Scaling Equilibrium Propagation to Deeper Neural Network Architectures

Equilibrium propagation has been proposed as a biologically plausible alternative to the backpropagation algorithm. The local nature of gradient computations, combined with the use of convergent RNNs to reach equilibrium states, make this approach well-suited for implementation on neuromorphic hardware. However, previous studies on equilibrium propagation have been restricted to networks containing only dense layers or relatively small architectures with a few convolutional layers followed by a final dense layer. These networks have a significant gap in accuracy compared to similarly sized feedforward networks trained with backpropagation. In this work, we introduce the Hopfield-Resnet architecture, which incorporates residual (or skip) connections in Hopfield networks with clipped ReLU as the activation function. The proposed architectural enhancements enable the training of networks with nearly twice the number of layers reported in prior works. For example, Hopfield-Resnet13 achieves 93.92% accuracy on CIFAR-10, which is ≈3.5% higher than the previous best result and comparable to that provided by Resnet13 trained using backpropagation.