On the synaptic matrix eigenvalues of sparsely connected neural networks

Fuente: arXiv
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Main Authors: Ansari, Mohd. Gayas, Shukla, Pragya
Format: Preprint
Published: 2026
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author Ansari, Mohd. Gayas
Shukla, Pragya
author_facet Ansari, Mohd. Gayas
Shukla, Pragya
contents The spectral behaviour of the synaptic matrix, representing the neuronal connection strengths, is an important tool to analyze the stability and transient dynamics of a typical brain as well as its learning process and memory capacity. The complexity of the brain due to large number of neurons as well as underlying transient mechanisms e.g. homeostasis, seizure or synaptic plasticity can lead to networks with time-varying degree and type of sparsity. This renders an exact determination of the synaptic matrix not only technically difficult but also meaningless, leaving its statistical analysis as the best available theoretical approach. This motivates us to pursue a spectral analysis of the synaptic matrix models with different type of sparsity and thereby analyze latter's role on various aspects of network dynamics and stability. Our results have potential relevance for detemining the type of synaptic sparsity required to induce a specific brain function or desired transient mechanism e.g for pharmacological effects or physiological modulators.
format Preprint
id arxiv_https___arxiv_org_abs_2606_00326
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the synaptic matrix eigenvalues of sparsely connected neural networks
Ansari, Mohd. Gayas
Shukla, Pragya
Neurons and Cognition
Disordered Systems and Neural Networks
The spectral behaviour of the synaptic matrix, representing the neuronal connection strengths, is an important tool to analyze the stability and transient dynamics of a typical brain as well as its learning process and memory capacity. The complexity of the brain due to large number of neurons as well as underlying transient mechanisms e.g. homeostasis, seizure or synaptic plasticity can lead to networks with time-varying degree and type of sparsity. This renders an exact determination of the synaptic matrix not only technically difficult but also meaningless, leaving its statistical analysis as the best available theoretical approach. This motivates us to pursue a spectral analysis of the synaptic matrix models with different type of sparsity and thereby analyze latter's role on various aspects of network dynamics and stability. Our results have potential relevance for detemining the type of synaptic sparsity required to induce a specific brain function or desired transient mechanism e.g for pharmacological effects or physiological modulators.
title On the synaptic matrix eigenvalues of sparsely connected neural networks
topic Neurons and Cognition
Disordered Systems and Neural Networks
url https://arxiv.org/abs/2606.00326