  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.
