Transition to chaos in random networks with cell-type-specific connectivity

TL;DR

This paper investigates how cell-type-specific connectivity influences neural network dynamics, revealing a phase transition to chaos and deriving a new spectral radius formula for block-structured matrices, with implications for network capacity.

Contribution

It extends the dynamic mean field method to cell-type-specific networks and derives a novel spectral radius formula for block-structured random matrices.

Findings

Networks exhibit a phase transition from silent to chaotic activity.

Derived a new spectral radius formula for block-structured matrices.

Hyper-excitable neurons can enhance network computational capacity.

Abstract

In neural circuits, statistical connectivity rules strongly depend on neuronal type. Here we study dynamics of neural networks with cell-type specific connectivity by extending the dynamic mean field method, and find that these networks exhibit a phase transition between silent and chaotic activity. By analyzing the locus of this transition, we derive a new result in random matrix theory: the spectral radius of a random connectivity matrix with block-structured variances. We apply our results to show how a small group of hyper-excitable neurons within the network can significantly increase the network's computational capacity.