8 papers
Volume stability of plank covers
Egor Bakaev, Amir Yehudayoff
We prove a longstanding conjecture of András Bezdek on the stability of plank covers of the planar disk . If a sufficiently small disk is removed, then every fin…
Optimal partial plank coverings
Egor Bakaev, Alexander Polyanskii
A plank of width in a Euclidean space is the set of points lying between two parallel hyperplanes at distance from each other. Bang's theorem says that if a family of plank…
A simplex-based measure of symmetry
Egor Bakaev, Amir Yehudayoff
For compact convex sets , denote by the smallest size of a homothet of that contains . We define a measure of symmetry based on the -si…
A note on the affine plank conjecture
Egor Bakaev, Amir Yehudayoff
In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in is covered by planks, then the total relative width of the planks is at leas…
Approximation Depth of Convex Polytopes
Egor Bakaev, Florestan Brunck, Amir Yehudayoff
We study approximations of polytopes in the standard model for computing polytopes using Minkowski sums and (convex hulls of) unions. Specifically, we study the ability to approxim…
On the Depth of Monotone ReLU Neural Networks and ICNNs
Egor Bakaev, Florestan Brunck, Christoph Hertrich +2
We study two models of ReLU neural networks: monotone networks (ReLU) and input convex neural networks (ICNN). Our focus is on expressivity, mostly in terms of depth, and we pr…
Better Neural Network Expressivity: Subdividing the Simplex
Egor Bakaev, Florestan Brunck, Christoph Hertrich +2
This work studies the expressivity of ReLU neural networks with a focus on their depth. A sequence of previous works showed that hidden layers are suffi…
Linear Families of Triangles and Orthology
Egor Bakaev, Pavel Kozhevnikov
Two triangles are called orthologic if the perpendiculars from the vertices of one of them to the sides of the other are concurrent. In this paper, we explore the concept of orthol…