arXiv:2512.21208v3 Announce Type: replace Abstract: 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 Lyapunov criterion for controlling this profile. Under explicit regularity, coercivity, and dissipation assu
Source: arXiv cs.LG — read the full report at the original publisher.