随机脉冲网络具稳定性和简单谱特性，为能效计算提供理论支撑
Random Spiking Neural Networks are Stable and Spectrally Simple
- 通过布尔函数分析揭示脉冲网络的低频谱集中特性
- 宽层脉冲网络平均稳定，输入扰动影响小
- 适合关注能效与鲁棒性的神经网络研究者
脉冲神经网络（SNN）是节能计算的有前景范式，但其理论基础——尤其是稳定性与鲁棒性——相比人工神经网络仍不充分。本文从布尔函数分析视角研究离散时间漏电积分-发放（LIF）SNN，聚焦分类任务中的噪声敏感性与稳定性，量化输入扰动对输出的影响。主要结果表明，宽LIF-SNN分类器在平均意义下具有稳定性，这由其傅里叶谱集中在低频分量所解释。由此提出谱简单性概念，形式化地将谱集中与深度网络中观察到的简单性偏置相联系。在此框架下，证明随机LIF-SNN倾向于简单函数。训练网络实验验证了这些稳定性特性在实践中依然存在。结果为理解SNN的稳定性和鲁棒性提供了新见解。
原文摘要 · Abstract (English)
Spiking neural networks (SNNs) are a promising paradigm for energy-efficient computation, yet their theoretical foundations-especially regarding stability and robustness-remain limited compared to artificial neural networks. In this work, we study discrete-time leaky integrate-and-fire (LIF) SNNs through the lens of Boolean function analysis. We focus on noise sensitivity and stability in classification tasks, quantifying how input perturbations affect outputs. Our main result shows that wide LIF-SNN classifiers are stable on average, a property explained by the concentration of their Fourier spectrum on low-frequency components. Motivated by this, we introduce the notion of spectral simplicity, which formalizes simplicity in terms of Fourier spectrum concentration and connects our analysis to the simplicity bias observed in deep networks. Within this framework, we show that random LIF-SNNs are biased toward simple functions. Experiments on trained networks confirm that these stability properties persist in practice. Together, these results provide new insights into the stability and robustness properties of SNNs.
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