45 citations · 105 across the 23 of their papers we have counts for
9 papers · 1 filter
Geometry of Polynomial Neural Networks
Kaie Kubjas, Jiayi Li, Maximilian Wiesmann
We study the expressivity and learning process for polynomial neural networks (PNNs) with monomial activation functions. The weights of the network parametrize the neuromanifold. I…
Algebraic degree of optimization over a variety with an application to -norm distance degree
Kaie Kubjas, Olga Kuznetsova, Luca Sodomaco
We study an optimization problem with the feasible set being a real algebraic variety and whose parametric objective function is gradient-solvable with respect to the par…
Exact solutions in low-rank approximation with zeros
Kaie Kubjas, Luca Sodomaco, Elias Tsigaridas
Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the criti…
Uniqueness of nonnegative matrix factorizations by rigidity theory
Robert Krone, Kaie Kubjas
Nonnegative matrix factorizations are often encountered in data mining applications where they are used to explain datasets by a small number of parts. For many of these applicatio…
How to flatten a soccer ball
Kaie Kubjas, Pablo A. Parrilo, Bernd Sturmfels
This is an experimental case study in real algebraic geometry, aimed at computing the image of a semialgebraic subset of 3-space under a polynomial map into the plane. For general…
The geometry of rank-one tensor completion
Thomas Kahle, Kaie Kubjas, Mario Kummer +1
The geometry of the set of restrictions of rank-one tensors to some of their coordinates is studied. This gives insight into the problem of rank-one completion of partial tensors.…
Positive semidefinite rank and nested spectrahedra
Kaie Kubjas, Elina Robeva, Richard Z. Robinson
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general…
Algebraic boundary of matrices of nonnegative rank at most three
Rob H. Eggermont, Emil Horobet, Kaie Kubjas
The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component.…
Conformal blocks, Berenstein-Zelevinsky triangles and group-based models
Kaie Kubjas, Christopher Manon
Work of Buczynska, Wisniewski, Sturmfels and Xu, and the second author has linked the group-based phylogenetic statistical model associated with the group Z/2Z with the Wess-Zumino…