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

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 improves stability while preserving plasticity, achieving a 75\% and 64\% average accuracy on Split MNIST and Split CIFAR10 respectively. These findings show that Equilibrium Propagation can be adapted to alleviate catastrophic forgetting without forgoing the traits which made it compelling in the first place.