arXiv:2603.07388cs.LGcs.AI2026-03

用稀疏性解释模型如何泛化到分布外数据,突破传统学习范式。

Sparsity and Out-of-Distribution Generalization

  • 基于特征稀疏性构建可泛化的假设空间
  • 证明了在特征重叠条件下,稀疏模型能跨分布保持性能
  • 适用于关注泛化能力与模型可解释性的研究者

自1946年古德曼提出“格鲁”悖论以来,分布外(OOD)泛化一直是认识论的核心问题,如今也成为机器学习与人工智能对齐的关键挑战。本文提出一个严谨的OOD泛化理论框架,包含三个核心要素:其一,经验总是通过特定特征通道(如视觉、听觉)呈现;其二,奥卡姆剃刀原则偏好稀疏假设,即依赖尽可能少的特征;其三,只要训练与测试分布在其相关特征上的限制足够重叠,稀疏假设就能实现泛化,即便在其他特征上任意发散。本文证明了一个定理,将经典样本复杂度界(Blumer et al.)推广至OOD场景。随后,进一步将稀疏分类器推广至子空间杂凑(subspace juntas),其中真实分类器仅依赖于特征的低维线性子空间。

原文摘要 · Abstract (English)

Explaining out-of-distribution generalization has been a central problem in epistemology since Goodman's "grue" puzzle in 1946. Today it's a central problem in machine learning, including AI alignment. Here we propose a principled account of OOD generalization with three main ingredients. First, the world is always presented to experience not as an amorphous mass, but via distinguished features (for example, visual and auditory channels). Second, Occam's Razor favors hypotheses that are "sparse," meaning that they depend on as few features as possible. Third, sparse hypotheses will generalize from a training to a test distribution, provided the two distributions sufficiently overlap on their restrictions to the features that are either actually relevant or hypothesized to be. The two distributions could diverge arbitrarily on other features. We prove a simple theorem that formalizes the above intuitions, generalizing the classic sample complexity bound of Blumer et al. to an OOD context. We then generalize sparse classifiers to subspace juntas, where the ground truth classifier depends solely on a low-dimensional linear subspace of the features.

分布外泛化稀疏性理论分析子空间学习

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