Graphon Signal Processing for Spiking and Biological Neural Networks

TL;DR

This paper introduces Graphon Signal Processing (GnSP), a novel framework that enhances neural network analysis by providing stable, efficient spectral methods for stimulus identification in biological and simulated neural data.

Contribution

It applies GnSP to neural networks, demonstrating improved stimulus classification and robustness, and is the first to do so in biological neural networks.

Findings

GnSP yields low-dimensional, trial-invariant embeddings for neural data.

Embeddings improve stimulus classification over PCA and baseline GSP methods.

Embeddings are stable across network stochasticity, size, and noise.

Abstract

Graph Signal Processing (GSP) extends classical signal processing to signals defined on graphs, enabling filtering, spectral analysis, and sampling of data generated by networks of various kinds. Graphon Signal Processing (GnSP) develops this framework further by employing the theory of graphons. Graphons are measurable functions on the unit square that represent graphs and limits of convergent graph sequences. The use of graphons provides stability of GSP methods to stochastic variability in network data and improves computational efficiency for very large networks. We use GnSP to address the stimulus identification problem (SIP) in computational and biological neural networks. The SIP is an inverse problem that aims to infer the unknown stimulus s from the observed network output f. We first validate the approach in spiking neural network simulations and then analyze calcium imaging recordings. Graphon-based spectral projections yield trial-invariant, lowdimensional embeddings that improve stimulus classification over Principal Component Analysis and discrete GSP baselines. The embeddings remain stable under variations in network stochasticity, providing robustness to different network sizes and noise levels. To the best of our knowledge, this is the first application of GnSP to biological neural networks, opening new avenues for graphon-based analysis in neuroscience.