Towards Neuromorphic Gradient Descent: Exact Gradients and Low-Variance Online Estimates for Spiking Neural Networks

Spiking Neural Networks (SNNs) are biologically-plausible models that can run on low-powered non-Von Neumann neuromorphic hardware, positioning them as promising alternatives to conventional Deep Neural Networks (DNNs) for energy-efficient edge computing and robotics. Over the past few years, the Gradient Descent (GD) and Error Backpropagation (BP) algorithms used in DNNs have inspired various training methods for SNNs. However, the non-local and the reverse nature of BP, combined with the inherent non-differentiability of spikes, represent fundamental obstacles to computing gradients with SNNs directly on neuromorphic hardware. Therefore, novel approaches are required to overcome the limitations of GD and BP and enable online gradient computation on neuromorphic hardware.

In this thesis, I address the limitations of GD and BP with SNNs by proposing three algorithms. First, I extend a recent method that computes exact gradients with temporally-coded SNNs by relaxing the firing constraint of temporal coding and allowing multiple spikes per neuron. My proposed method generalizes the computation of exact gradients with SNNs and enhances the tradeoffs between performance and various other aspects of spiking neurons. Next, I introduce a novel alternative to BP that computes low-variance gradient estimates in a local and online manner. Compared to other alternatives to BP, the proposed method demonstrates an improved convergence rate and increased performance with DNNs. Finally, I combine these two methods and propose an algorithm that estimates gradients with SNNs in a manner that is compatible with the constraints of neuromorphic hardware. My empirical results demonstrate the effectiveness of the resulting algorithm in training SNNs without performing BP.