Continual Learning as a Multiphase Moving-Boundary Problem

Abstract

Continual learning struggles to balance retaining past knowledge with absorbing new tasks. Stefan-CL elegantly resolves this stability-plasticity dilemma through the physics of melting. It frames consolidated knowledge as a protected "solid" and unused capacity as an adaptable "liquid." As the network learns, this boundary expands, governed by a "latent heat" tuning dial. By mathematically freezing the learned interior, Stefan-CL cuts forgetting to near zero, matching memory-heavy baselines without storing raw data, forging a beautiful, physics-grounded path for AI.