ICLR 2025 Papers

Multi-Source Domain Generalization (DG) is the task of training on multiple source domains and achieving high classification performance on unseen target domains. Recent methods combine robust features from web-scale pretrained backbones with new features learned from source data, and this has dramatically improved benchmark results. However, it remains unclear if DG finetuning methods are becoming better over time, or if improved benchmark performance is simply an artifact of stronger pre-training. Prior studies have shown that perceptual similarity to pre-training data correlates with zero-shot performance, but we find the effect limited in the DG setting. Instead, we posit that having perceptually similar data in pretraining is not enough; and that it is how well these data were learned that determines performance. This leads us to introduce the Alignment Hypothesis, which states that the final DG performance will be high if and only if alignment of image and class label text embeddings is high. Our experiments confirm the Alignment Hypothesis is true, and we use it as an analysis tool of existing DG methods evaluated on DomainBed datasets by splitting evaluation data into In-pretraining (IP) and Out-of-pretraining (OOP). We show that all evaluated DG methods struggle on DomainBed-OOP, while recent methods excel on DomainBed-IP. Put together, our findings highlight the need for DG methods which can generalize beyond pretraining alignment. We release DomainBed-OOP at https://huggingface.co/datasets/PTeterwak/DomainBed_OOP.

Neural networks often learn simple explanations that fit the majority of the data while memorizing exceptions that deviate from these explanations. This behavior leads to poor generalization when the learned explanations rely on spurious correlations. In this work, we formalize $\textit{the interplay between memorization and generalization}$, showing that spurious correlations would particularly lead to poor generalization when are combined with memorization. Memorization can reduce training loss to zero, leaving no incentive to learn robust, generalizable patterns. To address this, we propose $\textit{memorization-aware training}$ (MAT), which uses held-out predictions as a signal of memorization to shift a model's logits. MAT encourages learning robust patterns invariant across distributions, improving generalization under distribution shifts.

The weak-to-strong generalization phenomenon is the driver for important machine learning applications including highly data-efficient learning and, most recently, performing superalignment. While decades of research have resulted in numerous algorithms that produce strong empirical performance, understanding what aspects of data enable weak-to-strong generalization has been understudied. We propose a simple data-centric mechanism that characterizes weak-to-strong generalization: the overlap density. Intuitively, generalization tracks the number of points that contain overlaps, i.e., both easy patterns (learnable by a weak model) and challenging patterns (only learnable by a stronger model), as with such points, weak predictions can be used to learn challenging patterns by stronger models. And, we provide a practical overlap detection algorithm to find overlap density from data. Finally, we provide an algorithm to learn, among multiple sources of data, which to query when seeking to maximize overlap density and thereby enhance weak-to-strong generalization. We provide a theoretical result showing that the generalization benefit is a function of the overlap density and a regret bound of our data selection algorithm. Empirically, we validate the mechanism and the overlap detection algorithm on a wide array of settings.

Counting constitutes a core skill underlying a wide range of tasks, such as formal language recognition, multi-hop reasoning and simulating algorithms. Generaliz- ing counting inductively is central to task success on out-of-distribution (OOD) instances where testing inputs are longer than those seen in training. While there is a large body of literature reporting poor length generalization in language models, few papers have tried to distill the “reasoning” failure to the simplest case of count- ing failure. We aim to provide a broader picture on whether various language model architectures can a) learn to count, and b) generalize counting inductively. This work provides extensive empirical results on architectures ranging from RNNs, Transformers, State-Space Models and RWKV. We present carefully-designed task formats, auxiliary tasks and positional embeddings to avoid limitations in general- ization with OOD-position and OOD-vocabulary. We find that while traditional RNNs trivially achieve inductive counting, Transformers have to rely on positional embeddings (PEs) to count OOD. Further analyses on interpreting the learned solution reveal that different PEs encode different inductive biases that facilitate counting in different task formats. As counting is the basis for many arguments concerning the expressivity of Transformers, our finding calls for the community to reexamine the application scope of primitive functions defined in formal charac- terizations. Finally, modern RNNs also largely underperform traditional RNNs in generalizing counting inductively, hinting at the tradeoff modern RNNs struggle to balance between parallelized training and maintaining their recurrent nature.

Canonicalization, a popular method for generating invariant or equivariant function classes from arbitrary function sets, involves initial data projection onto a reduced input space subset, followed by applying any learning method to the projected dataset. Despite recent research on the expressive power and continuity of functions represented by canonicalization, its generalization capabilities remain less explored. This paper addresses this gap by theoretically examining the generalization benefits and sample complexity of canonicalization, comparing them with group averaging, another popular technique for creating invariant or equivariant function classes. Our findings reveal two distinct regimes where canonicalization may outperform or underperform compared to group averaging, with precise quantification of this phase transition in terms of sample size, group action characteristics, and a newly introduced concept of alignment. To the best of our knowledge, this study represents the first theoretical exploration of such behavior, offering insights into the relative effectiveness of canonicalization and group averaging under varying conditions.

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold---referred to as critical complexity---where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28 LLMs including both open-sourced models such as LLaMA and Qwen families, and closed-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

Large language models (LLMs) have demonstrated remarkable in-context learning (ICL) abilities. However, existing theoretical analysis of ICL primarily exhibits two limitations: \textbf{(a) Limited \textit{i.i.d.} Setting.} Most studies focus on supervised function learning tasks where prompts are constructed with \textit{i.i.d.} input-label pairs. This \textit{i.i.d.} assumption diverges significantly from real language learning scenarios where prompt tokens are interdependent. \textbf{(b) Lack of Emergence Explanation.} Most literature answers \textbf{\textit{what}} ICL does from an implicit optimization perspective but falls short in elucidating \textbf{\textit{how}} ICL emerges and the impact of pre-training phase on ICL. In our paper, to extend (a), we adopt a more practical paradigm, \textbf{\textit{auto-regressive next-token prediction (AR-NTP)}}, which closely aligns with the actual training of language models. Specifically, within AR-NTP, we emphasize prompt token-dependency, which involves predicting each subsequent token based on the preceding sequence. To address (b), we formalize a systematic pre-training and ICL framework, highlighting the layer-wise structure of sequences and topics, alongside a two-level expectation. In conclusion, we present data-dependent, topic-dependent and optimization-dependent PAC-Bayesian generalization bounds for pre-trained LLMs, investigating that \textbf{\textit{ICL emerges from the generalization of sequences and topics}}. Our theory is supported by experiments on numerical linear dynamic systems, synthetic GINC and real-world language datasets.

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.

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks. A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Finally, extensive tests including trajectory prediction of a real irregular object and model predictive control of a quadrotor with various uncertainties, are implemented, indicating significant improvements over state-of-the-art model-based and learning-based methods.

Federated Learning (FL) on graphs enables collaborative model training to enhance performance without compromising the privacy of each client. However, existing methods often overlook the mutable nature of graph data, which frequently introduces new nodes and leads to shifts in label distribution. Since they focus solely on performing well on each client's local data, they are prone to overfitting to their local distributions (i.e., local overfitting), which hinders their ability to generalize to unseen data with diverse label distributions. In contrast, our proposed method, FedLoG, effectively tackles this issue by mitigating local overfitting. Our model generates global synthetic data by condensing the reliable information from each class representation and its structural information across clients. Using these synthetic data as a training set, we alleviate the local overfitting problem by adaptively generalizing the absent knowledge within each local dataset. This enhances the generalization capabilities of local models, enabling them to handle unseen data effectively. Our model outperforms baselines in our proposed experimental settings, which are designed to measure generalization power to unseen data in practical scenarios. Our code is available at https://github.com/sung-won-kim/FedLoG

Learning disentangled representations of concepts and re-composing them in unseen ways is crucial for generalizing to out-of-domain situations. However, the underlying properties of concepts that enable such disentanglement and compositional generalization remain poorly understood. In this work, we propose the principle of interaction asymmetry which states: "Parts of the same concept have more complex interactions than parts of different concepts". We formalize this via block diagonality conditions on the $(n+1)$th order derivatives of the generator mapping concepts to observed data, where different orders of "complexity" correspond to different $n$. Using this formalism, we prove that interaction asymmetry enables both disentanglement and compositional generalization. Our results unify recent theoretical results for learning concepts of objects, which we show are recovered as special cases with $n=0$ or $1$. We provide results for up to $n=2$, thus extending these prior works to more flexible generator functions, and conjecture that the same proof strategies generalize to larger $n$. Practically, our theory suggests that, to disentangle concepts, an autoencoder should penalize its latent capacity and the interactions between concepts during decoding. We propose an implementation of these criteria using a flexible Transformer-based VAE, with a novel regularizer on the attention weights of the decoder. On synthetic image datasets consisting of objects, we provide evidence that this model can achieve comparable object disentanglement to existing models that use more explicit object-centric priors.

Invariant risk minimization is an important general machine learning framework that has recently been interpreted as a total variation model (IRM-TV). However, how to improve out-of-distribution (OOD) generalization in the IRM-TV setting remains unsolved. In this paper, we extend IRM-TV to a Lagrangian multiplier model named OOD-TV-IRM. We find that the autonomous TV penalty hyperparameter is exactly the Lagrangian multiplier. Thus OOD-TV-IRM is essentially a primal-dual optimization model, where the primal optimization minimizes the entire invariant risk and the dual optimization strengthens the TV penalty. The objective is to reach a semi-Nash equilibrium where the balance between the training loss and OOD generalization is maintained. We also develop a convergent primal-dual algorithm that facilitates an adversarial learning scheme. Experimental results show that OOD-TV-IRM outperforms IRM-TV in most situations.

In-Context Learning (ICL) has significantly expanded the general-purpose nature of large language models, allowing them to adapt to novel tasks using merely the inputted context. This has motivated a series of papers that analyze tractable synthetic domains and postulate precise mechanisms that may underlie ICL. However, the use of relatively distinct setups that often lack a sequence modeling nature to them makes it unclear how general the reported insights from such studies are. Motivated by this, we propose a synthetic sequence modeling task that involves learning to simulate a finite mixture of Markov chains. As we show, models trained on this task reproduce most well-known results on ICL, hence offering a unified setting for studying the concept. Building on this setup, we demonstrate we can explain a model’s behavior by decomposing it into four broad algorithms that combine a fuzzy retrieval vs. inference approach with either unigram or bigram statistics of the context. These algorithms engage in a competitive dynamics to dominate model behavior, with the precise experimental conditions dictating which algorithm ends up superseding others: e.g., we find merely varying context size or amount of training yields (at times sharp) transitions between which algorithm dictates the model behavior, revealing a mechanism that explains the transient nature of ICL. In this sense, we argue ICL is best thought of as a mixture of different algorithms, each with its own peculiarities, instead of a monolithic capability. This also implies that making general claims about ICL that hold universally across all settings may be infeasible.

The heavy-ball momentum method accelerates gradient descent with a momentum term but lacks accelerated convergence for general smooth strongly convex problems. This work introduces the Accelerated Over-Relaxation Heavy-Ball (AOR-HB) method, the first variant with provable global and accelerated convergence for such problems. AOR-HB closes a long-standing theoretical gap, extends to composite convex optimization and min-max problems, and achieves optimal complexity bounds. It offers three key advantages: (1) broad generalization ability, (2) potential to reshape acceleration techniques, and (3) conceptual clarity and elegance compared to existing methods.

Why do larger language models generalize better? To explore this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla scaling laws. We introduce a novel, fully empirical Freedman-type martingale concentration inequality that tightens existing bounds by accounting for the variance of the loss function. The generalization bound can be broken into three contributions: the number of parameters per token, the loss variance, and the quantization error at a fixed bitrate. As language models are scaled up, the number of parameters per data point stays constant; however, both the loss variance and the quantization error decrease, implying that larger models should have \emph{smaller} generalization gaps. We examine why larger models tend to be more quantizable from an information theoretic perspective, showing that the rate at which they can integrate new information grows slower than their capacity on the compute optimal frontier. From these findings we produce a scaling law for the generalization gap, showing that our bounds decrease in a predictable way.

The world is understood from various modalities, such as appearance, sound, language, etc. Since each modality only partially represents objects in a certain physical meaning, leveraging additional ones is beneficial in both theory and practice. However, exploiting novel modalities normally requires cross-modal pairs corresponding to the same instance, which is extremely resource-consuming and sometimes even impossible, making knowledge exploration of novel modalities largely restricted. To seek practical multi-modal learning, here we study Out-of-Modal (OOM) Generalization as an initial attempt to generalize to an unknown modality without given instance-level modal correspondence. Specifically, we consider Semi-Supervised and Unsupervised scenarios of OOM Generalization, where the first has scarce correspondences and the second has none, and propose connect & explore (COX) to solve these problems. COX first connects OOM data and known In-Modal (IM) data through a variational information bottleneck framework to extract shared information. Then, COX leverages the shared knowledge to create emergent correspondences, which is theoretically justified from an information-theoretic perspective. As a result, the label information on OOM data emerges along with the correspondences, which help explore the OOM data with unknown knowledge, thus benefiting generalization results. We carefully evaluate the proposed COX method under various OOM generalization scenarios, verifying its effectiveness and extensibility.

The energy-based model provides a unified framework for various learning models where an energy value is assigned to each configuration of random variables based on probability. Recently, different methods have been proposed to derive an energy value out of the logits of a classifier for out-of-distribution (OOD) detection or OOD generalization. However, these methods mainly focus on the energy difference between in-distribution and OOD data samples, neglecting the energy difference among in-distribution data samples. In this paper, we show that the energy among in-distribution data also requires attention. We propose to investigate the energy difference between in-distribution data samples. Both empirically and theoretically, we show that previous methods for subpopulation shift (\emph{e.g.}, long-tail classification) such as data re-weighting and margin control apply implicit energy regularization and we provide a unified framework from the energy perspective. With the influence function, we further extend the energy regularization framework to OOD generalization scenarios where the distribution shift is more implicit compared to the long-tail recognition scenario. We conduct experiments on long-tail datasets, subpopulation shift benchmarks, and OOD generalization benchmarks to show the effectiveness of the proposed energy regularization.

The impressive capabilities of large language models (LLMs) have sparked debate over whether these models genuinely generalize to unseen tasks or predominantly rely on memorizing vast amounts of pretraining data. To explore this issue, we introduce an extended concept of memorization, distributional memorization, which measures the correlation between the LLM output probabilities and the pretraining data frequency. To effectively capture task-specific pretraining data frequency, we propose a novel task-gram language model, which is built by counting the co-occurrence of semantically related $n$-gram pairs from task inputs and outputs in the pretraining corpus. Using the Pythia models trained on the Pile dataset, we evaluate four distinct tasks: machine translation, factual question answering, world knowledge understanding, and math reasoning. Our findings reveal varying levels of memorization, with the strongest effect observed in factual question answering. Furthermore, while model performance improves across all tasks as LLM size increases, only factual question answering shows an increase in memorization, whereas machine translation and reasoning tasks exhibit greater generalization, producing more novel outputs. This study demonstrates that memorization plays a larger role in simpler, knowledge-intensive tasks, while generalization is the key for harder, reasoning-based tasks, providing a scalable method for analyzing large pretraining corpora in greater depth.

Superalignment, where humans act as weak supervisors for superhuman models, has become a crucial problem with the rapid development of Large Language Models (LLMs). Recent work has preliminarily studied this problem by using weak models to supervise strong models, and discovered that weakly supervised strong students can consistently outperform weak teachers towards the alignment target, leading to a weak-to-strong generalization phenomenon. However, we are concerned that behind such a promising phenomenon, whether there exists an issue of weak-to-strong deception, where strong models deceive weak models by exhibiting well-aligned in areas known to weak models but producing misaligned behaviors in cases weak models do not know. We take an initial step towards exploring this security issue in a specific but realistic multi-objective alignment case, where there may be some alignment targets conflicting with each other (e.g., helpfulness v.s. harmlessness). We aim to explore whether, in such cases, strong models might deliberately make mistakes in areas known to them but unknown to weak models within one alignment dimension, in exchange for a higher reward in another dimension. Through extensive experiments in both the reward modeling and preference optimization scenarios, we find: (1) The weak-to-strong deception phenomenon exists across all settings. (2) The deception intensifies as the capability gap between weak and strong models increases. (3) Bootstrapping with an intermediate model can mitigate the deception to some extent, though its effectiveness remains limited. Our work highlights the urgent need to pay more attention to the true reliability of superalignment.