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Graphon Signal Processing for Spiking and Biological Neural Networks
Journal article   Open access   Peer reviewed

Graphon Signal Processing for Spiking and Biological Neural Networks

Takuma Sumi and Georgi S Medvedev
Neural computation, v 38(6), pp 1090-1115
23 Apr 2026
DOI: https://doi.org/10.1162/NECO.a.1522
PMID: 42048399
url
https://arxiv.org/pdf/2508.17246View
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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 sfrom 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, low-dimensional 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.

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