47 citations · 232 across the 39 of their papers we have counts for
3 papers · 1 filter
Critical Points of Degenerate Metrics on Algebraic Varieties: A Tale of Overparametrization
Giovanni Luca Marchetti, Erin Connelly, Paul Breiding +1
We study the critical points over an algebraic variety of an optimization problem defined by a quadratic objective that is degenerate. This scenario arises in machine learning when…
Homotopy Iterators
Paul Breiding, Taylor Brysiewicz, Hannah Friedman
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for…
Probabilistic intersection theory in Riemannian homogeneous spaces
Paul Breiding, Peter Bürgisser, Antonio Lerario +1
Let be a Riemannian homogeneous space, where is a compact Lie group with closed subgroup . Classical intersection theory states that the de Rham cohomology ring of $…