Zeroth-Order Forward-Only SNN Training Inspiring Neuromorphic On-Chip Learning

The human brain is a biologically instantiated ondevice neural system that integrates both learning and inference in a unified architecture, which enables rapid and flexible learning on-the-fly. This extraordinary online learning ability is realized through biological learning mechanisms operating on a well-initialized innate model. This work considers the on-chip edge learning upon pretrained models with zeroth-order (ZO) methods. ZO optimization methods, which resemble bio-plausible perturbation-based learning, offer a promising approach that enables learning with only forward passes and hence can significantly reduce the complexity of on-chip hardware implementation. However, in this work we show that applying ZO methods to spiking neural networks (SNNs) is non-trivial due to the step-function nature of spiking activation. We analyze the challenges posed by the spiking activation, and reveal a variance amplification effect of it. Based on this insight, we propose a subspace-based ZO (SZO) method that leverages the intrinsic lowdimensional structure of the SNN optimization trajectory. By learning in a low-dimensional subspace, SZO substantially enhances ZO learning efficacy, achieving accuracy comparable to firstorder (FO) methods with faster learning speed than full-space BP. We evaluate SZO on model training from scratch, continual training, and unsupervised adaptation. Experimental results demonstrate that SZO closely approaches FO training performance for the first time while offering fast learning speed. Code is available at https://github.com/LeviD536/SZO.