NeurIPS 2024 论文列表

Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical optimization problems, leading to the emergence of differentiable optimization layers that permit gradient back-propagation. However, real-world scenarios often involve large-scale datasets and numerous constraints, presenting significant challenges. Current methods for differentiating optimization problems typically rely on implicit differentiation, which necessitates costly computations on the Jacobian matrices, resulting in low efficiency. In this paper, we introduce BPQP, a differentiable convex optimization framework designed for efficient end-to-end learning. To enhance efficiency, we reformulate the backward pass as a simplified and decoupled quadratic programming problem by leveraging the structural properties of the Karush–Kuhn–Tucker (KKT) matrix. This reformulation enables the use of first-order optimization algorithms in calculating the backward pass gradients, allowing our framework to potentially utilize any state-of-the-art solver. As solver technologies evolve, BPQP can continuously adapt and improve its efficiency. Extensive experiments on both simulated and real-world datasets demonstrate that BPQP achieves a significant improvement in efficiency—typically an order of magnitude faster in overall execution time compared to other differentiable optimization layers. Our results not only highlight the efficiency gains of BPQP but also underscore its superiority over differential optimization layer baselines.

Distributionally Robust Optimization (DRO) accounts for uncertainty in data distributions by optimizing the model performance against the worst possible distribution within an ambiguity set. In this paper, we propose a DRO framework that relies on a new distance inspired by Unbalanced Optimal Transport (UOT). The proposed UOT distance employs a soft penalization term instead of hard constraints, enabling the construction of an ambiguity set that is more resilient to outliers. Under smoothness conditions, we establish strong duality of the proposed DRO problem. Moreover, we introduce a computationally efficient Lagrangian penalty formulation for which we show that strong duality also holds. Finally, we provide empirical results that demonstrate that our method offers improved robustness to outliers and is computationally less demanding for regression and classification tasks.

Stochastic second-order methods are known to achieve fast local convergence in strongly convex optimization by relying on noisy Hessian estimates to precondition the gradient. Yet, most of these methods achieve superlinear convergence only when the stochastic Hessian noise diminishes, requiring an increase in the per-iteration cost as time progresses. Recent work in \cite{na2022hessian} addressed this issue via a Hessian averaging scheme that achieves a superlinear convergence rate without increasing the per-iteration cost. However, the considered method exhibits a slow global convergence rate, requiring up to $\tilde{\mathcal{O}}(\kappa^2)$ iterations to reach the superlinear rate of $\tilde{\mathcal{O}}((1/t)^{t/2})$, where $\kappa$ is the problem's condition number. In this paper, we propose a novel stochastic Newton proximal extragradient method that significantly improves these bounds, achieving a faster global linear rate and reaching the same fast superlinear rate in $\tilde{\mathcal{O}}(\kappa)$ iterations. We achieve this by developing a novel extension of the Hybrid Proximal Extragradient (HPE) framework, which simultaneously achieves fast global and local convergence rates for strongly convex functions with access to a noisy Hessian oracle.

We propose a new variant of the Adam optimizer called MicroAdam that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed into the optimizer state, thereby reducing its memory footprint significantly. We control the resulting compression error via a novel instance of the classical *error feedback* mechanism from distributed optimization in which *the error correction information is itself compressed* to allow for practical memory gains. We prove that the resulting approach maintains theoretical convergence guarantees competitive to those of AMSGrad, while providing good practical performance. Specifically, we show that MicroAdam can be implemented efficiently on GPUs: on both million-scale (BERT) and billion-scale (LLaMA) models, MicroAdam provides practical convergence competitive to that of the uncompressed Adam baseline, with lower memory usage and similar running time. Our code is available at https://github.com/IST-DASLab/MicroAdam.

In this article, we study the behaviour of continuous-time gradient methods on a two-layer linear network with square loss. A dichotomy between SGD and GD is revealed: GD preserves the rank at initialization while (label noise) SGD diminishes the rank regardless of the initialization. We demonstrate this rank deficiency by studying the time evolution of the *determinant* of a matrix of parameters. To further understand this phenomenon, we derive the stochastic differential equation (SDE) governing the eigenvalues of the parameter matrix. This SDE unveils a *replusive force* between the eigenvalues: a key regularization mechanism which induces rank deficiency. Our results are well supported by experiments illustrating the phenomenon beyond linear networks and regression tasks.

Adam has been shown to outperform gradient descent on large language models by a larger margin than on other tasks, but it is unclear why. We show that a key factor in this performance gap is the heavy-tailed class imbalance found in language tasks. When trained with gradient descent, the loss of infrequent words decreases more slowly than the loss of frequent ones. This leads to a slow decrease on the average loss as most samples come from infrequent words. On the other hand, Adam and sign-based methods are less sensitive to this problem. To establish that this behavior is caused by class imbalance, we show empirically that it can be reproduced across architectures and data types, on language transformers, vision CNNs, and linear models. On a linear model with cross-entropy loss, we show that class imbalance leads to imbalanced, correlated gradients and Hessians that have been hypothesized to benefit Adam. We also prove that, in continuous time, gradient descent converges slowly on low-frequency classes while sign descent does not.

Collaborative learning is an important tool to train multiple clients more effectively by enabling communication among clients. Identifying helpful clients, however, presents challenging and often introduces significant overhead. In this paper, we model **client-selection** and **model-training** as two interconnected optimization problems, proposing a novel bilevel optimization problem for collaborative learning. We introduce **CoBo**, a *scalable* and *elastic*, SGD-type alternating optimization algorithm that efficiently addresses these problem with theoretical convergence guarantees. Empirically, **CoBo** achieves superior performance, surpassing popular personalization algorithms by 9.3% in accuracy on a task with high heterogeneity, involving datasets distributed among 80 clients.

To improve performance in contemporary deep learning, one is interested in scaling up the neural network in terms of both the number and the size of the layers. When ramping up the width of a single layer, graceful scaling of training has been linked to the need to normalize the weights and their updates in the "natural norm" particular to that layer. In this paper, we significantly generalize this idea by defining the modular norm, which is the natural norm on the full weight space of any neural network architecture. The modular norm is defined recursively in tandem with the network architecture itself. We show that the modular norm has several promising applications. On the practical side, the modular norm can be used to normalize the updates of any base optimizer so that the learning rate becomes transferable across width and depth. This means that the user does not need to compute optimizer-specific scale factors in order to scale training. On the theoretical side, we show that for any neural network built from "well-behaved" atomic modules, the gradient of the network is Lipschitz-continuous in the modular norm, with the Lipschitz constant admitting a simple recursive formula. This characterization opens the door to porting standard ideas in optimization theory over to deep learning. We have created a Python package called Modula that automatically normalizes weight updates in the modular norm of the architecture. Both the Modula package and code for our experiments are provided in the supplementary material.

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related tasks. The attention mechanism in the Transformer architecture is a critical component of LLMs, as it allows the model to selectively focus on specific input parts. The softmax unit, which is a key part of the attention mechanism, normalizes the attention scores. Hence, the performance of LLMs in various NLP tasks depends significantly on the crucial role played by the attention mechanism with the softmax unit. In-context learning is one of the celebrated abilities of recent LLMs. Without further parameter updates, Transformers can learn to predict based on few in-context examples. However, the reason why Transformers becomes in-context learners is not well understood. Recently, in-context learning has been studied from a mathematical perspective with simplified linear self-attention without softmax unit. Based on a linear regression formulation $\min_x\| Ax - b \|_2$, existing works show linear Transformers' capability of learning linear functions in context. The capability of Transformers with softmax unit approaching full Transformers, however, remains unexplored. In this work, we study the in-context learning based on a softmax regression formulation $\min_{x} \| \langle \exp(Ax), {\bf 1}_n \rangle^{-1} \exp(Ax) - b \|_2$. We show the upper bounds of the data transformations induced by a single self-attention layer with softmax unit and by gradient-descent on a $\ell_2$ regression loss for softmax prediction function. Our theoretical results imply that when training self-attention-only Transformers for fundamental regression tasks, the models learned by gradient-descent and Transformers show great similarity.

Although Large Visual Language Models (LVLMs) have demonstrated exceptional abilities in understanding multimodal data, they invariably suffer from hallucinations, leading to a disconnection between the generated text and the corresponding images. Almost all current visual contrastive decoding methods attempt to mitigate these hallucinations by introducing visual uncertainty information that appropriately widens the contrastive logits gap between hallucinatory and targeted ones. However, due to uncontrollable nature of the global visual uncertainty, they struggle to precisely induce the hallucinatory tokens, which severely limits their effectiveness in mitigating hallucinations and may even lead to the generation of undesired hallucinations. To tackle this issue, we conducted the theoretical analysis to promote the effectiveness of contrast decoding. Building on this insight, we introduce a novel optimization strategy named Hallucination-Induced Optimization (HIO). This strategy seeks to amplify the contrast between hallucinatory and targeted tokens relying on a fine-tuned theoretical preference model (i.e., Contrary Bradley-Terry Model), thereby facilitating efficient contrast decoding to alleviate hallucinations in LVLMs. Extensive experimental research demonstrates that our HIO strategy can effectively reduce hallucinations in LVLMs, outperforming state-of-the-art methods across various benchmarks.

Curvature information -- particularly, the largest eigenvalue of the loss Hessian, known as the sharpness -- often forms the basis for learning rate tuners. However, recent work has shown that the curvature information undergoes complex dynamics during training, going from a phase of increasing sharpness to eventual stabilization. We analyze the closed-loop feedback effect between learning rate tuning and curvature. We find that classical learning rate tuners may yield greater one-step loss reduction, yet they ultimately underperform in the long term when compared to constant learning rates in the full batch regime. These models break the stabilization of the sharpness, which we explain using a simplified model of the joint dynamics of the learning rate and the curvature. To further investigate these effects, we introduce a new learning rate tuning method, Curvature Dynamics Aware Tuning (CDAT), which prioritizes long term curvature stabilization over instantaneous progress on the objective. In the full batch regime, CDAT shows behavior akin to prefixed warm-up schedules on deep learning objectives, outperforming tuned constant learning rates. In the mini batch regime, we observe that stochasticity introduces confounding effects that explain the previous success of some learning rate tuners at appropriate batch sizes. Our findings highlight the critical role of understanding the joint dynamics of the learning rate and curvature, beyond greedy minimization, to diagnose failures and design effective adaptive learning rate tuners.

Internet of Things and Deep Learning are synergetically and exponentially growing industrial fields with a massive call for their unification into a common framework called Edge AI. While on-device inference is a well-explored topic in recent research, backpropagation remains an open challenge due to its prohibitive computational and memory costs compared to the extreme resource constraints of embedded devices. Drawing on tensor decomposition research, we tackle the main bottleneck of backpropagation, namely the memory footprint of activation map storage. We investigate and compare the effects of activation compression using Singular Value Decomposition and its tensor variant, High-Order Singular Value Decomposition. The application of low-order decomposition results in considerable memory savings while preserving the features essential for learning, and also offers theoretical guarantees to convergence. Experimental results obtained on main-stream architectures and tasks demonstrate Pareto-superiority over other state-of-the-art solutions, in terms of the trade-off between generalization and memory footprint.

Per-example gradient norms are a vital ingredient for estimating gradient noise scale (GNS) with minimal variance. Observing the tensor contractions required to compute them, we propose a method with minimal FLOPs in 3D or greater tensor regimes by simultaneously computing the norms while computing the parameter gradients. Using this method we are able to observe the GNS of different layers at higher accuracy than previously possible. We find that the total GNS of contemporary transformer models is predicted well by the GNS of only the normalization layers. As a result, focusing only on the normalization layer, we develop a custom kernel to compute the per-example gradient norms while performing the LayerNorm backward pass with zero throughput overhead. Tracking GNS on only those layers, we are able to guide a practical batch size schedule that reduces training time by 18% on a Chinchilla-optimal language model.

In recent years, Dynamic Sparse Training (DST) has emerged as an alternative to post-training pruning for generating efficient models. In principle, DST allows for a much more memory efficient training process, as it maintains sparsity throughout the entire training run. However, current DST implementations fail to capitalize on this. Because sparse matrix multiplication is much less efficient than dense matrix multiplication on GPUs, most implementations simulate sparsity by masking weights. In this paper, we leverage recent advances in semi-structured sparse training to apply DST in the domain of classification with large output spaces, where memory-efficiency is paramount. With a label space of possibly millions of candidates, the classification layer alone will consume several gigabytes of memory. Switching from a dense to a fixed fan-in sparse layer updated with sparse evolutionary training (SET); however, severely hampers training convergence, especially at the largest label spaces. We find that the gradients fed back from the classifier into the text encoder make it much more difficult to learn good input representations, despite using a dense encoder. By employing an intermediate layer or adding an auxiliary training objective, we recover most of the generalisation performance of the dense model. Overall, we demonstrate the applicability of DST in a challenging domain, characterized by a highly skewed label distribution, that lies outside of DST's typical benchmark datasets, and enable end-to-end training with millions of labels on commodity hardware.

Teaching is a potentially effective approach for understanding interactions among multiple intelligences. Previous explorations have convincingly shown that teaching presents additional opportunities for observation and demonstration within the learning model, such as data distillation and selection. However, the underlying optimization principles and convergence of interactive teaching lack theoretical analysis, and in this regard co-teaching serves as a notable prototype. In this paper, we discuss its role as a reduction of the larger loss landscape derived from Sharpness-Aware Minimization (SAM). Then, we classify it as an iterative parameter estimation process using Expectation-Maximization. The convergence of this typical interactive teaching is achieved by continuously optimizing a variational lower bound on the log marginal likelihood. This lower bound represents the expected value of the log posterior distribution of the latent variables under a scaled, factorized variational distribution. To further enhance interactive teaching's performance, we incorporate SAM's strong generalization information into interactive teaching, referred as Sharpness Reduction Interactive Teaching (SRIT). This integration can be viewed as a novel sequential optimization process. Finally, we validate the performance of our approach through multiple experiments.

Despite advances using low-rank adapters and quantization, pretraining of large models on consumer hardware has not been possible without model sharding, offloading during training, or per-layer gradient updates. To address these limitations, we propose Low-Rank Adapters for Quantized Training (LoQT), a method for efficiently training quantized models. LoQT uses gradient-based tensor factorization to initialize low-rank trainable weight matrices that are periodically merged into quantized full-rank weight matrices. Our approach is suitable for both pretraining and fine-tuning models. We demonstrate this for language modeling and downstream task adaptation, finding that LoQT enables efficient training of models up to 7B parameters on a 24GB GPU. We also demonstrate the feasibility of training a 13B model using per-layer gradient updates on the same hardware.

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose a novel method by reformulating them into functionally constrained problems. Our method achieves near-optimal rates for both smooth and nonsmooth problems. To the best of our knowledge, this is the first near-optimal algorithm that works under standard assumptions of smoothness or Lipschitz continuity for the objective functions.

Recently, a wide range of memory-efficient LLM training algorithms have gained substantial popularity. These methods leverage the low-rank structure of gradients to project optimizer states into a subspace using projection matrix found by singular value decomposition (SVD). However, convergence of these algorithms is highly dependent on the update rules of their projection matrix. In this work, we provide the \emph{first} convergence guarantee for arbitrary update rules of projection matrix. This guarantee is generally applicable to optimizers that can be analyzed with Hamiltonian Descent, including most common ones, such as LION, Adam. Inspired by our theoretical understanding, we propose Online Subspace Descent, a new family of subspace descent optimizer without SVD. Instead of updating projection matrix with eigenvectors, Online Subspace Descent updates projection matrix wtih online PCA. Online Subspace Descent is flexible and introduces only minimum overhead to training. We demonstrate that, for the task of pretraining LLaMA models ranging from 60M to 1B parameters on the C4 dataset, Online Subspace Descent achieves lower perplexity than state-of-the-art low-rank training methods across different settings and narrows the gap with full-rank baselines.

Class incremental learning (CIL) trains a network on sequential tasks with separated categories in each task but suffers from catastrophic forgetting, where models quickly lose previously learned knowledge when acquiring new tasks. The generalized CIL (GCIL) aims to address the CIL problem in a more real-world scenario, where incoming data have mixed data categories and unknown sample size distribution. Existing attempts for the GCIL either have poor performance or invade data privacy by saving exemplars. In this paper, we propose a new exemplar-free GCIL technique named generalized analytic continual learning (GACL). The GACL adopts analytic learning (a gradient-free training technique) and delivers an analytical (i.e., closed-form) solution to the GCIL scenario. This solution is derived via decomposing the incoming data into exposed and unexposed classes, thereby attaining a weight-invariant property, a rare yet valuable property supporting an equivalence between incremental learning and its joint training. Such an equivalence is crucial in GCIL settings as data distributions among different tasks no longer pose challenges to adopting our GACL. Theoretically, this equivalence property is validated through matrix analysis tools. Empirically, we conduct extensive experiments where, compared with existing GCIL methods, our GACL exhibits a consistently leading performance across various datasets and GCIL settings. Source code is available at https://github.com/CHEN-YIZHU/GACL.