arXiv cs.AI· Kim Phuc Tran·· 12 小时前AI 评分18
以人为中心的学习力学：受保护风险约束下的可观测熵控制
Human-Centered Learning Mechanics: Observable Entropy Control under Protected-Risk Constraints
AI 导读
研究提出在任务、风险与干预三类约束分别指定下进行熵调控学习的理论框架，指出熵减本身并非安全标准，可能不改变预测或伴随受保护群体风险上升。通过噪声校准的对数行列式泛函导出精确谱力公式，并给出可观测速度与预测零速度的度量分解；对多个受保护风险推导出指定子空间与范数预算内的精确极小极大可行性证书及锥投影公式。可复现数学检验与小规模真实数据实验同时暴露了可行干预与失效情形。
正文 · 原文
Abstract:Entropy reduction is not a safety criterion: it can leave predictions unchanged or accompany increasing risk for a protected group. We study entropy-regulated learning under separately specified task, risk, and intervention constraints. A noise-calibrated log-determinant functional yields an exact spectral force formula and a metric decomposition into observable and prediction-null velocities. For scalar feedback, we characterize the complete interval of coefficients preserving a task-descent fraction and meeting an entropy-rate request; restricting intervention to observable directions can make that interval empty. For several protected risks, we derive an exact minimax certificate of feasibility within a specified subspace and norm budget, an exact robust extension for uncertain constraint rows, and a cone-projection formula for the entropy reduction remaining after protection. These formulas use standard convex geometry but identify when apparently active entropy control has no admissible effect. Barrier comparisons, finite-step curvature and gradient-error margins, and fresh-data audits give distinct conditional guarantees for risk thresholds. Human authority enters through the specification and release policy; the mathematics does not identify compression with alignment or certify human well-being. A memorization counterexample separates fresh-input information from sample-level information, and a noisy sample-code assumption supports a conditional generalization bound. Reproducible mathematical checks and a small real-data experiment expose both feasible interventions and failures. The resulting theory characterizes admissible entropy regulation and its limitations, rather than asserting universal accuracy or safety improvements.
| Comments: | Submitted to JMLR |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| Cite as: | arXiv:2605.22940 [cs.LG] |
| (or arXiv:2605.22940v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22940 arXiv-issued DOI via DataCite |
Submission history
From: Kim Phuc Tran [view email]
[v1]
Thu, 21 May 2026 18:16:39 UTC (5,168 KB)
[v2]
Fri, 16 Oct 2026 09:24:08 UTC (95 KB)
来源：arXiv cs.AI · arxiv.org