Continual Learning through Control Minimization

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.

When you teach a neural network something new, the network usually overwrites what came before. This problem is called catastrophic forgetting, and stands in the way of building systems that keep learning over time. The common fix is to mark which internal connections mattered for the old task and discourage changes to those connections. The trouble is that the network still computes how to update itself based on the new task alone, and the protective rule is bolted on afterward. By then, the update being corrected already points in a harmful direction. We tried something closer to how the brain seems to work. On each neuron, two pressures act at once, one driving the new task and one defending the old. The network must find an update that respects old knowledge while pursuing the new, rather than producing a harmful update and correcting after the fact. Networks trained this way remember old skills far better while still picking up new ones, and never need to replay old training data. Until now, only methods that keep a memory bank of past examples performed well in the hardest setting; our method closes most of that distance without any memory bank.