信息论视角下的AI可靠性与安全权衡及知识蒸馏动力学研究
Information-Theoretic Reliability--Safety Bounds and Finite-Alignment Dynamics in AI Knowledge Distillation
把蒸馏里的安全退化问题做成了可计算的数学模型，还给出临界转变的可检验预测，做模型对齐和蒸馏的人可以看看推导思路。
一项 arXiv 研究建立了可靠性与安全之间权衡的通用不等式，边界由参数 Kh 决定，该参数衡量隐藏层区分良性输入与危险输入的能力。研究者构建了 Boltzmann-machine 模型，推导出可靠性与安全之间的两个精确关系，曲线形状由危险判别容量 K 控制。在知识蒸馏场景下，教师响应会重整化学生模型的权衡参数。研究用重整化群方法分析多代蒸馏，得到精确递推关系，并给出能力损失与稳定传输之间临界转变的可检验预测。
Information-Theoretic Reliability--Safety Bounds and Finite-Alignment Dynamics in AI Knowledge Distillation
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.
