A Unified Total Variation Framework for Membrane Potential Perturbation Dynamic
Zhao-Rong Lai, Xiwen Yuan, Ziliang Chen, Liangda Fang, Yongsen Zheng
Abstract
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.
BibTeX
@inproceedings{
lai2026a,
title={A Unified Total Variation Framework for Membrane Potential Perturbation Dynamic},
author={Zhao-Rong Lai and Xiwen Yuan and Ziliang Chen and Liangda Fang and Yongsen Zheng},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=LDo9numrx6}
}