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

תקציר מקורי באנגליתarXiv: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 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 the pathlifting Jacobian, also provide a way to compute it without backpropagation and whose computation cost is super efficient in practice c