Dendritic Neural Networks with Equilibrium Propagation

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation (BP), but its effectiveness can degrade in deeper and more challenging learning settings. In parallel, dendritic neural networks have demonstrated improved performance and generalization when trained with BP, suggesting that structured, biologically inspired architectures may enhance learning. In this work, we investigate the integration of dendritic neural networks with equilibrium propagation using an advanced EP framework. We evaluate the proposed dendritic EP model on MNIST, Kuzushiji-MNIST (KMNIST), and Fashion-MNIST (FMNIST), considering both shallow and deeper architectures. Our results show that dendritic EP achieves performance comparable to standard EP on simple tasks, while providing consistent improvements on more challenging datasets and deeper models. In particular, dendritic EP significantly outperforms standard EP on KMNIST and FMNIST, and approaches the performance of dendritic networks trained with backpropagation through time.To further understand these improvements, we analyze the evolution of hidden states during the free phase. We observe that dendritic EP exhibits higher activation magnitudes and more distributed hidden-state activity compared to standard EP, indicating that dendritic structure alters the internal network dynamics. These findings suggest that incorporating dendritic structure can enhance the effectiveness of biologically plausible learning algorithms, especially in regimes where standard EP struggles. Our work highlights the importance of architectural design for improving biologically inspired training methods.