[2604.04154] Non-Equilibrium Stochastic Dynamics as a Unified Framework for Insight and Repetitive Learning: A Kramers Escape Approach to Continual Learning

Condensed Matter > Statistical Mechanics arXiv:2604.04154 (cond-mat) [Submitted on 5 Apr 2026] Title:Non-Equilibrium Stochastic Dynamics as a Unified Framework for Insight and Repetitive Learning: A Kramers Escape Approach to Continual Learning Authors:Gunn Kim View a PDF of the paper titled Non-Equilibrium Stochastic Dynamics as a Unified Framework for Insight and Repetitive Learning: A Kramers Escape Approach to Continual Learning, by Gunn Kim View PDF HTML (experimental) Abstract:Continual learning in artificial neural networks is fundamentally limited by the stability--plasticity dilemma: systems that retain prior knowledge tend to resist acquiring new knowledge, and vice versa. Existing approaches, most notably elastic weight consolidation~(EWC), address this empirically without a physical account of why plasticity eventually collapses as tasks accumulate. Separately, the distinction between sudden insight and gradual skill acquisition through repetitive practice has lacked a unified theoretical description. Here, we show that both problems admit a common resolution within non-equilibrium statistical physics. We model the state of a learning system as a particle evolving under Langevin dynamics on a double-well energy landscape, with the noise amplitude governed by a time-dependent effective temperature $T(t)$. The probability density obeys a Fokker--Planck equation, and transitions between metastable states are governed by the Kramers escape rate $k = (\omega_0\omega...