# Random Spiking Neural Networks are Stable and Spectrally Simple

arXiv: https://arxiv.org/abs/2511.00904 · HTML: https://mlsanity.com/paper/2511.00904/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 2 Nov 2025.

## Builds on (most cited first, 14 of 14)

- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Efficient Neuromorphic Signal Processing with Loihi 2](https://mlsanity.com/paper/2111.03746/) (2021)
- [Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attacks](https://mlsanity.com/paper/2110.12976/) (2021)
- [Memory and information processing in neuromorphic systems](https://mlsanity.com/paper/1506.03264/) (2015)
- [LyaNet: A Lyapunov Framework for Training Neural ODEs](https://mlsanity.com/paper/2202.02526/) (2022)
- [SpiNNaker2: A Large-Scale Neuromorphic System for Event-Based and Asynchronous Machine Learning](https://mlsanity.com/paper/2401.04491/) (2024)
- [Robust Design of Deep Neural Networks against Adversarial Attacks based on Lyapunov Theory](https://mlsanity.com/paper/1911.04636/) (2019)
- [Roadmap to Neuromorphic Computing with Emerging Technologies](https://mlsanity.com/paper/2407.02353/) (2024)
- [Robust Stable Spiking Neural Networks](https://mlsanity.com/paper/2405.20694/) (2024)
- [Noise Sensitivity and Stability of Deep Neural Networks for Binary Classification](https://mlsanity.com/paper/2308.09374/) (2023)

## Built on by (most cited first, 1 of 1)

- [Convex Optimization of Spiking Neural Networks with Global and Approximation Guarantees](https://mlsanity.com/paper/2605.08022/) (2026)

## Abstract (arXiv)

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.