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

Excerpt

arXiv:2609.18682v2 Announce Type: replace-cross Abstract: 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 p