11 citations · 47 across the 48 of their papers we have counts for
58 papers
Shallower ReLU Network Representations via Exact Linear Algebra
Kilian Rueß, Gennadiy Averkov, Florestan Brunck +7
We study the depth required by ReLU networks to exactly represent piecewise linear functions, focusing specifically on the maximum function. This problem has recently received sign…
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…
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…
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…
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…
On the Expressiveness of Rational ReLU Neural Networks With Bounded Depth
Gennadiy Averkov, Christopher Hojny, Maximilian Merkert
To confirm that the expressive power of ReLU neural networks grows with their depth, the function has been considered in the literature. A conject…