SOURCE-LINKED INTELLIGENCE

Rank and computation of the pathlifting Jacobian of a DAG ReLU network

arXiv · AI, language, vision and robotics · article · Sep 16, 2026 · UTC

This paper provides a self-contained proof of the rank of the pathlifting Jacobian of a DAG ReLU network by performing an induction on the network's number of hidden nodes. In fact, the induction is elementary, and the key recipe is to consider the skeleton matrix of the network, a sparse matrix encoding the network paths, and transform the representation of one of its hidden neurons into an output node. The proof relies on intermediate propositions which link the pathlifting, its Jacobian, the network parameters, and its skeleton matrix, which, on top of permitting to conclude on the rank of

Read original source ↗ Open in workspace

recordType

paper

region

Global