We address this by analyzing the policy gradient dynamics of single-layer Transformers on a synthetic graph traversal task that cannot be solved without Chain-of-Thought but admits a simple iterative solution. We prove that despite training solely on final-answer correctness, policy gradient drives the Transformer to converge to a structured, interpretable algorithm that iteratively traverses the graph vertex-by-vertex. We characterize the distributional properties required for this emergence, identifying the critical role of "simple examples": instances requiring fewer reasoning steps. When the training distribution places sufficient mass on these simpler examples, the Transformer learns a generalizable traversal strategy that extrapolates to longer chains; when this mass vanishes, policy gradient learning becomes infeasible. We corroborate our theoretical results through experiments on synthetic data and with real-world language models on mathematical reasoning tasks, validating that our theoretical findings carry over to practical settings.

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains.

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.

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this "hypergradient" needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.

We propose a categorical semantics of gradient-based machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as as MSE and Softmax cross-entropy, shedding new light on their similarities and differences. Our approach to gradient-based learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realized in the discrete setting of boolean circuits. Finally, we demonstrate the practical significance of our framework with an implementation in Python.

The strength of modern generative models lies in their ability to be controlled through text-based prompts. Typical "hard" prompts are made from interpretable words and tokens, and must be hand-crafted by humans. There are also "soft" prompts, which consist of continuous feature vectors. These can be discovered using powerful optimization methods, but they cannot be easily interpreted, re-used across models, or plugged into a text-based interface. We describe an approach to robustly optimize hard text prompts through efficient gradient-based optimization. Our approach automatically generates hard text-based prompts for both text-to-image and text-to-text applications. In the text-to-image setting, the method creates hard prompts for diffusion models, allowing API users to easily generate, discover, and mix and match image concepts without prior knowledge on how to prompt the model. In the text-to-text setting, we show that hard prompts can be automatically discovered that are effective in tuning LMs for classification.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

Modern language models often have open weights but closed training data. We formalize the problem of data approximation from model weights and propose several baselines and metrics. We develop a gradient-based approach that selects the highest-matching data from a large public text corpus and show its effectiveness at recovering useful data given only weights of the original and finetuned models. Even when none of the true training data is known, our method is able to locate a small subset of public Web documents can be used to train a model to close to the original model performance given models trained for both classification and supervised-finetuning. On the AG News classification task, our method improves performance from 65% (using randomly selected data) to 80%, approaching the expert benchmark of 88%. When applied to a model trained with SFT on MSMARCO web documents, our method reduces perplexity from 3.3 to 2.3, compared to an expert LLAMA model's perplexity of 2.0.

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.

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

We describe PromptBoosting, a query-efficient procedure for building a text classifier from a neural language model (LM) without access to the LM's parameters, gradients, or hidden representations. This form of "black-box" classifier training has become increasingly important as the cost of training and inference in large-scale LMs grows. But existing black-box LM classifier learning approaches are themselves computationally inefficient, typically specializing LMs to the target task by searching in a large space of (discrete or continuous) prompts using zeroth-order optimization methods. Instead of directly optimizing in prompt space, PromptBoosting obtains a small pool of prompts via a gradient-free approach and then constructs a large pool of weak learners by pairing these prompts with different elements of the LM's output distribution. These weak learners are then ensembled using the AdaBoost algorithm. The entire learning process requires only a small number of forward passes and no backward pass. Experiments show that PromptBoosting achieves state-of-the-art performance in multiple black-box few-shot classification tasks, and matches or outperforms full fine-tuning in both few-shot and standard learning paradigms, while training 10x faster than existing black-box methods.

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

We present a method to formulate algorithm discovery as program search, and apply it to discover optimization algorithms for deep neural network training. We leverage efficient search techniques to explore an infinite and sparse program space. To bridge the large generalization gap between proxy and target tasks, we also introduce program selection and simplification strategies. Our method discovers a simple and effective optimization algorithm, Lion (Evo\textbf{Lved Sign Momentum}). It is more memory-efficient than Adam as it only keeps track of the momentum. Different from adaptive optimizers, its update has the same magnitude for each parameter calculated through the sign operation. We compare Lion with widely used optimizers, such as Adam and Adafactor, for training a variety of models on different tasks. On image classification, Lion boosts the accuracy of ViT by up to 2% on ImageNet and saves up to 5x the pre-training compute on JFT. On vision-language contrastive learning, we achieve 88.3% zero-shot and 91.1% fine-tuning accuracy on ImageNet, surpassing the previous best results by 2% and 0.1%, respectively. On diffusion models, Lion outperforms Adam by achieving a better FID score and reducing the training compute by up to 2.3x. For autoregressive, masked language modeling, and fine-tuning, Lion exhibits a similar or better performance compared to Adam. Our analysis of Lion reveals that its performance gain grows with the training batch size. It also requires a smaller learning rate than Adam due to the larger norm of the update produced by the sign function. Additionally, we examine the limitations of Lion and identify scenarios where its improvements are small or not statistically significant. The implementation of Lion is publicly available.

The computation necessary for training Transformer-based language models has skyrocketed in recent years. This trend has motivated research on efficient training algorithms designed to improve training, validation, and downstream performance faster than standard training. In this work, we revisit three categories of such algorithms: dynamic architectures (layer stacking, layer dropping), batch selection (selective backprop, RHO loss), and efficient optimizers (Lion, Sophia). When pre-training BERT and T5 with a fixed computation budget using such methods, we find that their training, validation, and downstream gains vanish compared to a baseline with a fully-decayed learning rate. We define an evaluation protocol that enables computation to be done on arbitrary machines by mapping all computation time to a reference machine which we call reference system time. We discuss the limitations of our proposed protocol and release our code to encourage rigorous research in efficient training procedures: https://github.com/JeanKaddour/NoTrainNoGain.

There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

We introduce novel variants of momentum by incorporating the variance of the stochastic loss function. The variance characterizes the confidence or uncertainty of the local features of the averaged loss surface across the i.i.d. subsets of the training data defined by the mini-batches. We show two applications of the gradient of the variance of the loss function. First, as a bias to the conventional momentum update to encourage conformity of the local features of the loss function (e.g. local minima) across mini-batches to improve generalization and the cumulative training progress made per epoch. Second, as an alternative direction for "exploration" in the parameter space, especially, for non-convex objectives, that exploits both the optimistic and pessimistic views of the loss function in the face of uncertainty. We also introduce a novel data-driven stochastic regularization technique through the parameter update rule that is model-agnostic and compatible with arbitrary architectures. We further establish connections to probability distributions over loss functions and the REINFORCE policy gradient update with baseline in RL. Finally, we incorporate the new variants of momentum proposed into Adam, and empirically show that our methods improve the rate of convergence of training based on our experiments on the MNIST and CIFAR-10 datasets.

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on *algorithmically-efficient deep learning*, which seeks to reduce training costs not at the hardware or implementation level, but through changes in the semantics of the training program. In this paper, we present a structured and comprehensive overview of the research in this field. First, we formalize the *algorithmic speedup* problem, then we use fundamental building blocks of algorithmically efficient training to develop a taxonomy. Our taxonomy highlights commonalities of seemingly disparate methods and reveals current research gaps. Next, we present evaluation best practices to enable comprehensive, fair, and reliable comparisons of speedup techniques. To further aid research and applications, we discuss common bottlenecks in the training pipeline (illustrated via experiments) and offer taxonomic mitigation strategies for them. Finally, we highlight some unsolved research challenges and present promising future directions.

Training algorithms, broadly construed, are an essential part of every deep learning pipeline. Training algorithm improvements that speed up training across a wide variety of workloads (e.g., better update rules, tuning protocols, learning rate schedules, or data selection schemes) could save time, save computational resources, and lead to better, more accurate, models. Unfortunately, as a community, we are currently unable to reliably identify training algorithm improvements, or even determine the state-of-the-art training algorithm. In this work, using concrete experiments, we argue that real progress in speeding up training requires new benchmarks that resolve three basic challenges faced by empirical comparisons of training algorithms: (1) how to decide when training is complete and precisely measure training time, (2) how to handle the sensitivity of measurements to exact workload details, and (3) how to fairly compare algorithms that require hyperparameter tuning. In order to address these challenges, we introduce a new, competitive, time-to-result benchmark using multiple workloads running on fixed hardware, the AlgoPerf: Training Algorithms benchmark. Our benchmark includes a set of workload variants that make it possible to detect benchmark submissions that are more robust to workload changes than current widely-used methods. Finally, we evaluate baseline submissions constructed using various optimizers that represent current practice, as well as other optimizers that have recently received attention in the literature. These baseline results collectively demonstrate the feasibility of our benchmark, show that non-trivial gaps between methods exist, and set a provisional state-of-the-art for future benchmark submissions to try and surpass.

D-Adaptation is an approach to automatically setting the learning rate which asymptotically achieves the optimal rate of convergence for minimizing convex Lipschitz functions, with no back-tracking or line searches, and no additional function value or gradient evaluations per step. Our approach is the first hyper-parameter free method for this class without additional multiplicative log factors in the convergence rate. We present extensive experiments for SGD and Adam variants of our method, where the method automatically matches hand-tuned learning rates across more than a dozen diverse machine learning problems, including large-scale vision and language problems. An open-source implementation is available.

Simulators offer the possibility of safe, low-cost development of self-driving systems. However, current driving simulators exhibit na\"ive behavior models for background traffic. Hand-tuned scenarios are typically added during simulation to induce safety-critical situations. An alternative approach is to adversarially perturb the background traffic trajectories. In this paper, we study this approach to safety-critical driving scenario generation using the CARLA simulator. We use a kinematic bicycle model as a proxy to the simulator's true dynamics and observe that gradients through this proxy model are sufficient for optimizing the background traffic trajectories. Based on this finding, we propose KING, which generates safety-critical driving scenarios with a 20% higher success rate than black-box optimization. By solving the scenarios generated by KING using a privileged rule-based expert algorithm, we obtain training data for an imitation learning policy. After fine-tuning on this new data, we show that the policy becomes better at avoiding collisions. Importantly, our generated data leads to reduced collisions on both held-out scenarios generated via KING as well as traditional hand-crafted scenarios, demonstrating improved robustness.

We propose a tuning-free dynamic SGD step size formula, which we call Distance over Gradients (DoG). The DoG step sizes depend on simple empirical quantities (distance from the initial point and norms of gradients) and have no ``learning rate'' parameter. Theoretically, we show that a slight variation of the DoG formula enjoys strong parameter-free convergence guarantees for stochastic convex optimization assuming only locally bounded stochastic gradients. Empirically, we consider a broad range of vision and language transfer learning tasks, and show that DoG's performance is close to that of SGD with tuned learning rate. We also propose a per-layer variant of DoG that generally outperforms tuned SGD, approaching the performance of tuned Adam. A PyTorch implementation is available at https://github.com/formll/dog

We propose a method for jointly inferring labels across a collection of data samples, where each sample consists of an observation and a prior belief about the label. By implicitly assuming the existence of a generative model for which a differentiable predictor is the posterior, we derive a training objective that allows learning under weak beliefs. This formulation unifies various machine learning settings; the weak beliefs can come in the form of noisy or incomplete labels, likelihoods given by a different prediction mechanism on auxiliary input, or common-sense priors reflecting knowledge about the structure of the problem at hand. We demonstrate the proposed algorithms on diverse problems: classification with negative training examples, learning from rankings, weakly and self-supervised aerial imagery segmentation, co-segmentation of video frames, and coarsely supervised text classification.

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam, and (2) accelerated schemes, such as heavy-ball and Nesterov momentum. In this paper, we propose a new optimization algorithm, Lookahead, that is orthogonal to these previous approaches and iteratively updates two sets of weights. Intuitively, the algorithm chooses a search direction by looking ahead at the sequence of fast weights generated by another optimizer. We show that Lookahead improves the learning stability and lowers the variance of its inner optimizer with negligible computation and memory cost. We empirically demonstrate Lookahead can significantly improve the performance of SGD and Adam, even with their default hyperparameter settings on ImageNet, CIFAR-10/100, neural machine translation, and Penn Treebank.

Adaptive gradient-based optimizers, particularly Adam, have left their mark in training large-scale deep learning models. The strength of such optimizers is that they exhibit fast convergence while being more robust to hyperparameter choice. However, they often generalize worse than non-adaptive methods. Recent studies have tied this performance gap to flat minima selection: adaptive methods tend to find solutions in sharper basins of the loss landscape, which in turn hurts generalization. To overcome this issue, we propose a new memory-augmented version of Adam that promotes exploration towards flatter minima by using a buffer of critical momentum terms during training. Intuitively, the use of the buffer makes the optimizer overshoot outside the basin of attraction if it is not wide enough. We empirically show that our method improves the performance of several variants of Adam on standard supervised language modelling and image classification tasks.

Modern machine learning requires system designers to specify aspects of the learning pipeline, such as losses, architectures, and optimizers. Meta-learning, or learning-to-learn, instead aims to learn those aspects, and promises to unlock greater capabilities with less manual effort. One particularly ambitious goal of meta-learning is to train general-purpose in-context learning algorithms from scratch, using only black-box models with minimal inductive bias. Such a model takes in training data, and produces test-set predictions across a wide range of problems, without any explicit definition of an inference model, training loss, or optimization algorithm. In this paper we show that Transformers and other black-box models can be meta-trained to act as general-purpose in-context learners. We characterize transitions between algorithms that generalize, algorithms that memorize, and algorithms that fail to meta-train at all, induced by changes in model size, number of tasks, and meta-optimization. We further show that the capabilities of meta-trained algorithms are bottlenecked by the accessible state size (memory) determining the next prediction, unlike standard models which are thought to be bottlenecked by parameter count. Finally, we propose practical interventions such as biasing the training distribution that improve the meta-training and meta-generalization of general-purpose in-context learning algorithms.

Differentiable matching layers and residual connection paradigms, often implemented via entropy-regularized Optimal Transport (OT), serve as critical mechanisms in structural prediction and architectural scaling. However, recovering discrete permutations or maintaining identity mappings via annealing εto 0 is notoriously unstable. In this work, we identify a fundamental mechanism for this failure: Premature Mode Collapse. By analyzing the non-normal dynamics of the Sinkhorn fixed-point map, we reveal a theoretical thermodynamic speed limit: standard exponential cooling outpaces the contraction rate of the inference operator, which degrades as O(1/ε). To address this, we propose Efficient Piecewise Hybrid Adaptive Stability Control (EPH-ASC), an adaptive scheduling algorithm that monitors the stability of the inference process. We demonstrate that EPH-ASC is essential for stabilizing Manifold-Constrained Hyper-Connections (mHC) during large-scale training on the FineWeb-Edu dataset, effectively preventing late-stage gradient explosions by enforcing a linear stability law.

Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared with SGD or even fail to converge due to unstable and extreme learning rates. Recent work has put forward some algorithms such as AMSGrad to tackle this issue but they failed to achieve considerable improvement over existing methods. In our paper, we demonstrate that extreme learning rates can lead to poor performance. We provide new variants of Adam and AMSGrad, called AdaBound and AMSBound respectively, which employ dynamic bounds on learning rates to achieve a gradual and smooth transition from adaptive methods to SGD and give a theoretical proof of convergence. We further conduct experiments on various popular tasks and models, which is often insufficient in previous work. Experimental results show that new variants can eliminate the generalization gap between adaptive methods and SGD and maintain higher learning speed early in training at the same time. Moreover, they can bring significant improvement over their prototypes, especially on complex deep networks. The implementation of the algorithm can be found at https://github.com/Luolc/AdaBound .

A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based approach to this problem. We first introduce an algorithm for efficiently calculating metagradients -- gradients through model training -- at scale. We then introduce a "smooth model training" framework that enables effective optimization using metagradients. With metagradient descent (MGD), we greatly improve on existing dataset selection methods, outperform accuracy-degrading data poisoning attacks by an order of magnitude, and automatically find competitive learning rate schedules.

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an equivalent number of gradient descent updates and show explicitly that stochastic gradient descent acts to regularize generalization error by decorrelating nearby updates. These calculations depends on the details of the model only through the mean and covariance of the gradient distribution, which may be readily measured for particular models of interest. We discuss further improvements to these calculations and comment on possible implications for stochastic optimization.

Pretraining large language models (LLMs) on vast and heterogeneous datasets is crucial for achieving state-of-the-art performance across diverse downstream tasks. However, current training paradigms treat all samples equally, overlooking the importance or relevance of individual samples throughout the training process. Existing reweighting strategies, which primarily focus on group-level data importance, fail to leverage fine-grained instance-level information and do not adapt dynamically to individual sample importance as training progresses. In this paper, we introduce novel algorithms for dynamic, instance-level data reweighting aimed at improving both the efficiency and effectiveness of LLM pretraining. Our methods adjust the weight of each training sample based on its loss value in an online fashion, allowing the model to dynamically focus on more informative or important samples at the current training stage. In particular, our framework allows us to systematically devise reweighting strategies deprioritizing redundant or uninformative data, which we find tend to work best. Furthermore, we develop a new theoretical framework for analyzing the impact of loss-based reweighting on the convergence of gradient-based optimization, providing the first formal characterization of how these strategies affect convergence bounds. We empirically validate our approach across a spectrum of tasks, from pretraining 7B and 1.4B parameter LLMs to smaller-scale language models and linear regression problems, demonstrating that our loss-based reweighting approach can lead to faster convergence and significantly improved performance.

The recent development of Large Language Models (LLMs) has been accompanied by an effervescence of novel ideas and methods to better optimize the loss of deep learning models. Claims from those methods are myriad: from faster convergence to removing reliance on certain hyperparameters. However, the diverse experimental protocols used to validate these claims make direct comparisons between methods challenging. This study presents a comprehensive evaluation of recent optimization techniques across standardized LLM pretraining scenarios, systematically varying model size, batch size, and training duration. Through careful tuning of each method, we provide guidance to practitioners on which optimizer is best suited for each scenario. For researchers, our work highlights promising directions for future optimization research. Finally, by releasing our code and making all experiments fully reproducible, we hope our efforts can help the development and rigorous benchmarking of future methods.

This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a given function. A neural network can also be seen as an additive expansion where the scalar product of the responses of the last hidden layer and its weights provide the final output of the network. Instead of training the network as a whole, the proposed algorithm trains the network sequentially in T steps. First, the bias term of the network is initialized with a constant approximation that minimizes the average loss of the data. Then, at each step, a portion of the network, composed of J neurons, is trained to approximate the pseudo-residuals on the training data computed from the previous iterations. Finally, the T partial models and bias are integrated as a single NN with T times J neurons in the hidden layer. Extensive experiments in classification and regression tasks, as well as in combination with deep neural networks, are carried out showing a competitive generalization performance with respect to neural networks trained with different standard solvers, such as Adam, L-BFGS, SGD and deep models. Furthermore, we show that the proposed method design permits to switch off a number of hidden units during test (the units that were last trained) without a significant reduction of its generalization ability. This permits the adaptation of the model to different classification speed requirements on the fly.

This work presents a novel objective function for the unsupervised training of neural network sentence encoders. It exploits signals from paragraph-level discourse coherence to train these models to understand text. Our objective is purely discriminative, allowing us to train models many times faster than was possible under prior methods, and it yields models which perform well in extrinsic evaluations.

The goal of domain generalization algorithms is to predict well on distributions different from those seen during training. While a myriad of domain generalization algorithms exist, inconsistencies in experimental conditions -- datasets, architectures, and model selection criteria -- render fair and realistic comparisons difficult. In this paper, we are interested in understanding how useful domain generalization algorithms are in realistic settings. As a first step, we realize that model selection is non-trivial for domain generalization tasks. Contrary to prior work, we argue that domain generalization algorithms without a model selection strategy should be regarded as incomplete. Next, we implement DomainBed, a testbed for domain generalization including seven multi-domain datasets, nine baseline algorithms, and three model selection criteria. We conduct extensive experiments using DomainBed and find that, when carefully implemented, empirical risk minimization shows state-of-the-art performance across all datasets. Looking forward, we hope that the release of DomainBed, along with contributions from fellow researchers, will streamline reproducible and rigorous research in domain generalization.

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.

Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of thumb, or sometimes brute-force search. Much more appealing is the idea of developing automatic approaches which can optimize the performance of a given learning algorithm to the task at hand. In this work, we consider the automatic tuning problem within the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). The tractable posterior distribution induced by the GP leads to efficient use of the information gathered by previous experiments, enabling optimal choices about what parameters to try next. Here we show how the effects of the Gaussian process prior and the associated inference procedure can have a large impact on the success or failure of Bayesian optimization. We show that thoughtful choices can lead to results that exceed expert-level performance in tuning machine learning algorithms. We also describe new algorithms that take into account the variable cost (duration) of learning experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization on a diverse set of contemporary algorithms including latent Dirichlet allocation, structured SVMs and convolutional neural networks.

This paper addresses the scalability challenge of architecture search by formulating the task in a differentiable manner. Unlike conventional approaches of applying evolution or reinforcement learning over a discrete and non-differentiable search space, our method is based on the continuous relaxation of the architecture representation, allowing efficient search of the architecture using gradient descent. Extensive experiments on CIFAR-10, ImageNet, Penn Treebank and WikiText-2 show that our algorithm excels in discovering high-performance convolutional architectures for image classification and recurrent architectures for language modeling, while being orders of magnitude faster than state-of-the-art non-differentiable techniques. Our implementation has been made publicly available to facilitate further research on efficient architecture search algorithms.

Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve optimization, such as unsupervised pretraining. However, modern neural networks are able to achieve negligible training error on complex tasks, using only direct training with stochastic gradient descent. We introduce a simple analysis technique to look for evidence that such networks are overcoming local optima. We find that, in fact, on a straight path from initialization to solution, a variety of state of the art neural networks never encounter any significant obstacles.

Learned optimization has emerged as a promising alternative to hand-crafted optimizers, with the potential to discover stronger learned update rules that enable faster, hyperparameter-free training of neural networks. A critical element for practically useful learned optimizers, that can be used off-the-shelf after meta-training, is strong meta-generalization: the ability to apply the optimizers to new tasks. Recent state-of-the-art work in learned optimizers, VeLO (Metz et al., 2022), requires a large number of highly diverse meta-training tasks along with massive computational resources, 4000 TPU months, to achieve meta-generalization. This makes further improvements to such learned optimizers impractical. In this work, we identify several key elements in learned optimizer architectures and meta-training procedures that can lead to strong meta-generalization. We also propose evaluation metrics to reliably assess quantitative performance of an optimizer at scale on a set of evaluation tasks. Our proposed approach, Celo, makes a significant leap in improving the meta-generalization performance of learned optimizers and also outperforms tuned state-of-the-art optimizers on a diverse set of out-of-distribution tasks, despite being meta-trained for just 24 GPU hours.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

Large language models (LLMs) have recently emerged as powerful tools for tackling many language-processing tasks. Despite their success, training and fine-tuning these models is still far too computationally and memory intensive. In this paper, we identify and characterise the important components needed for effective model convergence using gradient descent. In doing so we find that the intermediate activations used to implement backpropagation can be excessively compressed without incurring any degradation in performance. This result leads us to a cheap and memory-efficient algorithm for both fine-tuning and pre-training LLMs. The proposed algorithm simply divides the tokens up into smaller sub-tokens before projecting them onto a fixed 1-dimensional subspace during the forward pass. These features are then coarsely reconstructed during the backward pass to implement the update rules. We confirm the effectiveness of our algorithm as being complimentary to many state-of-the-art PEFT methods on the VTAB-1k fine-tuning benchmark. Furthermore, we outperform QLoRA for fine-tuning LLaMA and show competitive performance against other memory-efficient pre-training methods on the large-scale C4 dataset.

Training large language models (LLMs) is often bottlenecked by extreme memory demands, with optimizer states dominating the footprint. Recent works mitigates this cost by projecting gradients into low-dimensional subspaces using sophisticated update strategies. In this paper, we analyze the dynamics of gradient space and its underlying subspaces. We find that while a small subspace captures most gradient energy, a significant portion still resides in the residual bulk; moreover, the influence of the core subspace diminishes over time and in deeper layers. We also observe that the gradient space exhibits near-flat curvature, calling for algorithms that explicitly account for this geometry. Motivated by these insights, we introduce a suite of randomized algorithms, GrassWalk and GrassJump, which exploit subspace and achieve state-of-the-art memory savings while improving performance on LLaMA-1B and LLaMA-7B pretraining.

We analyze how well pre-trained large language models (e.g., Llama2, GPT-4, Claude 3, etc) can do linear and non-linear regression when given in-context examples, without any additional training or gradient updates. Our findings reveal that several large language models (e.g., GPT-4, Claude 3) are able to perform regression tasks with a performance rivaling (or even outperforming) that of traditional supervised methods such as Random Forest, Bagging, or Gradient Boosting. For example, on the challenging Friedman #2 regression dataset, Claude 3 outperforms many supervised methods such as AdaBoost, SVM, Random Forest, KNN, or Gradient Boosting. We then investigate how well the performance of large language models scales with the number of in-context exemplars. We borrow from the notion of regret from online learning and empirically show that LLMs are capable of obtaining a sub-linear regret.

Training or finetuning large-scale language models (LLMs) requires substantial computation resources, motivating recent efforts to explore parameter-efficient adaptation to downstream tasks. One approach is to treat these models as black boxes and use forward passes (Inference APIs) to interact with them. Current research focuses on adapting these black-box models to downstream tasks using gradient-free prompt optimization, but this often involves an expensive process of searching task-specific prompts. Therefore, we are motivated to study black-box language model adaptation without prompt search. Specifically, we introduce a label-enhanced cross-attention network called CrossTune, which models the semantic relatedness between the input text sequence and task-specific label descriptions. Its effectiveness is examined in the context of few-shot text classification. To improve the generalization of CrossTune, we utilize ChatGPT to generate additional training data through in-context learning. A switch mechanism is implemented to exclude low-quality ChatGPT-generated data. Through extensive experiments on seven benchmark text classification datasets, we demonstrate that our proposed approach outperforms the previous state-of-the-art gradient-free black-box tuning method by 5.7% on average. Even without using ChatGPT-augmented data, CrossTune performs better or comparably than previous black-box tuning methods, suggesting the effectiveness of our approach.

Learned optimizers are powerful alternatives to hand-designed update rules like Adam, yet they have seen limited practical adoption since they often fail to meta-generalize beyond their training distribution and incur high meta-training cost. For instance, prior work, VeLO, scaled meta-training to 4,000 TPU months (sim10times GPT-3 compute) to meta-train a general-purpose optimizer but it failed to generalize beyond 600M parameters tasks. In this work, we present a surprising finding: by crafting a simple normalized optimizer architecture and augmenting meta-training, it becomes feasible to meta-train a performant general-purpose learned update rule on a tiny fraction of VeLO compute, 4.5 GPU hours to be precise. Our learned update rule scales stably to a billion-scale pretraining task (GPT-3 XL 1.3B) which is six orders of magnitude larger than its meta-training distribution. Furthermore, it shows strong performance across diverse out-of-distribution tasks and is compatible with modern optimization harness that includes orthogonalization, distinct update rules for input-output and hidden weights, and decoupled weight decay. In all, this work paves the way for practically applicable learnable optimization algorithms, unlocking exploration of richer meta-training and data curation recipes to further improve performance.

Adaptive optimization methods are widely recognized as among the most popular approaches for training Deep Neural Networks (DNNs). Techniques such as Adam, AdaGrad, and AdaHessian utilize a preconditioner that modifies the search direction by incorporating information about the curvature of the objective function. However, despite their adaptive characteristics, these methods still require manual fine-tuning of the step-size. This, in turn, impacts the time required to solve a particular problem. This paper presents an optimization framework named SANIA to tackle these challenges. Beyond eliminating the need for manual step-size hyperparameter settings, SANIA incorporates techniques to address poorly scaled or ill-conditioned problems. We also explore several preconditioning methods, including Hutchinson's method, which approximates the Hessian diagonal of the loss function. We conclude with an extensive empirical examination of the proposed techniques across classification tasks, covering both convex and non-convex contexts.

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

Large language models (LLMs) have revolutionized natural language understanding and generation but face significant memory bottlenecks during training. GaLore, Gradient Low-Rank Projection, addresses this issue by leveraging the inherent low-rank structure of weight gradients, enabling substantial memory savings without sacrificing performance. Recent works further extend GaLore from various aspects, including low-bit quantization and higher-order tensor structures. However, there are several remaining challenges for GaLore, such as the computational overhead of SVD for subspace updates and the integration with state-of-the-art training parallelization strategies (e.g., FSDP). In this paper, we present GaLore 2, an efficient and scalable GaLore framework that addresses these challenges and incorporates recent advancements. In addition, we demonstrate the scalability of GaLore 2 by pre-training Llama 7B from scratch using up to 500 billion training tokens, highlighting its potential impact on real LLM pre-training scenarios.

Learning the distance metric between pairs of examples is of great importance for learning and visual recognition. With the remarkable success from the state of the art convolutional neural networks, recent works have shown promising results on discriminatively training the networks to learn semantic feature embeddings where similar examples are mapped close to each other and dissimilar examples are mapped farther apart. In this paper, we describe an algorithm for taking full advantage of the training batches in the neural network training by lifting the vector of pairwise distances within the batch to the matrix of pairwise distances. This step enables the algorithm to learn the state of the art feature embedding by optimizing a novel structured prediction objective on the lifted problem. Additionally, we collected Online Products dataset: 120k images of 23k classes of online products for metric learning. Our experiments on the CUB-200-2011, CARS196, and Online Products datasets demonstrate significant improvement over existing deep feature embedding methods on all experimented embedding sizes with the GoogLeNet network.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

A common architectural choice for deep metric learning is a convolutional neural network followed by global average pooling (GAP). Albeit simple, GAP is a highly effective way to aggregate information. One possible explanation for the effectiveness of GAP is considering each feature vector as representing a different semantic entity and GAP as a convex combination of them. Following this perspective, we generalize GAP and propose a learnable generalized sum pooling method (GSP). GSP improves GAP with two distinct abilities: i) the ability to choose a subset of semantic entities, effectively learning to ignore nuisance information, and ii) learning the weights corresponding to the importance of each entity. Formally, we propose an entropy-smoothed optimal transport problem and show that it is a strict generalization of GAP, i.e., a specific realization of the problem gives back GAP. We show that this optimization problem enjoys analytical gradients enabling us to use it as a direct learnable replacement for GAP. We further propose a zero-shot loss to ease the learning of GSP. We show the effectiveness of our method with extensive evaluations on 4 popular metric learning benchmarks. Code is available at: GSP-DML Framework

We present a novel approach to feature labeling using gradient descent in token-space. While existing methods typically use language models to generate hypotheses about feature meanings, our method directly optimizes label representations by using a language model as a discriminator to predict feature activations. We formulate this as a multi-objective optimization problem in token-space, balancing prediction accuracy, entropy minimization, and linguistic naturalness. Our proof-of-concept experiments demonstrate successful convergence to interpretable single-token labels across diverse domains, including features for detecting animals, mammals, Chinese text, and numbers. Although our current implementation is constrained to single-token labels and relatively simple features, the results suggest that token-space gradient descent could become a valuable addition to the interpretability researcher's toolkit.

Optimization and generalization are two essential aspects of statistical machine learning. In this paper, we propose a framework to connect optimization with generalization by analyzing the generalization error based on the optimization trajectory under the gradient flow algorithm. The key ingredient of this framework is the Uniform-LGI, a property that is generally satisfied when training machine learning models. Leveraging the Uniform-LGI, we first derive convergence rates for gradient flow algorithm, then we give generalization bounds for a large class of machine learning models. We further apply our framework to three distinct machine learning models: linear regression, kernel regression, and two-layer neural networks. Through our approach, we obtain generalization estimates that match or extend previous results.

The performance of algorithms for neural architecture search strongly depends on the parametrization of the search space. We use contrastive learning to identify networks across different initializations based on their data Jacobians, and automatically produce the first architecture embeddings independent from the parametrization of the search space. Using our contrastive embeddings, we show that traditional black-box optimization algorithms, without modification, can reach state-of-the-art performance in Neural Architecture Search. As our method provides a unified embedding space, we perform for the first time transfer learning between search spaces. Finally, we show the evolution of embeddings during training, motivating future studies into using embeddings at different training stages to gain a deeper understanding of the networks in a search space.

We present a submission to the SemEval 2025 shared task on unlearning sensitive content from LLMs. Our approach employs negative preference optimization using low-rank adaptation. We show that we can utilize this combination to efficiently compute additional regularization terms, which help with unlearning stabilization. The results of our approach significantly exceed the shared task baselines.

Soft prompt tuning achieves superior performances across a wide range of few-shot tasks. However, the performances of prompt tuning can be highly sensitive to the initialization of the prompts. We also empirically observe that conventional prompt tuning methods cannot encode and learn sufficient task-relevant information from prompt tokens. In this work, we develop an information-theoretic framework that formulates soft prompt tuning as maximizing mutual information between prompts and other model parameters (or encoded representations). This novel view helps us to develop a more efficient, accurate and robust soft prompt tuning method InfoPrompt. With this framework, we develop two novel mutual information based loss functions, to (i) discover proper prompt initialization for the downstream tasks and learn sufficient task-relevant information from prompt tokens and (ii) encourage the output representation from the pretrained language model to be more aware of the task-relevant information captured in the learnt prompt. Extensive experiments validate that InfoPrompt can significantly accelerate the convergence of the prompt tuning and outperform traditional prompt tuning methods. Finally, we provide a formal theoretical result for showing to show that gradient descent type algorithm can be used to train our mutual information loss.

Training with larger mini-batches improves the convergence rate and can yield superior performance. However, training with large mini-batches becomes prohibitive for Large Language Models (LLMs), due to the large GPU memory requirement. To address this problem, an effective approach is finding small mini-batch coresets that closely match the gradient of larger mini-batches. However, this approach becomes infeasible and ineffective for LLMs, due to the highly imbalanced mixture of sources in language data, use of the Adam optimizer, and the very large gradient dimensionality of LLMs. In this work, we address the above challenges by proposing Coresets for Training LLMs (CoLM). First, we show that mini-batch coresets found by gradient matching do not contain representative examples of the small sources w.h.p., and thus including all examples of the small sources in the mini-batch coresets is crucial for optimal performance. Second, we normalize the gradients by their historical exponential to find mini-batch coresets for training with Adam. Finally, we leverage zeroth-order methods to find smooth gradient of the last V-projection matrix and sparsify it to keep the dimensions with the largest normalized gradient magnitude. We apply CoLM to fine-tuning Phi-2, Phi-3, Zephyr, and Llama-3 models with LoRA on MathInstruct and SuperGLUE benchmark. Remarkably, CoLM reduces the memory requirement of fine-tuning by 2x and even outperforms training with 4x larger mini-batches. Moreover, CoLM seamlessly integrates with existing memory-efficient training methods like LoRA, further reducing the memory requirements of training LLMs. Our code is available at https://github.com/BigML-CS-UCLA/CoLM.

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.

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and f-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-k loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3times faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

In this work, we address the problem of modifying textual attributes of sentences. Given an input sentence and a set of attribute labels, we attempt to generate sentences that are compatible with the conditioning information. To ensure that the model generates content compatible sentences, we introduce a reconstruction loss which interpolates between auto-encoding and back-translation loss components. We propose an adversarial loss to enforce generated samples to be attribute compatible and realistic. Through quantitative, qualitative and human evaluations we demonstrate that our model is capable of generating fluent sentences that better reflect the conditioning information compared to prior methods. We further demonstrate that the model is capable of simultaneously controlling multiple attributes.

Text embeddings are essential for many tasks, such as document retrieval, clustering, and semantic similarity assessment. In this paper, we study how to contrastively train text embedding models in a compute-optimal fashion, given a suite of pre-trained decoder-only language models. Our innovation is an algorithm that produces optimal configurations of model sizes, data quantities, and fine-tuning methods for text-embedding models at different computational budget levels. The resulting recipe, which we obtain through extensive experiments, can be used by practitioners to make informed design choices for their embedding models. Specifically, our findings suggest that full fine-tuning and low-rank adaptation fine-tuning produce optimal models at lower and higher computational budgets respectively.

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

It is widely believed that the implicit regularization of SGD is fundamental to the impressive generalization behavior we observe in neural networks. In this work, we demonstrate that non-stochastic full-batch training can achieve comparably strong performance to SGD on CIFAR-10 using modern architectures. To this end, we show that the implicit regularization of SGD can be completely replaced with explicit regularization even when comparing against a strong and well-researched baseline. Our observations indicate that the perceived difficulty of full-batch training may be the result of its optimization properties and the disproportionate time and effort spent by the ML community tuning optimizers and hyperparameters for small-batch training.

A novel gradient boosting framework is proposed where shallow neural networks are employed as ``weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered outperforming results against state-of-the-art boosting methods in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of each model components and model hyperparameters.

At present, the mechanisms of in-context learning in Transformers are not well understood and remain mostly an intuition. In this paper, we suggest that training Transformers on auto-regressive objectives is closely related to gradient-based meta-learning formulations. We start by providing a simple weight construction that shows the equivalence of data transformations induced by 1) a single linear self-attention layer and by 2) gradient-descent (GD) on a regression loss. Motivated by that construction, we show empirically that when training self-attention-only Transformers on simple regression tasks either the models learned by GD and Transformers show great similarity or, remarkably, the weights found by optimization match the construction. Thus we show how trained Transformers become mesa-optimizers i.e. learn models by gradient descent in their forward pass. This allows us, at least in the domain of regression problems, to mechanistically understand the inner workings of in-context learning in optimized Transformers. Building on this insight, we furthermore identify how Transformers surpass the performance of plain gradient descent by learning an iterative curvature correction and learn linear models on deep data representations to solve non-linear regression tasks. Finally, we discuss intriguing parallels to a mechanism identified to be crucial for in-context learning termed induction-head (Olsson et al., 2022) and show how it could be understood as a specific case of in-context learning by gradient descent learning within Transformers. Code to reproduce the experiments can be found at https://github.com/google-research/self-organising-systems/tree/master/transformers_learn_icl_by_gd .

Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. This success is partially attributed to architectural innovations such as convolutional and long short-term memory networks. The main motivation for these architectural innovations is that they capture better domain knowledge, and importantly are easier to optimize than more basic architectures. Recently, more complex architectures such as Neural Turing Machines and Memory Networks have been proposed for tasks including question answering and general computation, creating a new set of optimization challenges. In this paper, we discuss a low-overhead and easy-to-implement technique of adding gradient noise which we find to be surprisingly effective when training these very deep architectures. The technique not only helps to avoid overfitting, but also can result in lower training loss. This method alone allows a fully-connected 20-layer deep network to be trained with standard gradient descent, even starting from a poor initialization. We see consistent improvements for many complex models, including a 72% relative reduction in error rate over a carefully-tuned baseline on a challenging question-answering task, and a doubling of the number of accurate binary multiplication models learned across 7,000 random restarts. We encourage further application of this technique to additional complex modern architectures.

Current pre-trained language models rely on large datasets for achieving state-of-the-art performance. However, past research has shown that not all examples in a dataset are equally important during training. In fact, it is sometimes possible to prune a considerable fraction of the training set while maintaining the test performance. Established on standard vision benchmarks, two gradient-based scoring metrics for finding important examples are GraNd and its estimated version, EL2N. In this work, we employ these two metrics for the first time in NLP. We demonstrate that these metrics need to be computed after at least one epoch of fine-tuning and they are not reliable in early steps. Furthermore, we show that by pruning a small portion of the examples with the highest GraNd/EL2N scores, we can not only preserve the test accuracy, but also surpass it. This paper details adjustments and implementation choices which enable GraNd and EL2N to be applied to NLP.

Recent work on mini-batch consistency (MBC) for set functions has brought attention to the need for sequentially processing and aggregating chunks of a partitioned set while guaranteeing the same output for all partitions. However, existing constraints on MBC architectures lead to models with limited expressive power. Additionally, prior work has not addressed how to deal with large sets during training when the full set gradient is required. To address these issues, we propose a Universally MBC (UMBC) class of set functions which can be used in conjunction with arbitrary non-MBC components while still satisfying MBC, enabling a wider range of function classes to be used in MBC settings. Furthermore, we propose an efficient MBC training algorithm which gives an unbiased approximation of the full set gradient and has a constant memory overhead for any set size for both train- and test-time. We conduct extensive experiments including image completion, text classification, unsupervised clustering, and cancer detection on high-resolution images to verify the efficiency and efficacy of our scalable set encoding framework. Our code is available at github.com/jeffwillette/umbc

Large language models (LLMs) have shown increasing power on various natural language processing (NLP) tasks. However, tuning these models for downstream tasks usually needs exorbitant costs or is unavailable due to commercial considerations. Recently, black-box tuning has been proposed to address this problem by optimizing task-specific prompts without accessing the gradients and hidden representations. However, most existing works have yet fully exploited the potential of gradient-free optimization under the scenario of few-shot learning. In this paper, we describe BBT-RGB, a suite of straightforward and complementary techniques for enhancing the efficiency and performance of black-box optimization. Specifically, our method includes three plug-and-play components: (1) Two-stage derivative-free optimization strategy that facilitates fast convergence and mitigates overfitting; (2) Automatic verbalizer construction with its novel usage under few-shot settings; (3) Better prompt initialization policy based on instruction search and auto-selected demonstration. Extensive experiments across various tasks on natural language understanding and inference demonstrate the effectiveness of our method. Our codes are publicly available at https://github.com/QiushiSun/BBT-RGB.

Going beyond stochastic gradient descent (SGD), what new phenomena emerge in wide neural networks trained by adaptive optimizers like Adam? Here we show: The same dichotomy between feature learning and kernel behaviors (as in SGD) holds for general optimizers as well, including Adam -- albeit with a nonlinear notion of "kernel." We derive the corresponding "neural tangent" and "maximal update" limits for any architecture. Two foundational advances underlie the above results: 1) A new Tensor Program language, NEXORT, that can express how adaptive optimizers process gradients into updates. 2) The introduction of bra-ket notation to drastically simplify expressions and calculations in Tensor Programs. This work summarizes and generalizes all previous results in the Tensor Programs series of papers.

The composition of training data mixtures is critical for effectively training large language models (LLMs), as it directly impacts their performance on downstream tasks. Our goal is to identify an optimal data mixture to specialize an LLM for a specific task with access to only a few examples. Traditional approaches to this problem include ad-hoc reweighting methods, importance sampling, and gradient alignment techniques. This paper focuses on gradient alignment and introduces Dynamic Gradient Alignment (DGA), a scalable online gradient alignment algorithm. DGA dynamically estimates the pre-training data mixture on which the models' gradients align as well as possible with those of the model on the specific task. DGA is the first gradient alignment approach that incurs minimal overhead compared to standard pre-training and outputs a competitive model, eliminating the need for retraining the model. Experimentally, we demonstrate significant improvements over importance sampling in two key scenarios: (i) when the pre-training set is small and importance sampling overfits due to limited data; and (ii) when there is insufficient specialized data, trapping importance sampling on narrow pockets of data. Our findings underscore the effectiveness of gradient alignment methods in optimizing training data mixtures, particularly in data-constrained environments, and offer a practical solution for enhancing LLM performance on specific tasks with limited data availability.

This report is a reproducibility study of the paper "CDUL: CLIP-Driven Unsupervised Learning for Multi-Label Image Classification" (Abdelfattah et al, ICCV 2023). Our report makes the following contributions: (1) We provide a reproducible, well commented and open-sourced code implementation for the entire method specified in the original paper. (2) We try to verify the effectiveness of the novel aggregation strategy which uses the CLIP model to initialize the pseudo labels for the subsequent unsupervised multi-label image classification task. (3) We try to verify the effectiveness of the gradient-alignment training method specified in the original paper, which is used to update the network parameters and pseudo labels. The code can be found at https://github.com/cs-mshah/CDUL

In this work we propose a simple and efficient framework for learning sentence representations from unlabelled data. Drawing inspiration from the distributional hypothesis and recent work on learning sentence representations, we reformulate the problem of predicting the context in which a sentence appears as a classification problem. Given a sentence and its context, a classifier distinguishes context sentences from other contrastive sentences based on their vector representations. This allows us to efficiently learn different types of encoding functions, and we show that the model learns high-quality sentence representations. We demonstrate that our sentence representations outperform state-of-the-art unsupervised and supervised representation learning methods on several downstream NLP tasks that involve understanding sentence semantics while achieving an order of magnitude speedup in training time.

Training neural networks requires significant computational resources and energy. Methods like mixed-precision and quantization-aware training reduce bit usage, yet they still depend heavily on computationally expensive gradient-based optimization. In this work, we propose a paradigm shift: eliminate gradients altogether. One might hope that, in a finite quantized space, finding optimal weights with out gradients would be easier but we theoretically prove that this problem is NP-hard even in simple settings where the continuous case is efficiently solvable. To address this, we introduce a novel heuristic optimization framework that avoids full weight updates and significantly improves efficiency. Empirically, our method achieves performance comparable to that of full-precision gradient-based training on standard datasets and architectures, while using up to 3x less energy and requiring up to 5x fewer parameter updates.

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elaborate on this basic idea. This paper makes two contributions: it introduces SmoothGrad, a simple method that can help visually sharpen gradient-based sensitivity maps, and it discusses lessons in the visualization of these maps. We publish the code for our experiments and a website with our results.

Despite the recent progresses, particularly in developing Language Models, there are fundamental challenges and unanswered questions about how such models can continually learn/memorize, self-improve, and find effective solutions. In this paper, we present a new learning paradigm, called Nested Learning (NL), that coherently represents a machine learning model with a set of nested, multi-level, and/or parallel optimization problems, each of which with its own context flow. Through the lenses of NL, existing deep learning methods learns from data through compressing their own context flow, and in-context learning naturally emerges in large models. NL suggests a philosophy to design more expressive learning algorithms with more levels, resulting in higher-order in-context learning and potentially unlocking effective continual learning capabilities. We advocate for NL by presenting three core contributions: (1) Expressive Optimizers: We show that known gradient-based optimizers, such as Adam, SGD with Momentum, etc., are in fact associative memory modules that aim to compress the gradients' information (by gradient descent). Building on this insight, we present other more expressive optimizers with deep memory and/or more powerful learning rules; (2) Self-Modifying Learning Module: Taking advantage of NL's insights on learning algorithms, we present a sequence model that learns how to modify itself by learning its own update algorithm; and (3) Continuum Memory System: We present a new formulation for memory system that generalizes the traditional viewpoint of long/short-term memory. Combining our self-modifying sequence model with the continuum memory system, we present a continual learning module, called Hope, showing promising results in language modeling, knowledge incorporation, and few-shot generalization tasks, continual learning, and long-context reasoning tasks.

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.

Training large neural language models on large datasets is resource- and time-intensive. These requirements create a barrier to entry, where those with fewer resources cannot build competitive models. This paper presents various techniques for making it possible to (a) train a large language model using resources that a modest research lab might have, and (b) train it in a reasonable amount of time. We provide concrete recommendations for practitioners, which we illustrate with a case study: a T5 model for Danish, the first for this language.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

We propose a new dataset distillation algorithm using reparameterization and convexification of implicit gradients (RCIG), that substantially improves the state-of-the-art. To this end, we first formulate dataset distillation as a bi-level optimization problem. Then, we show how implicit gradients can be effectively used to compute meta-gradient updates. We further equip the algorithm with a convexified approximation that corresponds to learning on top of a frozen finite-width neural tangent kernel. Finally, we improve bias in implicit gradients by parameterizing the neural network to enable analytical computation of final-layer parameters given the body parameters. RCIG establishes the new state-of-the-art on a diverse series of dataset distillation tasks. Notably, with one image per class, on resized ImageNet, RCIG sees on average a 108% improvement over the previous state-of-the-art distillation algorithm. Similarly, we observed a 66% gain over SOTA on Tiny-ImageNet and 37% on CIFAR-100.

Two major sources of training data exist for post-training modern language models: online (model-generated rollouts) data, and offline (human or other-model demonstrations) data. These two types of data are typically used by approaches like Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT), respectively. In this paper, we show that these approaches are not in contradiction, but are instances of a single optimization process. We derive a Unified Policy Gradient Estimator, and present the calculations of a wide spectrum of post-training approaches as the gradient of a common objective under different data distribution assumptions and various bias-variance tradeoffs. The gradient estimator is constructed with four interchangeable parts: stabilization mask, reference policy denominator, advantage estimate, and likelihood gradient. Motivated by our theoretical findings, we propose Hybrid Post-Training (HPT), an algorithm that dynamically selects different training signals. HPT is designed to yield both effective exploitation of demonstration and stable exploration without sacrificing learned reasoning patterns. We provide extensive experiments and ablation studies to verify the effectiveness of our unified theoretical framework and HPT. Across six mathematical reasoning benchmarks and two out-of-distribution suites, HPT consistently surpasses strong baselines across models of varying scales and families.

Natural Language Processing (NLP) systems are increasingly taking the form of multi-stage pipelines involving multiple distinct language models (LMs) and prompting strategies. Here we address the question of how to fine-tune such systems to improve their performance. We cast this as a problem of optimizing the underlying LM weights and the prompting strategies together, and consider a challenging but highly realistic scenario in which we have no gold labels for any intermediate stages in the pipeline. To address this challenge, we evaluate approximate optimization strategies in which we bootstrap training labels for all pipeline stages and use these to optimize the pipeline's prompts and fine-tune its weights alternatingly. In experiments with multi-hop QA, mathematical reasoning, and feature-based classification, we find that simple approaches for optimizing the prompts and weights together outperform directly optimizing weights alone and prompts alone by up to 65% and 5%, respectively, on average across LMs and tasks. We will release our new optimizers in DSPy at http://dspy.ai

Prompt tuning, a recently emerging paradigm, enables the powerful vision-language pre-training models to adapt to downstream tasks in a parameter -- and data -- efficient way, by learning the ``soft prompts'' to condition frozen pre-training models. Though effective, it is particularly problematic in the few-shot scenario, where prompt tuning performance is sensitive to the initialization and requires a time-consuming process to find a good initialization, thus restricting the fast adaptation ability of the pre-training models. In addition, prompt tuning could undermine the generalizability of the pre-training models, because the learnable prompt tokens are easy to overfit to the limited training samples. To address these issues, we introduce a novel Gradient-RegulAted Meta-prompt learning (GRAM) framework that jointly meta-learns an efficient soft prompt initialization for better adaptation and a lightweight gradient regulating function for strong cross-domain generalizability in a meta-learning paradigm using only the unlabeled image-text pre-training data. Rather than designing a specific prompt tuning method, our GRAM can be easily incorporated into various prompt tuning methods in a model-agnostic way, and comprehensive experiments show that GRAM brings about consistent improvement for them in several settings (i.e., few-shot learning, cross-domain generalization, cross-dataset generalization, etc.) over 11 datasets. Further, experiments show that GRAM enables the orthogonal methods of textual and visual prompt tuning to work in a mutually-enhanced way, offering better generalizability beyond the uni-modal prompt tuning methods.

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This accounts for gradients being local linear approximations which lose their relevance as the iterate moves along the loss landscape. This work questions the use of a single EMA to accumulate past gradients and empirically demonstrates how this choice can be sub-optimal: a single EMA cannot simultaneously give a high weight to the immediate past, and a non-negligible weight to older gradients. Building on this observation, we propose AdEMAMix, a simple modification of the Adam optimizer with a mixture of two EMAs to better take advantage of past gradients. Our experiments on language modeling and image classification show -- quite surprisingly -- that gradients can stay relevant for tens of thousands of steps. They help to converge faster, and often to lower minima: e.g., a 1.3B parameter AdEMAMix LLM trained on 101B tokens performs comparably to an AdamW model trained on 197B tokens (+95%). Moreover, our method significantly slows-down model forgetting during training. Our work motivates further exploration of different types of functions to leverage past gradients, beyond EMAs.

Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on items' ranks), their derivatives are either undefined or zero everywhere. This makes them unsuitable for gradient-based optimisation, which is the usual method of learning appropriate scoring functions. Commonly used LTR loss functions are only loosely related to the evaluation metrics, causing a mismatch between the optimisation objective and the evaluation criterion. In this paper, we address this mismatch by proposing NeuralNDCG, a novel differentiable approximation to NDCG. Since NDCG relies on the non-differentiable sorting operator, we obtain NeuralNDCG by relaxing that operator using NeuralSort, a differentiable approximation of sorting. As a result, we obtain a new ranking loss function which is an arbitrarily accurate approximation to the evaluation metric, thus closing the gap between the training and the evaluation of LTR models. We introduce two variants of the proposed loss function. Finally, the empirical evaluation shows that our proposed method outperforms previous work aimed at direct optimisation of NDCG and is competitive with the state-of-the-art methods.

Recent diagnostic datasets on compositional generalization, such as SCAN (Lake and Baroni, 2018) and COGS (Kim and Linzen, 2020), expose severe problems in models trained from scratch on these datasets. However, in contrast to this poor performance, state-of-the-art models trained on larger and more general datasets show better generalization ability. In this work, to reconcile this inconsistency, we conduct an empirical analysis by training Transformer models on a variety of training sets with different data factors, including dataset scale, pattern complexity, example difficulty, etc. First, we show that increased dataset complexity can lead to better generalization behavior on multiple different generalization challenges. To further understand this improvement, we show two axes of the benefit from more complex datasets: they provide more diverse examples so compositional understanding becomes more effective, and they also prevent ungeneralizable memorization of the examples due to reduced example repetition frequency. Finally, we explore how training examples of different difficulty levels influence generalization differently. On synthetic datasets, simple examples invoke stronger compositionality than hard examples do. On larger-scale real language datasets, while hard examples become more important potentially to ensure decent data coverage, a balanced mixture of simple and hard examples manages to induce the strongest generalizability. The code and data for this work are available at https://github.com/owenzx/data4comp