Event-Based Backpropagation can compute Exact Gradients for Spiking Neural Networks

TL;DR

This paper introduces EventProp, a novel exact backpropagation algorithm for spiking neural networks that handles discrete spike events without approximation, enabling precise training and advancing brain-inspired hardware development.

Contribution

It derives the first exact backpropagation method for continuous-time spiking neural networks using the adjoint method, handling spike discontinuities directly.

Findings

Achieved competitive performance on Yin-Yang and MNIST datasets.

Demonstrated exact gradient computation for spiking neural networks.

Enabled error backpropagation at spike times without approximations.

Abstract

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.