Equilibrium Propagation with Continual Weight Updates

Maxence Ernoult, Julie Grollier, Damien Querlioz, Yoshua Bengio, Benjamin Scellier

TL;DR: We propose a continual version of Equilibrium Propagation, where neuron and synapse dynamics occur simultaneously throughout the second phase, with theoretical guarantees and numerical simulations.

Abstract:

Equilibrium Propagation (EP) is a learning algorithm that bridges Machine Learning and Neuroscience, by computing gradients closely matching those of Backpropagation Through Time (BPTT), but with a learning rule local in space.
Given an input x and associated target y, EP proceeds in two phases: in the first phase neurons evolve freely towards a first steady state; in the second phase output neurons are nudged towards y until they reach a second steady state.
However, in existing implementations of EP, the learning rule is not local in time:
the weight update is performed after the dynamics of the second phase have converged and requires information of the first phase that is no longer available physically.
This is a major impediment to the biological plausibility of EP and its efficient hardware implementation.
In this work, we propose a version of EP named Continual Equilibrium Propagation (C-EP) where neuron and synapse dynamics occur simultaneously throughout the second phase, so that the weight update becomes local in time. We prove theoretically that, provided the learning rates are sufficiently small, at each time step of the second phase the dynamics of neurons and synapses follow the gradients of the loss given by BPTT (Theorem 1).
We demonstrate training with C-EP on MNIST and generalize C-EP to neural networks where neurons are connected by asymmetric connections. We show through experiments that the more the network updates follows the gradients of BPTT, the best it performs in terms of training. These results bring EP a step closer to biology while maintaining its intimate link with backpropagation.

Code: https://drive.google.com/open?id=1oZtzBTu8zZgvAopyK2sQg2bpcsrzwTrp

Keywords: Biologically Plausible Neural Networks, Equilibrium Propagation