47 citations · 232 across the 39 of their papers we have counts for
45 papers
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 $…
Computing Arrangements of Hypersurfaces
Paul Breiding, Bernd Sturmfels, Kexin Wang
We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in .
Typical ranks of random order-three tensors
Paul Breiding, Sarah Eggleston, Andrea Rosana
In this paper we study typical ranks of real tensors. In the case the typical ranks are contained in ,…
Degree of the subspace variety
Paul Breiding, Pierpaola Santarsiero
Subspace varieties are algebraic varieties whose elements are tensors with bounded multilinear rank. In this paper, we compute their degrees by computing their volumes.