Optimal Protocols for Continual Learning via Statistical Physics and Control Theory

Francesco Mori, Stefano Sarao Mannelli, Francesca Mignacco

Keywords: machine learning theory, statistical physics, online learning, continual learning, optimal control theory

TL;DR: This theoretical work combines statistical physics and control theory to design optimal task-selection protocols mitigating catastrophic forgetting while preserving performance in continual learning, validated on synthetic and real-world data.

Abstract: Artificial neural networks often struggle with _catastrophic forgetting_ when learning multiple tasks sequentially, as training on new tasks degrades the performance on previously learned tasks. Recent theoretical work has addressed this issue by analysing learning curves in synthetic frameworks under predefined training protocols. However, these protocols relied on heuristics and lacked a solid theoretical foundation assessing their optimality. In this paper, we fill this gap by combining exact equations for training dynamics, derived using statistical physics techniques, with optimal control methods. We apply this approach to teacher-student models for continual learning and multi-task problems, obtaining a theory for task-selection protocols maximising performance while minimising forgetting. Our theoretical analysis offers non-trivial yet interpretable strategies for mitigating catastrophic forgetting, shedding light on how optimal learning protocols modulate established effects, such as the influence of task similarity on forgetting. Finally, we validate our theoretical findings with experiments on real-world data.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 3852