Continual Learning through Control Minimization
Sander de Haan, Yassine Taoudi-Benchekroun, Pau Vilimelis Aceituno, Benjamin F. Grewe
TL;DR
This work reframes continual learning as a control problem in which learning and prior-task preservation compete within neural dynamics, introducing Equilibrium Fisher Control (EFC). By converting parameter-space regularizers into neuron-specific preservation signals and operating the learning process at equilibrium, EFC induces a continual-natural gradient that implicitly encodes prior-task curvature without storing full Fisher matrices. Theoretical results show that the equilibrium-based preconditioning filters interference from earlier tasks and supports class-incremental convergence, with tighter forgetting bounds than traditional regularization methods. Empirically, EFC recovers curvature-like structure dynamically, matches full-Fisher baselines on forgetting profiles, and achieves strong performance on Split-MNIST, Split-CIFAR10, and Split-Tiny-ImageNet without replay, indicating practical viability and potential biological relevance.
Abstract
Catastrophic forgetting remains a fundamental challenge for neural networks when tasks are trained sequentially. In this work, we reformulate continual learning as a control problem where learning and preservation signals compete within neural activity dynamics. We convert regularization penalties into preservation signals that protect prior-task representations. Learning then proceeds by minimizing the control effort required to integrate new tasks while competing with the preservation of prior tasks. At equilibrium, the neural activities produce weight updates that implicitly encode the full prior-task curvature, a property we term the continual-natural gradient, requiring no explicit curvature storage. Experiments confirm that our learning framework recovers true prior-task curvature and enables task discrimination, outperforming existing methods on standard benchmarks without replay.