5 papers
Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects
Kevin Dao, Jose Israel Rodriguez
We provide counterexamples to the unimodal minimal filling architecture conjecture for polynomial neural networks (PNNs) with power activation functions. Fixing the input and outpu…
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…