提出函数空间稳定性边界，判断模型能否靠稳定解释泛化。
A Function-Space Stability Boundary for Generalization in Interpolating Learning Systems
- 用函数空间轨迹分析训练过程对单样本扰动的敏感性
- 小稳定性证书意味着可由稳定解释泛化，大则不行
- 适合研究泛化机制、优化器选择或鲁棒性设计的人
现代学习系统常在插值训练数据的同时仍具备良好泛化能力，但算法稳定性是否能解释此现象尚不明确。本文将训练建模为函数空间中的轨迹，衡量沿该轨迹对单样本扰动的敏感性。提出收缩传播条件，并通过展开递推关系获得稳定性证书。证书值较小时，表明稳定性可解释泛化；同时证明存在风险低的插值区域，其中收缩敏感性无法成立，说明稳定性并非普遍解释。实验验证了证书增长能预测不同优化器、步长和数据扰动下的泛化差异。该框架识别出稳定性可解释泛化的情形，以及需依赖其他机制的情况。
原文摘要 · Abstract (English)
Modern learning systems often interpolate training data while still generalizing well, yet it remains unclear when algorithmic stability explains this behavior. We model training as a function-space trajectory and measure sensitivity to single-sample perturbations along this trajectory. We propose a contractive propagation condition and a stability certificate obtained by unrolling the resulting recursion. A small certificate implies stability-based generalization, while we also prove that there exist interpolating regimes with small risk where such contractive sensitivity cannot hold, showing that stability is not a universal explanation. Experiments confirm that certificate growth predicts generalization differences across optimizers, step sizes, and dataset perturbations. The framework therefore identifies regimes where stability explains generalization and where alternative mechanisms must account for success.
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