Generative Replay for Equilibrium Propagation: Toward Edge-Friendly Continual Learning in Hopfield Networks

Victor Cook, Gilles Sassatelli, Thierry Gil, Mohamed Watfa, Marina Reyboz

Equilibrium Propagation (EqProp) offers a biologically grounded and hardware-aligned alternative to backpropagation for training Hopfield Networks. However, its behavior in continual learning settings remains largely unexplored. This work confronts catastrophic forgetting in EqProp-trained Hopfield Networks from the inside out, eliminating the need for external data buffers or architectural overhead that standard Experience Replay \textbf{(ER)} and Generative Replay \textbf{(Gen-Replay)} inevitably require. We introduce an Energy-Based Generative Replay strategy \textbf{(EB-Gen)} which exploits the intrinsic generative dynamics of Hopfield Networks, allowing a single model to act as both classifier and replay samples generator. Samples capturing past task knowledge are generated by relaxing a frozen copy of the network, enabling rehearsal solely through internally generated pseudo-data. We evaluate the proposed method in the Class-Incremental setting, using the split versions of the MNIST and CIFAR10 benchmarks and compare it with FineTune, Experience Replay, Generative Replay, Sleep-Like Replay Consolidation (SRC) and Joint training. Our results show that EB-Gen significantly…