The Hebbian Forward-Forward Algorithm

We introduce Hebbian Forward-Forward (HebbFF), a gradient-free alternative to the Forward-Forward (FF) algorithm. HebbFF replaces local gradient computations in FF with classical Hebbian plasticity modulated by a goodness-based gating rule. This change eliminates gradient calculations entirely, reducing computational overhead and memory usage. On MNIST and FashionMNIST, HebbFF matches FF in accuracy while training substantially faster and using less VRAM. Compared to backpropagation, HebbFF achieves lower predictive performance but offers a more resource-efficient and biologically plausible training paradigm. HebbFF therefore establishes a stronger baseline than FF for exploring scalable, gradient-free learning in deep networks.