Predicting neural network dynamics via graphical analysis

TL;DR

This paper introduces a graph-based method to predict the nonlinear dynamics of neural networks, specifically CTLNs, by analyzing fixed points and activation sequences derived from the network's connectivity graph.

Contribution

It presents novel graph-based rules and algorithms for predicting neural activity patterns and attractors in CTLNs, advancing understanding of network dynamics from connectivity.

Findings

Graph-based rules determine fixed points in CTLNs.

Algorithm predicts neural activation sequences from graph structure.

Graph symmetries influence the network's attractor set.

Abstract

Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinatorial Threshold-Linear Networks (CTLNs) in order to understand how the pattern of connectivity, as encoded by a directed graph, shapes the emergent nonlinear dynamics of the corresponding network. Important aspects of these dynamics are controlled by the stable and unstable fixed points of the network, and we show how these fixed points can be determined via graph-based rules. We also present an algorithm for predicting sequences of neural activation from the underlying directed graph, and examine the effect of graph symmetries on a network's set of attractors.