知识蒸馏中 AI 可靠性—安全性的信息论界与有限对齐动力学
Information-Theoretic Reliability--Safety Bounds and Finite-Alignment Dynamics in AI Knowledge Distillation
AI 导读
这项理论研究建立了 AI 可靠性—安全性权衡的信息论界，边界由单一参数 Kh 决定，量化隐藏层区分良性与有害输入的能力。作者以 Boltzmann 机模型刻画响应行为，并推导可靠性与安全性的两个精确关系，结论与已有实验数据吻合。在知识蒸馏中，教师模型响应会引起学生模型权衡参数的重整化，多代蒸馏的重整化群流揭示出不动点结构与能力损失到稳定传输之间的临界转变预测。
正文 · 原文
Abstract:The reliability and safety of artificial intelligence (AI), together with their transfer and evolution through knowledge distillation, have attracted growing attention. We establish an information-theoretic bound on the reliability--safety trade-off and characterize the dynamics of this trade-off under knowledge distillation. We first prove a universal trade-off inequality that is independent of the specific model form. Its boundary is determined solely by a single parameter Kh, which quantifies the hidden layer's ability to distinguish benign from hazardous inputs. We then develop a canonical Boltzmann-machine model of AI response behavior and derive two exact relations between reliability and safety. The trade-off curve is determined by the hazard discrimination capacity K, while the overall answer tendency controls the operating point along the curve. These relations agree well with existing experimental data. In knowledge distillation, we find that teacher responses induce a renormalization of the student model's trade-off parameters. We further use a renormalization-group approach to study multigenerational distillation, deriving exact recursion relations and the associated renormalization-group-like flows for two representative direct intergenerational distillation protocols at arbitrary teacher--student alignment strength. These flows reveal fixed-point structures, long-term dynamics, and critical behavior, yielding testable predictions for the critical transition between capability loss and stable transmission.
| Subjects: | Statistical Mechanics (cond-mat.stat-mech); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.38651 [cond-mat.stat-mech] |
| (or arXiv:2610.38651v1 [cond-mat.stat-mech] for this version) | |
| https://doi.org/10.48550/arXiv.2610.38651 arXiv-issued DOI via DataCite |
Submission history
From: Miaomiao Yi [view email]
[v1]
Wed, 28 Oct 2026 11:04:21 UTC (4,112 KB)
来源：arXiv cs.AI · arxiv.org