Membrane Potential Perturbation Dynamic Is Total Variation

Membrane potential perturbation dynamic (MPPD) is an emerging approach to capture perturbation intensity and stabilize the performance of spiking neural networks (SNN). It discards the neuronal reset part to intuitively reduce fluctuations of dynamics, but this treatment may be insufficient in perturbation characterization. In this study, we prove that MPPD is total variation (TV), which is a widely-used methodology for robust signal reconstruction. Moreover, we propose a novel TV-$\ell_1$ framework for MPPD, which allows for a wider range of network functions and has better denoising advantage than the existing TV-$\ell_2$ framework, based on the coarea formula. Experiments show that MPPD-TV-$\ell_1$ achieves robust performance in both Gaussian noise training and adversarial training for image classification tasks. This finding may provide a new insight into the essence of perturbation characterization.