ICLR 2025 论文列表

Decentralized federated learning (DFL) captures FL settings where both (i) model updates and (ii) model aggregations are exclusively carried out by the clients without a central server. Existing DFL works have mostly focused on settings where clients conduct a fixed number of local updates between local model exchanges, overlooking heterogeneity and dynamics in communication and computation capabilities. In this work, we propose Decentralized Sporadic Federated Learning ($\texttt{DSpodFL}$), a DFL methodology built on a generalized notion of *sporadicity* in both local gradient and aggregation processes. $\texttt{DSpodFL}$ subsumes many existing decentralized optimization methods under a unified algorithmic framework by modeling the per-iteration (i) occurrence of gradient descent at each client and (ii) exchange of models between client pairs as arbitrary indicator random variables, thus capturing *heterogeneous and time-varying* computation/communication scenarios. We analytically characterize the convergence behavior of $\texttt{DSpodFL}$ for both convex and non-convex models and for both constant and diminishing learning rates, under mild assumptions on the communication graph connectivity, data heterogeneity across clients, and gradient noises. We show how our bounds recover existing results from decentralized gradient descent as special cases. Experiments demonstrate that $\texttt{DSpodFL}$ consistently achieves improved training speeds compared with baselines under various system settings.

Adversarially robust generalization of Graph Convolutional Networks (GCNs) has garnered significant attention in various security-sensitive application areas, driven by intrinsic adversarial vulnerability. Albeit remarkable empirical advancement, theoretical understanding of the generalization behavior of GCNs subjected to adversarial attacks remains elusive. To make progress on the mystery, we establish unified high-probability generalization bounds for GCNs in the context of node classification, by leveraging adversarial Transductive Rademacher Complexity (TRC) and developing a novel contraction technique on graph convolution. Our bounds capture the interaction between generalization error and adversarial perturbations, revealing the importance of key quantities in mitigating the negative effects of perturbations, such as low-dimensional feature projection, perturbation-dependent norm regularization, normalized graph matrix, proper number of network layers, etc. Furthermore, we provide TRC-based bounds of popular GCNs with $\ell_r$-norm-additive perturbations for arbitrary $r\geq 1$. A comparison of theoretical results demonstrates that specific network architectures (e.g., residual connection) can help alleviate the cumulative effect of perturbations during the forward propagation of deep GCNs. Experimental results on benchmark datasets validate our theoretical findings.

Multi-modal Large Language Models (MLLMs) frequently face challenges from concept drift when dealing with real-world streaming data, wherein distributions change unpredictably. This mainly includes gradual drift due to long-tailed data and sudden drift from Out-Of-Distribution (OOD) data, both of which have increasingly drawn the attention of the research community. While these issues have been extensively studied in the individual domain of vision or language, their impacts on MLLMs in concept drift settings remain largely underexplored. In this paper, we reveal the susceptibility and vulnerability of Vision-Language (VL) models to significant biases arising from gradual drift and sudden drift, particularly in the pre-training. To effectively address these challenges, we propose a unified framework that extends concept drift theory to the multi-modal domain, enhancing the adaptability of the VL model to unpredictable distribution changes. Additionally, a T-distribution based drift adapter is proposed to effectively mitigate the bias induced by the gradual drift, which also facilitates the model in distinguishing sudden distribution changes through explicit distribution modeling. Extensive experiments demonstrate our method enhances the efficiency and accuracy of image-text alignment in the pre-training of VL models, particularly in the concept drift scenario. Moreover, various downstream tasks exhibit significant improvements in our model's ability to adapt to the long-tailed open world. Furthermore, we create a set of multi-modal datasets called OpenMMlo, specifically tailored for the long-tailed open-world setting, to validate our findings. To foster the development of the multi-modal community, we have made both OpenMMlo datasets and our code publicly available at: https://github.com/XiaoyuYoung/ConceptDriftMLLMs.

Deep learning has achieved advancements across a variety of forefront fields. However, its inherent 'black box' characteristic poses challenges to the comprehension and trustworthiness of the decision-making processes within neural networks. To mitigate these challenges, we introduce InnerSightNet, an inner information analysis algorithm designed to illuminate the inner workings of deep neural networks through the perspectives of community. This approach is aimed at deciphering the intricate patterns of neurons within deep neural networks, thereby shedding light on the networks' information processing and decision-making pathways. InnerSightNet operates in three primary phases, 'neuronization-aggregation-evaluation'. Initially, it transforms learnable units into a structured network of neurons. Subsequently, these neurons are aggregated into distinct communities according to representation attributes. The final phase involves the evaluation of these communities' roles and functionalities, to unpick the information flow and decision-making. By transcending focus on single-layer or individual neuron, InnerSightNet broadens the horizon for deep neural network interpretation. InnerSightNet offers a unique vantage point, enabling insights into the collective behavior of communities within the overarching architecture, thereby enhancing transparency and trust in deep learning systems.

Recently, there have been numerous studies on feature learning with neural networks, specifically on learning single- and multi-index models where the target is a function of a low-dimensional projection of the input. Prior works have shown that in high dimensions, the majority of the compute and data resources are spent on recovering the low-dimensional projection; once this subspace is recovered, the remainder of the target can be learned independently of the ambient dimension. However, implications of feature learning in adversarial settings remain unexplored. In this work, we take the first steps towards understanding adversarially robust feature learning with neural networks. Specifically, we prove that the hidden directions of a multi-index model offer a Bayes optimal low-dimensional projection for robustness against $\ell_2$-bounded adversarial perturbations under the squared loss, assuming that the multi-index coordinates are statistically independent from the rest of the coordinates. Therefore, robust learning can be achieved by first performing standard feature learning, then robustly tuning a linear readout layer on top of the standard representations. In particular, we show that adversarially robust learning is just as easy as standard learning. Specifically, the additional number of samples needed to robustly learn multi-index models when compared to standard learning, does not depend on dimensionality.

Biological and artificial neural networks develop internal representations that enable them to perform complex tasks. In artificial networks, the effectiveness of these models relies on their ability to build task specific representation, a process influenced by interactions among datasets, architectures, initialization strategies, and optimization algorithms. Prior studies highlight that different initializations can place networks in either a lazy regime, where representations remain static, or a rich/feature learning regime, where representations evolve dynamically. Here, we examine how initialization influences learning dynamics in deep linear neural networks, deriving exact solutions for lambda-balanced initializations-defined by the relative scale of weights across layers. These solutions capture the evolution of representations and the Neural Tangent Kernel across the spectrum from the rich to the lazy regimes. Our findings deepen the theoretical understanding of the impact of weight initialization on learning regimes, with implications for continual learning, reversal learning, and transfer learning, relevant to both neuroscience and practical applications.

We study the problem of learning from truncated samples: instead of observing samples from some underlying population $p^\ast$, we observe only the examples that fall in some survival set $S \subset \mathbb{R}^d$ whose probability mass (measured with respect to $p^\ast$) is at least $\alpha$. Assuming membership oracle access to the truncation set $S$, prior works obtained algorithms for the case where $p^\ast$ is Gaussian or more generally an exponential family with strongly convex likelihood --- albeit with a super-polynomial dependency on the (inverse) survival mass $1/\alpha$ both in terms of runtime and in number of oracle calls to the set $S$. In this work we design a new learning method with runtime and query complexity polynomial in $1/\alpha$. Our result significantly improves over the prior works by focusing on efficiently solving the underlying optimization problem using a general purpose optimization algorithm with minimal assumptions.

We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case.

High-quality data is essential for training large generative models, yet the vast reservoir of real data available online has become nearly depleted. Consequently, models increasingly generate their own data for further training, forming Self-consuming Training Loops (STLs). However, the empirical results have been strikingly inconsistent: some models degrade or even collapse, while others successfully avoid these failures, leaving a significant gap in theoretical understanding to explain this discrepancy. This paper introduces the intriguing notion of *recursive stability* and presents the first theoretical generalization analysis, revealing how both model architecture and the proportion between real and synthetic data influence the success of STLs. We further extend this analysis to transformers in in-context learning, showing that even a constant-sized proportion of real data ensures convergence, while also providing insights into optimal synthetic data sizing.

Complex classification scenarios, including long-tailed learning, domain adaptation, and transfer learning, present substantial challenges for traditional algorithms. Conditional class probability (CCP) predictions have recently become critical components of many state-of-the-art algorithms designed to address these challenging scenarios. Among kernel methods, kernel logistic regression (KLR) is distinguished by its effectiveness in predicting CCPs through the minimization of the cross-entropy (CE) loss. Despite the empirical success of CCP-based approaches, the theoretical understanding of their performance, particularly regarding the CE loss, remains limited. In this paper, we bridge this gap by demonstrating that KLR-based algorithms achieve minimax optimal convergence rates for the CE loss under mild assumptions in these complex tasks, thereby establishing their theoretical efficiency in such demanding contexts.

Recent work in language modeling has raised the possibility of “self-improvement,” where an LLM evaluates and refines its own generations to achieve higher performance without external feedback. It is impossible for this self-improvement to create information that is not already in the model, so why should we expect that this will lead to improved capabilities? We offer a new theoretical perspective on the capabilities of self-improvement through a lens we refer to as “sharpening.” Motivated by the observation that language models are often better at verifying response quality than they are at generating correct responses, we formalize self-improvement as using the model itself as a verifier during post-training in order to ‘sharpen’ the model to one placing large mass on high-quality sequences, thereby amortizing the expensive inference-time computation of generating good sequences. We begin by introducing a new statistical framework for sharpening in which the learner has sample access to a pre-trained base policy. Then, we analyze two natural families of self improvement algorithms based on SFT and RLHF. We find that (i) the SFT-based approach is minimax optimal whenever the initial model has sufficient coverage, but (ii) the RLHF-based approach can improve over SFT-based self- improvement by leveraging online exploration, bypassing the need for coverage. We view these findings as a starting point toward a foundational understanding that can guide the design and evaluation of self-improvement algorithms.

We study the problem of learning multi-index models in high-dimensions using a two-layer neural network trained with the mean-field Langevin algorithm. Under mild distributional assumptions on the data, we characterize the effective dimension $d_{\mathrm{eff}}$ that controls both sample and computational complexity by utilizing the adaptivity of neural networks to latent low-dimensional structures. When the data exhibit such a structure, $d_{\mathrm{eff}}$ can be significantly smaller than the ambient dimension. We prove that the sample complexity grows almost linearly with $d_{\mathrm{eff}}$, bypassing the limitations of the information and generative exponents that appeared in recent analyses of gradient-based feature learning. On the other hand, the computational complexity may inevitably grow exponentially with $d_{\mathrm{eff}}$ in the worst-case scenario. Motivated by improving computational complexity, we take the first steps towards polynomial time convergence of the mean-field Langevin algorithm by investigating a setting where the weights are constrained to be on a compact manifold with positive Ricci curvature, such as the hypersphere. There, we study assumptions under which polynomial time convergence is achievable, whereas similar assumptions in the Euclidean setting lead to exponential time complexity.

This paper primarily investigates the convergence of the Neural Tangent Kernel (NTK) in classification problems. This study firstly show the strictly positive definiteness of NTK of multi-layer fully connected neural networks and residual neural networks. Then, through a contradiction argument, it indicates that, during training with the cross-entropy loss function, the neural network parameters diverge due to the strictly positive definiteness of the NTK. Consequently, the empirical NTK does not consistently converge but instead diverges as time approaches infinity. This finding implies that NTK theory is not applicable in this context, highlighting significant theoretical implications for the study of neural networks in classification problems. These results can also be easily generalized to other network structures, provided that the NTK is strictly positive definite.

Risk-sensitive linear quadratic regulator is one of the most fundamental problems in risk-sensitive optimal control. In this paper, we study online adaptive control of risk-sensitive linear quadratic regulator in the finite horizon episodic setting. We propose a simple least-squares greedy algorithm and show that it achieves $\widetilde{\mathcal{O}}(\log N)$ regret under a specific identifiability assumption, where $N$ is the total number of episodes. If the identifiability assumption is not satisfied, we propose incorporating exploration noise into the least-squares-based algorithm, resulting in an algorithm with $\widetilde{\mathcal{O}}(\sqrt{N})$ regret. To our best knowledge, this is the first set of regret bounds for episodic risk-sensitive linear quadratic regulator. Our proof relies on perturbation analysis of less-standard Riccati equations for risk-sensitive linear quadratic control, and a delicate analysis of the loss in the risk-sensitive performance criterion due to applying the suboptimal controller in the online learning process.

It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on the results of one or more Ordinary Least Squares (OLS) regressions, raising the question: given a dataset, can we certify the robustness of an OLS fit on this dataset to the removal of a given number of samples? Brute-force techniques quickly break down even on small datasets. Existing approaches which go beyond brute force either can only find candidate small subsets to remove (but cannot certify their non-existence) [BGM20, KZC21], are computationally intractable beyond low dimensional settings [MR22], or require very strong assumptions on the data distribution and too many samples to give reasonable bounds in practice [BP21, FH23]. We present an efficient algorithm for certifying the robustness of linear regressions to removals of samples. We implement our algorithm and run it on several landmark econometrics datasets with hundreds of dimensions and tens of thousands of samples, giving the first non-trivial certificates of robustness to sample removal for datasets of dimension $4$ or greater. We prove that under distributional assumptions on a dataset, the bounds produced by our algorithm are tight up to a $1 + o(1)$ multiplicative factor.

We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded $F_{1}$-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive a generalization bound that combines a covering number argument for compositionality, and the $F_{1}$-norm (or the related Barron norm) for large width adaptivity. We show that the global minimizer of the regularized loss of DNNs can fit for example the composition of two functions $f^{\*}=h\circ g$ from a small number of observations, assuming $g$ is smooth/regular and reduces the dimensionality (e.g. $g$ could be the quotient map of the symmetries of $f^{*}$), so that $h$ can be learned in spite of its low regularity. The measures of regularity we consider is the Sobolev norm with different levels of differentiability, which is well adapted to the $F_{1}$ norm. We compute scaling laws empirically and observe phase transitions depending on whether $g$ or $h$ is harder to learn, as predicted by our theory.

The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To relax this restrictive assumption, subsequent efforts have been devoted to establish "Gaussian equivalent principles" by studying scenarios of Gaussian universality where the asymptotic performance of ML methods on non-Gaussian data remains unchanged when replaced with Gaussian data having the *same mean and covariance*. Beyond the realm of Gaussian universality, there are few exact results on how the data distribution affects the learning performance. In this article, we provide a precise high-dimensional characterization of empirical risk minimization, for classification under a general mixture data setting of *linear factor models* that extends Gaussian mixtures. The Gaussian universality is shown to break down under this setting, in the sense that the asymptotic learning performance depends on the data distribution *beyond* the class means and covariances. To clarify the limitations of Gaussian universality in the classification of mixture data and to understand the impact of its breakdown, we specify conditions for Gaussian universality and discuss their implications for the choice of loss function.

In deep learning theory, a critical question is to understand how neural networks learn hierarchical features. In this work, we study the learning of hierarchical polynomials of multiple nonlinear features using three-layer neural networks. We examine a broad class of functions of the form $f^{\star}=g^{\star}\circ \mathbf{p}$, where $\mathbf{p}:\mathbb{R}^{d} \rightarrow \mathbb{R}^{r}$ represents multiple quadratic features with $r \ll d$ and $g^{\star}:\mathbb{R}^{r}\rightarrow \mathbb{R}$ is a polynomial of degree $p$. This can be viewed as a nonlinear generalization of the multi-index model, and also an expansion upon previous work on nonlinear feature learning that focused only on a single feature (i.e. $r = 1$). Our primary contribution shows that a three-layer neural network trained via layerwise gradient descent suffices for - complete recovery of the space spanned by the nonlinear features - efficient learning of the target function $f^{\star}=g^{\star}\circ \mathbf{p}$ or transfer learning of $f=g\circ \mathbf{p}$ with a different link function within $\widetilde{\mathcal{O}}(d^4)$ samples and polynomial time. For such hierarchical targets, our result substantially improves the sample complexity ${\Theta}(d^{2p})$ of the kernel methods, demonstrating the power of efficient feature learning. It is important to highlight that our results leverage novel techniques and thus manage to go beyond all prior settings such as single-index and multi-index models as well as models depending just on one nonlinear feature, contributing to a more comprehensive understanding of feature learning in deep learning.

Recent research in the field of machine learning has increasingly focused on the memorization capacity of Transformers, but how efficient they are is not yet well understood. We demonstrate that Transformers can memorize labels with $\tilde{O}(\sqrt{N})$ parameters in a next-token prediction setting for $N$ input sequences of length $n$, which is proved to be optimal up to logarithmic factors. This indicates that Transformers can efficiently perform memorization with little influence from the input length $n$ owing to the benefit of parameter sharing. We also analyze the memorization capacity in the sequence-to-sequence setting, and find that $\tilde{O}(\sqrt{nN})$ parameters are not only sufficient, but also necessary at least for Transformers with hardmax. These results suggest that while self-attention mechanisms can efficiently identify input sequences, the feed-forward network becomes a bottleneck when associating a label to each token.