NDOT: Neuronal Dynamics-based Online Training for Spiking Neural Networks

Spiking Neural Networks (SNNs) are attracting great attention for their energy-efficient and fast-inference properties in neuromorphic computing. However, the efficient training of deep SNNs poses challenges in gradient calculation due to the non-differentiability of their binary spike-generating activation functions. To address this issue, the surrogate gradient (SG) method is widely used, typically in combination with backpropagation through time (BPTT). Yet, BPTT's process of unfolding and back-propagating along the computational graph requires storing intermediate information at all time-steps, resulting in huge memory consumption and unable to meet online requirements. In this work, we propose Neuronal Dynamics-based Online Training (NDOT) for SNNs, which uses the neuronal dynamics-based continuous temporal dependency in gradient computation. NDOT enables forward-in-time learning by decomposing the full gradient into temporal and spatial gradients. To illustrate the intuition behind NDOT, we employ the Follow-the-Regularized-Leader (FTRL) algorithm. FTRL explicitly utilizes historical information and addresses limitations in instantaneous loss. Our proposed NDOT method uses neuronal dynamics to accurately capture temporal dependencies, functioning similarly to FTRL's explicit use of historical information. Experiments on CIFAR-10, CIFAR-100, and CIFAR10-DVS demonstrate the superior performance of our NDOT method on large-scale static and neuromorphic datasets within a small number of time steps. The codes are available at https://github.com/HaiyanJiang/SNN-NDOT.