Spiking neural networks (SNNs) are positioned to enable spatio-temporal information processing and ultra-low power event-driven neuromorphic hardware. However, SNNs are yet to reach the same performances of conventional deep artificial neural networks (ANNs), a long-standing challenge due to complex dynamics and non-differentiable spike events encountered in training. The existing SNN error backpropagation (BP) methods are limited in terms of scalability, lack of proper handling of spiking discontinuities, and/or mismatch between the rate-coded loss function and computed gradient. We present a hybrid macro/micro level backpropagation (HM2-BP) algorithm for training multi-layer SNNs. The temporal effects are precisely captured by the proposed spike-train level post-synaptic potential (S-PSP) at the microscopic level.

The paper presents a new approach for training spiking neural networks (SNNs) via backpropagation. The main contribution is a decomposition of the error gradient into a "macro" component that directly optimizes the rate-coded error, and a "micro" component that takes into account effects due to spike timing. The approach therefore creates a bridge between approaches that treat SNNs mainly like standard ANNs (optimizing the rate-coded error), and algorithms that work on the spike level such as SpikeProp, which have previously not been able to scale to larger problems. There are similarities to previously published methods such as from Lee et al. 2016 or Wu et al. 2017, which are discussed briefly, but there are novel contributions. Furthermore, the results on two tasks (MNIST and N-MNIST) show improvements over the state-of-the-art, although those improvements are small.

Spiking neural networks (SNNs) are positioned to enable spatio-temporal information processing and ultra-low power event-driven neuromorphic hardware. However, SNNs are yet to reach the same performances of conventional deep artificial neural networks (ANNs), a long-standing challenge due to complex dynamics and non-differentiable spike events encountered in training. The existing SNN error backpropagation (BP) methods are limited in terms of scalability, lack of proper handling of spiking discontinuities, and/or mismatch between the rate-coded loss function and computed gradient. We present a hybrid macro/micro level backpropagation (HM2-BP) algorithm for training multi-layer SNNs. The temporal effects are precisely captured by the proposed spike-train level post-synaptic potential (S-PSP) at the microscopic level.