Entropic Control for Homeostatic Optimization: Pre-empting Catastrophic Forgetting via Dynamic Feedback

Abstract

Supervised Fine-Tuning (SFT) of LLMs suffers from catastrophic forgetting, and prevailing mitigation strategies struggle to reconcile the plasticity-stability dilemma. To address this, we propose Entropic Control for Homeostatic Optimization (ECHO), a closed-loop control framework. By decomposing the KL divergence, we identify output entropy as a dominant observable component of KL variation. This enables us to leverage entropy as a computationally efficient online proxy to monitor forgetting risks in real-time, bypassing expensive reference-model inference. Consequently, ECHO employs an elastic controller that dynamically modulates the gradient weight of replay data via a proportional control law, using deviations from the pre-trained entropic equilibrium as an error signal. Empirical evaluations across 0.6B to 9B parameter architectures demonstrate that ECHO lies on, and in several comparisons extends, the observed plasticity-stability frontier and maintains high operational robustness against varying data mixing ratios.