From the 1 of 7 linked papers with an AI index.
7 papers
On the Log-submodularity for zonoids: from Mixed Volume inequalities to the Hypercube
Gennadiy Averkov, Katherina von Dichter, Ivan Soprunov
We prove a log-submodularity-type inequality for zonoids in , extending the three-dimensional result of Fradelizi, Madiman, Meyer, and Zvavitch. More generally, we co…
Shallower ReLU Network Representations via Exact Linear Algebra
Kilian RueÃ, Gennadiy Averkov, Florestan Brunck +7
We prove that the maximum of real numbers is exactly representable by a ReLU network with two hidden layers for every . The constructions are obtained by reducing the…
Mixed volumes of zonoids and the absolute value of the Grassmannian
Gennadiy Averkov, Katherina von Dichter, Simon Richard +1
The paper develops a combinatorial framework linking mixed volumes of zonoids with the absolute value image of the Grassmannian, and uses polyhedral computations to produce new Min…
Exact Flatness Constant for One-Point Convex Bodies and the Discrete Isominwidth Problem: The Planar Case
Gennadiy Averkov, Giulia Codenotti, Ansgar Freyer +1
A variant of the flatness problem from integer programming is studied, in which one considers convex bodies in with at most interior lattice points. The maximum…
Optimal Proximity Bound and Product Function Estimates in Integer Linear Programming
Iskander Aliev, Gennadiy Averkov, William Jones +1
We obtain an optimal proximity bound for integer linear programs in standard form max{cx: Ax=b, x nonnegative integer}, where A is an integer mxn matrix of rank m<n and b is an int…
Nonnegativity of signomials with Newton simplex over -convex sets
Gennadiy Averkov, Jonas Ellwanger, Thorsten Theobald +1
We study a class of signomials whose positive support is the set of vertices of a simplex and which may have several negative support points in the simplex. Various groups of autho…