arXiv：cs.AI· Xin Wang (Jeff), R. Tyrrell Rockafellar (Jeff), Xuegang (Jeff), Ban·· 5 小时前
DIF：面向深度约束学习的方向性影响函数
Constraint-Aware Influence Estimation in Deep Constrained Learning
AI 导读
研究者提出方向性影响函数（DIF），将约束学习的最优性条件建模为变分不等式（VI），把约束显式纳入影响估计，解决经典影响函数在约束场景下因扰动同时改变目标与可行域而失真的问题。在约束线性回归中，DIF 能复现留一法重训结果，而 IF 与基于惩罚的 IF 存在明显偏差；在公平约束 CNN 上，DIF 能准确预测数据移除后的测试损失变化，并与实际重训结果高度吻合。
正文
Abstract:Constrained learning has been increasingly applied to various domains to ensure explicit feasibility requirements due to fairness, safety, robustness, regularization, and physics or logic constraints. Understanding how training samples influence the solution (e.g., learned parameters) of constrained learning is crucial for interpretability and robustness. The classical influence function may become unreliable in constrained settings: data perturbations can reshape both the objective and the feasible region, leading to estimates that violate feasibility. In response, we propose the Directional Influence Function (DIF), a new estimator that explicitly incorporates the constraints into influence estimation. DIF formulates the optimality conditions of constrained learning as a variational inequality (VI) and analyzes how perturbing training data affects this VI. We validate DIF in constrained linear regression and demonstrate that it recovers leave-one-out retraining results, whereas IF and penalty-based IF exhibit significant bias. We further apply DIF to fairness-constrained CNNs, where DIF accurately predicts test loss changes under data removal and aligns closely with actual retraining. Our results establish DIF as an efficient and reliable tool for data attribution in constrained learning.
| Comments: | Need revision |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2607.23388 [cs.LG] |
| (or arXiv:2607.23388v4 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.23388 arXiv-issued DOI via DataCite |
Submission history
From: Xin Wang [view email]
[v1]
Sat, 25 Jul 2026 22:50:09 UTC (170 KB)
[v2]
Tue, 28 Jul 2026 03:42:07 UTC (1 KB) (withdrawn)
[v3]
Wed, 29 Jul 2026 01:25:56 UTC (170 KB)
[v4]
Tue, 13 Oct 2026 17:08:40 UTC (515 KB)
来源：arXiv：cs.AI · arxiv.org