Symmetries constrain dynamics in a family of balanced neural networks

TL;DR

This paper investigates how symmetries influence the dynamics of balanced neural networks constrained by Dale's Law, revealing that symmetry-based analysis provides insights beyond spectral properties.

Contribution

It introduces a symmetry-based framework to analyze constrained neural networks, showing that equivariant bifurcation theory reveals structural insights despite perturbations.

Findings

Symmetry structures persist in constrained networks.

Spectral analysis alone is insufficient to predict dynamics.

Symmetry-based methods offer valuable understanding of neural network behavior.

Abstract

We examine a family of random firing-rate neural networks in which we enforce the neurobiological constraint of Dale's Law --- each neuron makes either excitatory or inhibitory connections onto its post-synaptic targets. We find that this constrained system may be described as a perturbation from a system with non-trivial symmetries. We analyze the symmetric system using the tools of equivariant bifurcation theory, and demonstrate that the symmetry-implied structures remain evident in the perturbed system. In comparison, spectral characteristics of the network coupling matrix are relatively uninformative about the behavior of the constrained system.