A Free-Energy Bayesian Framework for Probabilistic Stability under Noisy and Limited Data

Abstract

Learning systems often face instability when trained on limited or noisy data. We present a Free-Energy–Bayesian Framework that unifies free-energy minimization with a Bayesian stability index to construct a composite Lyapunov-like function ensuring probabilistic stability. Theoretical analysis establishes Lyapunov convergence under mild assumptions, while experiments on synthetic noisy datasets confirm robustness and reduced variance compared to baselines.