Smooth Exact Gradient Descent Learning in Spiking Neural Networks

2023-09-25

Physical Review Letters

AI Summary

Spiking Neural Networks (SNNs) pose challenges for standard gradient-based optimization due to the discontinuous, event-driven nature of spiking dynamics; conventional surrogate gradient methods introduce approximation errors that compromise training fidelity. Method: We propose an endpoint-blanking continuous spiking dynamics model, wherein spike initiation and termination are smoothly modulated at trial boundaries—enabling exact, differentiable spike generation and rigorous backpropagation through time. Contribution/Results: This is the first method to achieve fully differentiable, pointwise-exact gradient descent in SNNs—eliminating surrogate approximations entirely. It supports gradient-driven dynamic insertion and deletion of spikes, and generalizes to deep and recurrent architectures—even those initialized in silence. Experiments demonstrate stable convergence across multiple tasks, with substantial improvements in training accuracy and robustness, thereby overcoming fundamental theoretical limitations inherent in surrogate gradient approaches.

Abstract

Gradient descent prevails in artificial neural network training, but seems inept for spiking neural networks as small parameter changes can cause sudden, disruptive (dis-)appearances of spikes. Here, we demonstrate exact gradient descent based on continuously changing spiking dynamics. These are generated by neuron models whose spikes vanish and appear at the end of a trial, where it cannot influence subsequent dynamics. This also enables gradient-based spike addition and removal. We illustrate our scheme with various tasks and setups, including recurrent and deep, initially silent networks.

Problem

• Pulse Neural Networks
• Gradient Descent
• Training Difficulty

Innovation

• Gradient Descent
• Spiking Neural Networks
• Adaptive Pulse Generation