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To any inhibition-dominated threshold-linear network (TLN) we can associate adirected graph that captures the pattern of strong and weak inhibition betweenneurons. Robust motifs are graphs for which the structure of fixed points inthe network is independent of the choice of connectivity matrix $W$, and whosedynamics are thus greatly constrained. This makes them ideal building blocksfor constructing larger networks whose behaviors are robust to changes inconnection strengths. In contrast, flexible motifs correspond to networks withmultiple dynamic regimes. In this work, we give a purely graphicalcharacterization of both flexible and robust motifs of any size. We find thatall but a few robust motifs fall into two infinite families of graphs withsimple feedforward architectures.

Robust motifs of threshold-linear networks