MPD-SGR: Robust Spiking Neural Networks with Membrane Potential Distribution-Driven Surrogate Gradient Regularization

The surrogate gradient (SG) method has shown significant promise in enhancing the performance of deep spiking neural networks (SNNs), but it also introduces vulnerabilities to adversarial attacks. Although spike coding strategies and neural dynamics parameters have been extensively studied for their impact on robustness, the critical role of gradient magnitude, which reflects the model's sensitivity to input perturbations, remains underexplored. In SNNs, the gradient magnitude is primarily determined by the interaction between the membrane potential distribution (MPD) and the SG function. In this study, we investigate the relationship between the MPD and SG and their implications for improving the robustness of SNNs. Our theoretical analysis reveals that reducing the proportion of membrane potentials lying within the gradient-available range of the SG function effectively mitigates the sensitivity of SNNs to input perturbations. Building upon this insight, we propose a novel MPD-driven surrogate gradient regularization (MPD-SGR) method, which enhances robustness by explicitly regularizing the MPD based on its interaction with the SG function. Extensive experiments across multiple image classification benchmarks and diverse network architectures confirm that the MPD-SGR method significantly enhances the resilience of SNNs to adversarial perturbations and exhibits strong generalizability across diverse network configurations, SG functions, and spike encoding schemes.