19 citations · 67 across the 17 of their papers we have counts for
5 papers · 1 filter
Arithmetic Circuits and Neural Networks for Regular Matroids
Christoph Hertrich, Stefan Kober, Georg Loho
We prove that there exist uniform -circuits of size to compute the basis generating polynomial of regular matroids on elements. By tropicalization, this…
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…
The Computational Complexity of Counting Linear Regions in ReLU Neural Networks
Moritz Stargalla, Christoph Hertrich, Daniel Reichman
An established measure of the expressive power of a given ReLU neural network is the number of linear regions into which it partitions the input space. There exist many different,…
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…
Depth-Bounds for Neural Networks via the Braid Arrangement
Moritz Grillo, Christoph Hertrich, Georg Loho
We contribute towards resolving the open question of how many hidden layers are required in ReLU networks for exactly representing all continuous and piecewise linear functions on…