AI RESEARCH

A Learning Stability Profile for Finite-Dimensional Learning Dynamics

arXiv CS.LG

ArXi:2512.21208v3 Announce Type: replace We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a collection of directional sensitivity operators that records how perturbations in inputs, parameter initialization, and update mechanisms propagate along a specified learning trajectory. The main result is a Lyapuno criterion for controlling this profile.