Spiking neural networks (SNNs) are gaining popularity in deep learning due to their low energy budget on neuromorphic hardware. However, they still face challenges in lacking sufficient robustness to guard safety-critical applications such as autonomous driving. Many studies have been conducted to defend SNNs from the threat of adversarial attacks. This paper aims to uncover the robustness of SNN through the lens of the stability of nonlinear systems. We are inspired by the fact that searching for parameters altering the leaky integrate-and-fire dynamics can enhance their robustness. Thus, we dive into the dynamics of membrane potential perturbation and simplify the formulation of the dynamics. We present that membrane potential perturbation dynamics can reliably convey the intensity of perturbation. Our theoretical analyses imply that the simplified perturbation dynamics satisfy input-output stability. Thus, we propose a training framework with modified SNN neurons and to reduce the mean square of membrane potential perturbation aiming at enhancing the robustness of SNN. Finally, we experimentally verify the effectiveness of the framework in the setting of Gaussian noise training and adversarial training on the image classification task.

翻译：脉冲神经网络（SNNs）因其在神经形态硬件上的低能耗特性，在深度学习领域日益受到关注。然而，其在面对自动驾驶等安全关键应用时，仍面临鲁棒性不足的挑战。已有大量研究致力于防御针对SNNs的对抗攻击。本文旨在从非线性系统稳定性的视角揭示SNNs的鲁棒性。我们受到以下发现的启发：通过调整参数改变泄漏积分发放动力学可以增强其鲁棒性。因此，我们深入研究了膜电位扰动的动力学特性，并简化了其动力学方程。我们证明了膜电位扰动动力学能够可靠地反映扰动强度。理论分析表明，简化后的扰动动力学满足输入-输出稳定性。基于此，我们提出了一种改进SNN神经元并旨在降低膜电位扰动均方值的训练框架，以增强SNN的鲁棒性。最后，我们在图像分类任务中，通过高斯噪声训练和对抗训练的实验设置，验证了该框架的有效性。