1 citations · 1 across the 5 of their papers we have counts for
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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…
Khovanskii bases for semimixed systems of polynomial equations -- a case of approximating stationary nonlinear Newtonian dynamics
Viktoriia Borovik, Paul Breiding, Javier del Pino +2
We provide an approach to counting roots of polynomial systems, where each polynomial is a general linear combination of prescribed, fixed polynomials. Our tools rely on the theory…
Euclidean distance degree and mixed volume
Paul Breiding, Frank Sottile, James Woodcock
We initiate a study of the Euclidean Distance Degree in the context of sparse polynomials. Specifically, we consider a hypersurface f=0 defined by a polynomial f that is general gi…
An algebraic geometry perspective on topological data analysis
Paul Breiding
A short survey on applications of algebraic geometry in topological data analysis.
Quantitative singularity theory for random polynomials
Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Motivated by Hilbert's 16th problem we discuss the probabilities of topological features of a system of random homogeneous polynomials. The distribution for the polynomials is the…