6 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…
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…
Computing Non-Obtuse Triangulations with Few Steiner Points
Mikkel Abrahamsen, Florestan Brunck, Jacobus Conradi +2
We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given pla…
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…
On the Non-Locality of Edge Insertions
Florestan Brunck
We challenge the idea that edge insertions are local improvement operations and show that the edge-insertion algorithm must sometimes insert an edge between vertices that are at th…