Robust motifs of threshold-linear networks

TL;DR

This paper characterizes robust and flexible motifs in inhibition-dominated threshold-linear networks using graph theory, identifying key structures that determine fixed point stability and network dynamics.

Contribution

It provides a purely graphical characterization of robust and flexible motifs in TLNs, revealing that most robust motifs are simple feedforward architectures.

Findings

Most robust motifs are from two infinite families of feedforward graphs.

Robust motifs have fixed point structures independent of connectivity matrix.

Flexible motifs exhibit multiple dynamic regimes.

Abstract

To any inhibition-dominated threshold-linear network (TLN) we can associate a directed graph that captures the pattern of strong and weak inhibition between neurons. Robust motifs are graphs for which the structure of fixed points in the network is independent of the choice of connectivity matrix $W$, and whose dynamics are thus greatly constrained. This makes them ideal building blocks for constructing larger networks whose behaviors are robust to changes in connection strengths. In contrast, flexible motifs correspond to networks with multiple dynamic regimes. In this work, we give a purely graphical characterization of both flexible and robust motifs of any size. We find that all but a few robust motifs fall into two infinite families of graphs with simple feedforward architectures.