Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks

TL;DR

The paper tackles the challenge of training neuromorphic spiking neural networks in a biologically plausible and hardware-friendly way, aiming to avoid weight-transport and multi-phase backpropagation. It introduces online pseudo-zeroth-order (OPZO) training, which decouples the model from the loss, injects noise during a single forward pass, and uses momentum-based top-down feedback to propagate error signals without spatial backpropagation. OPZO achieves competitive accuracy to spatial BP with surrogate gradients across neuromorphic and static datasets, including deeper networks and noisy ImageNet fine-tuning, while offering lower or comparable training costs. The approach blends online learning with a three-factor-like Hebbian update and demonstrates potential for on-chip SNN training on neuromorphic hardware, marking a step toward practical, hardware-efficient global learning for neuromorphic systems.

Abstract

Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training SNNs in a more biologically plausible and neuromorphic-hardware-friendly way is still challenging. Most recent methods leverage spatial and temporal backpropagation (BP), not adhering to neuromorphic properties. Despite the efforts of some online training methods, tackling spatial credit assignments by alternatives with comparable performance as spatial BP remains a significant problem. In this work, we propose a novel method, online pseudo-zeroth-order (OPZO) training. Our method only requires a single forward propagation with noise injection and direct top-down signals for spatial credit assignment, avoiding spatial BP's problem of symmetric weights and separate phases for layer-by-layer forward-backward propagation. OPZO solves the large variance problem of zeroth-order methods by the pseudo-zeroth-order formulation and momentum feedback connections, while having more guarantees than random feedback. Combining online training, OPZO can pave paths to on-chip SNN training. Experiments on neuromorphic and static datasets with fully connected and convolutional networks demonstrate the effectiveness of OPZO with similar performance compared with spatial BP, as well as estimated low training costs.

Figures (3)

• Figure 1: Illustration of different training methods. (a) Online training of SNNs with tracked traces for temporal credit assignment bellec2020solutionxiao2022online. (b-e) Different spatial credit assignment methods. (b) Spatial BP with SG propagates errors layer-by-layer with symmetric weights. (c) DFA nokland2016direct directly propagates error signals from the top layer to the middle ones with fixed random connections. (d) Single-point zeroth-order methods add perturbation during forward propagation, and afterward, the loss signal is passed to the middle layers. (e) The proposed OPZO method leverages momentum feedback connections based on perturbation vectors and directly propagates error signals to neurons with top-down connections.
• Figure 2: Results of gradient variances of OPZO, spatial BP with SG, and ZO$_{\text{sp}}$ on different datasets. "L$i$" denotes the $i$-th layer.
• Figure 3: Training dynamics of different methods on N-MNIST and DVS-CIFAR10.

Theorems & Definitions (14)

• Lemma 3.1
• Lemma 3.2
• Lemma 4.1
• Proposition 4.2
• Remark 4.3
• Proposition 4.4
• proof
• proof
• proof
• Remark 1.1