Principled Out-of-Distribution Generalization via Simplicity
Jiawei Ge, Amanda Wang, Shange Tang, Chi Jin
TL;DR
This paper proposes a theoretical framework that explains how the simplest models consistent with training data tend to generalize better out-of-distribution, supported by sample complexity guarantees for learning such models.
Contribution
It introduces a formal simplicity-based approach to OOD generalization and provides sharp sample complexity bounds for learning the simplest consistent model.
Findings
Simplest models aligned with human expectations generalize better OOD.
Established sample complexity guarantees for simplicity-based OOD learning.
Analyzed regimes with fixed and smoothness-based simplicity gaps.
Abstract
Modern foundation models exhibit remarkable out-of-distribution (OOD) generalization, solving tasks far beyond the support of their training data. However, the theoretical principles underpinning this phenomenon remain elusive. This paper investigates this problem by examining the compositional generalization abilities of diffusion models in image generation. Our analysis reveals that while neural network architectures are expressive enough to represent a wide range of models -- including many with undesirable behavior on OOD inputs -- the true, generalizable model that aligns with human expectations typically corresponds to the simplest among those consistent with the training data. Motivated by this observation, we develop a theoretical framework for OOD generalization via simplicity, quantified using a predefined simplicity metric. We analyze two key regimes: (1) the constant-gap…
Peer Reviews
Decision·Submitted to ICLR 2026
This paper tackles the important question of OOD generalization. The paper is a great read to understand what kind of model helps handle OOD best. It gives a clear principle: among all the models that can fit your data, the simplest one is the one you should trust to generalize. This is a very useful idea. This is a great way to frame the problem as simplicity or say regularization is not just for fighting noise; it is the main tool for selecting the one true model from all these perfect solutio
The main weakness is that there are not many experiments to support the paper empirically. The MLP experiment is very clean and simple, which is good for explaining the idea. However, this is very different from the complex tasks that real foundation models face. It is hard to be sure that this "simplicity" principle will work for real, large-scale computer vision or language problems.
The paper introduces a simplicity metric $R$ and formalizes the intuition that simplicity aligns with generalization into a rigorous theoretical framework for out-of-distribution (OOD) generalization. It makes a clear theoretical contribution toward understanding why and how machine learning models are able to generalize beyond their training distributions.
The paper uses diffusion model compositional generalization as a motivating background, but there remains a substantial gap between its empirical and theoretical analyses and real diffusion model settings: 1. The paper studies the negative log-likelihood loss, which is only a lower bound of the denoising score matching objective used in diffusion models [1]. 2. There is a large discrepancy between the OOD generalization behavior demonstrated in diffusion models (Section 3.1) and the simplified
The paper's observation that simplicity may be aligned with OOD generalization ability is interesting. The paper seems technically strong, in the sense that their learning-theoretical analysis of OOD generalization seems solid and clearly stated.
1. **Weak validation of the simplicity–generalization link** One of the paper’s central conceptual claims, arguably its most important contribution, is the proposed association between simplicity and out-of-distribution generalization. However, this connection is not validated in a convincing way. The authors first show that diffusion models can generalize on an extremely simple synthetic conditional generation task, and then abruptly pivot to a toy setting with identity-mapping learning experi
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Taxonomy
TopicsAdvanced Statistical Process Monitoring · Image and Signal Denoising Methods · Fault Detection and Control Systems
MethodsDiffusion