1 citations · 1 across the 5 of their papers we have counts for
5 papers
Minimal Filling Architectures for Polynomial Neural Networks
Kevin Dao, Jose Israel Rodriguez
Minimal filling architectures describe the smallest hidden-layer widths for which the neurovariety of a polynomial neural network fills its ambient function space. It was conjectur…
Euclidean distance degree defect of singular projective varieties
Laurenţiu G. Maxim, Jose Israel Rodriguez, Botong Wang
The unit Euclidean distance degree and the generic Euclidean distance degree are two well-studied invariants of projective varieties. These quantities measure the algebraic complex…
Rigid homotopies for sampling from algebraic varieties: a Waring structure complexity model
Abigail R. Jones, Kisun Lee, Jose Israel Rodriguez
Polynomial system solving has seen major progress in both theory and practice over the past decade. A landmark achievement was addressing Smale's 17th problem, establishing average…
The Euclidean distance degree of one-parameter anchored multiview varieties
Bella Finkel, Jose Israel Rodriguez
Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as thei…
Activation degree thresholds and expressiveness of polynomial neural networks
Bella Finkel, Jose Israel Rodriguez, Chenxi Wu +1
We study the expressive power of deep polynomial neural networks through the geometry of their neurovariety. We introduce the notion of the activation degree threshold of a network…