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Learning-to-Defer in Non-Stationary Time Series via Switching State-Space Models Variance Reduction for Expectations with Diffusion Teachers TASTE: A Designer-Annotated Multi-Dimensional Preference Dataset for AI-Generated Graphic Design Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference Decision-Path Patterns as Tree Reliability Signals: Path-based Adaptive Weighting for Random Forest Classification The General Theory of Localization Methods CASCADE Conformal Prediction: Uncertainty-Adaptive Prediction Intervals for Two-Stage Clinical Decision Support Symmetrization of Loss Functions for Robust Training of Neural Networks in the Presence of Noisy Labels Tail Annealing for Heavy-Tailed Flow Matching Variance-Reduced Manifold Sampling via Polynomial-Maximization Density Estimation Latent Laplace Diffusion for Irregular Multivariate Time Series Precision Physical Activity Prescription via Reinforcement Learning for Functional Actions Reducing Diffusion Model Memorization with Higher Order Langevin Dynamics Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? 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How Many Domains Suffice for Domain Generalization? A Tight Characterization via the Domain Shattering Dimension
Cynthia Dwork, Lunjia Hu, Han Shao · 2025-06-20 · via stat updates on arXiv.org

We study a fundamental question of domain generalization: given a family of domains (i.e., data distributions), how many randomly sampled domains do we need to collect data from in order to learn a model that performs reasonably well on every seen and unseen domain in the family? We model this problem in the PAC framework and introduce a new combinatorial measure, which we call the domain shattering dimension. We show that this dimension characterizes the domain sample complexity. Furthermore, we establish a tight quantitative relationship between the domain shattering dimension and the classic VC dimension, demonstrating that every hypothesis class that is learnable in the standard PAC setting is also learnable in our setting.

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