提出可验证的分布偏移风险上界，让模型在数据变化时仍可信。
Certified Learning under Distribution Shift: Sound Verification and Identifiable Structure
- 用可计算的偏移度量约束模型复杂度，给出风险上界
- 在非平凡规模下实现模型验证的可靠性
- 通过可识别性条件增强可解释性，而非事后解释
设预测器 $f$ 在分布 $P$ 上训练并在偏移分布 $Q$ 上评估。在可验证的正则性和复杂度约束下，分布偏移下的超额风险存在显式上界，该上界由可计算的偏移度量和模型参数决定。本文构建统一框架：(i) 通过显式不等式为分布偏移下的风险提供认证；(ii) 实现对学习模型在非平凡规模下的可靠验证；(iii) 通过可识别性条件强制可解释性，而非依赖事后解释。所有结论均明确列出假设，失败模式被隔离，不可认证区域也被刻画。
原文摘要 · Abstract (English)
Proposition. Let $f$ be a predictor trained on a distribution $P$ and evaluated on a shifted distribution $Q$. Under verifiable regularity and complexity constraints, the excess risk under shift admits an explicit upper bound determined by a computable shift metric and model parameters. We develop a unified framework in which (i) risk under distribution shift is certified by explicit inequalities, (ii) verification of learned models is sound for nontrivial sizes, and (iii) interpretability is enforced through identifiability conditions rather than post hoc explanations. All claims are stated with explicit assumptions. Failure modes are isolated. Non-certifiable regimes are characterized.
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