Optimization Method for Surrogate Function in Spiking Neural Networks Based on Membrane Potential Distribution

Spiking Neural Networks (SNNs) offer promising energy efficiency and temporal sparsity for edge intelligence, but their training remains difficult due to gradient mismatch, membrane potential drift, and discretization errors. In this paper, we propose a membrane potential-guided surrogate optimization(MPO) framework that dynamically aligns the surrogate function with the membrane potential distribution to enhance the gradient propagation. Specifically, we introduce a KL-divergence-based regularization to stabilize membrane potential dynamics, and an adaptive width constraint to synchronize the surrogate gradient range with neural activity statistics. Additionally, we design a spike discretization error metric and a correction strategy to mitigate temporal discretization effects. Experiments on CIFAR-10, CIFAR-100, and ImageNet show our method achieves 94.76%, 74.20%, and 65.70% top-1 accuracy respectively, while improving gradient stability and energy efficiency. This work provides a principled optimization scheme for robust and scalable SNN training in practical neuromorphic systems.