40 citations · 460 across the 64 of their papers we have counts for
9 papers · 1 filter
Towards finding hay in a haystack: explicit tensors of border rank greater than in
J. M. Landsberg, Mateusz Michałek
We write down an explicit sequence of tensors in , for all sufficiently large, having border rank at least , overcoming a longstanding barrier…
Vanishing Hessian, wild forms and their border VSP
Hang Huang, Mateusz Michałek, Emanuele Ventura
Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between…
Many faces of symmetric edge polytopes
Alessio D'Alì, Emanuele Delucchi, Mateusz Michałek
Symmetric edge polytopes are a class of lattice polytopes constructed from finite simple graphs. In the present paper we highlight their connections to the Kuramoto synchronization…
Secant varieties of toric varieties arising from simplicial complexes
M. Azeem Khadam, Mateusz Michałek, Piotr Zwiernik
Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affin…
Positivity Certificates via Integral Representations
Khazhgali Kozhasov, Mateusz Michałek, Bernd Sturmfels
Complete monotonicity is a strong positivity property for real-valued functions on convex cones. It is certified by the kernel of the inverse Laplace transform. We study this for n…
Best k-layer neural network approximations
Lek-Heng Lim, Mateusz Michalek, Yang Qi
We show that the empirical risk minimization (ERM) problem for neural networks has no solution in general. Given a training set with correspondin…
Gorenstein graphic matroids
Takayuki Hibi, Michał Lasoń, Kazunori Matsuda +2
The toric variety of a matroid is projectively normal, and therefore it is Cohen-Macaulay. We provide a complete graph-theoretic classification when the toric variety of a graphic…
Uniform matrix product states from an algebraic geometer's point of view
Adam Czapliński, Mateusz Michałek, Tim Seynnaeve
We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equ…
Toric geometry of path signature varieties
Laura Colmenarejo, Francesco Galuppi, Mateusz Michałek
In stochastic analysis, a standard method to study a path is to work with its signature. This is a sequence of tensors of different order that encode information of the path in a c…