On the Role of Temporal Granularity in the Robustness of Spiking Neural Networks

As the third generation of neural networks, Spiking Neural Networks (SNNs) have demonstrated remarkable potential across diverse applications owing to their unique temporal dynamics. In recent years, analyzing the robustness of SNNs from a temporal perspective has become an emerging research focus. However, most existing works examine only the overall temporal behavior of SNNs, typically applying adversarial attacks that rely on time-averaged gradients. In this study, we revisit SNN robustness through the lens of temporal granularity, emphasizing the distinct behaviors that occur at individual time steps. We first introduce a Temporal Granularity Attack (TG-Attack), which selectively perturbs gradients at specific time steps. This approach enables a finer-grained evaluation of SNN robustness across time and demonstrates higher attack success rates than traditional gradient-averaging methods. Furthermore, we theoretically show that the robustness of SNNs at a given time step is determined by the Hessian of the input-output gradient at that step, which we define as Temporal Sensitivity (TS). By calculating the Temporal Sensitivity Value (TSV) for each time step, robustness can be effectively estimated without generating adversarial examples. Finally, we propose a Temporal Granularity Regularization (TG-Reg) term that constrains the TSV across all time steps, thereby improving the model's overall robustness. Experimental evaluations confirm that our framework consistently outperforms existing state-of-the-art methods. Code is available at https://github.com/zju-bmi-lab/TG-SNN-code.