SSTDP: Supervised Spike Timing Dependent Plasticity for Efficient Spiking Neural Network Training

Abstract

Spiking Neural Networks (SNNs) are a pathway that could potentially empower low-power event-driven neuromorphic hardware due to their spatio-temporal information processing capability and high biological plausibility. Although SNNs are currently more efficient than artificial neural networks (ANNs), they are not as accurate as ANNs. Error backpropagation is the most common method for directly training neural networks, promoting the prosperity of ANNs in various deep learning fields. However, since the signals transmitted in the SNN are non-differentiable discrete binary spike events, the activation function in the form of spikes presents difficulties for the gradient-based optimization algorithms to be directly applied in SNNs, leading to a performance gap (i.e., accuracy and latency) between SNNs and ANNs. This paper introduces a new learning algorithm, called SSTDP, which bridges the gap between backpropagation (BP)-based learning and spike-time-dependent plasticity (STDP)-based learning to train SNNs efficiently. The scheme incorporates the global optimization process from BP and the efficient weight update derived from STDP. It not only avoids the non-differentiable derivation in the BP process but also utilizes the local feature extraction property of STDP. Consequently, our method can lower the possibility of vanishing spikes in BP training and reduce the number of time steps to reduce network latency. In SSTDP, we employ temporal-based coding and use Integrate-and-Fire (IF) neuron as the neuron model to provide considerable computational benefits. Our experiments show the effectiveness of the proposed SSTDP learning algorithm on the SNN by achieving the best classification accuracy 99.3% on the Caltech 101 dataset, 98.1% on the MNIST dataset, and 91.3% on the CIFAR-10 dataset compared to other SNNs trained with other learning methods. It also surpasses the best inference accuracy of the directly trained SNN with 25~32× less inference latency. Moreover, we analyze event-based computations to demonstrate the efficacy of the SNN for inference operation in the spiking domain, and SSTDP methods can achieve 1.3~37.7× fewer addition operations per inference. The code is available at: https://github.com/MXHX7199/SNN-SSTDP.

Keywords: deep learning; efficient training; gradient descent backpropagation; neuromorphic computing; spike-time-dependent plasticity; spiking neural network.

Figure 1

An example of BP-based learning and STDP-based learning. (A) Forward and backward propagation of the SNN. (B) If the post-synaptic neuron fires after the pre-synaptic spike arrives, the synaptic weight between pre- and post-synaptic neuron increases. The magnitude of change increases in proportion to Δt_pot. The reverse order leads to a decrease in synaptic weight in proportion to Δt_dep.

Figure 2

A multi-layer neural network is composed of an input layer, one or more hidden layers, and an output layer. The workload of natural ANN training with real-valued activation (A); and SNN training with spatio-temporal spike trains (B).

Figure 3

An example about the input image is converted into the input spike train by the (A) rate-based coding scheme (Han et al., 2020) and (B) Time-To-First-Spike time-based coding scheme (Rathi et al., 2020). The time window represents the length of the spike train, which is equal to the number of time steps.

Figure 4

The illustration of the forward process and error backpropagation in the SSTDP method. The blue frame arrows represent forward propagation, and the red frame arrows represent backward propagation. In the forward phase, the neurons in the SNN integrate the received spikes with corresponding weights into the membrane potential and calculate the error based on the prediction results of the network. In the backward phase, the final error is backward past through the hidden layers based on the chain rule to obtain the partial derivative of the final error with respect to the time. The synaptic weights are modified with spatial (local weight updates from STDP) and temporal information (globally rectified from BP) to reduce the network error.

Figure 5

(A) The original image input to the SNN. (B) The orignial spike train input to the neurons and the processed version generated by neurons. (C) The reconstructed image at the first 33 time steps after time-based coding.

Figure 6

The accuracy evolution curve for training with our method on the MNIST dataset.

Figure 7

The accuracy evolution curve for training with our method on the MNIST dataset varies as the learning rate schedule.

Figure 8

The Inference test accuracy curve of the SNN trained with SSTDP method varies as the time steps.

Figure 9

The Inference computational cost (FSR) evolution curve comparisons between SSTDP and the two baseline SNNs (STiDi-BP and BP-STDP).

Figure 10

The Inference computational cost (addition operation) evolution curve comparisons between SSTDP and the two baseline SNNs (STiDi-BP and BP-STDP).