# Directed Simplicial Complexes

Features inside a neural network are often carried by groups of neurons acting together, and a circuit drawn as pairwise edges misses the joint effect of suppressing such a group. The new construction treats the network as a structural causal model, uses counterfactual ablations that stay on the neural manifold to progressively suppress a set of neurons, and admits neuron groups into a directed simplicial complex by a statistical relevance test. On two small handcrafted multilayer perceptrons the complexes recover the designed feature pathways, and their 1-skeletons agree with the edges kept by ACDC, EAP and EAP-IG that a weight graph can express.

Features inside a neural network are often carried by groups of neurons acting together, and a circuit drawn as pairwise edges misses the joint effect of suppressing such a group. The new construction treats the network as a structural causal model, uses counterfactual ablations that stay on the neural manifold to progressively suppress a set of neurons, and admits neuron groups into a directed simplicial complex by a statistical relevance test. On two small handcrafted multilayer perceptrons the complexes recover the designed feature pathways, and their 1-skeletons agree with the edges kept by ACDC, EAP and EAP-IG that a weight graph can express.