9 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…
OptFSST: Optimized FSST String Compression
Hedi Chehaidar, Mihail Stoian, Moritz Stargalla +1
Strings account for a substantial fraction of data in modern analytical systems, making lightweight compression with fast random access an important building block for efficient qu…
Parameterized Complexity of -Lipschitz Constants for Input Convex Neural Networks and -Norm Maximization over Zonotopes
Aritra Das, Vincent Froese, Moritz Grillo +6
Lipschitz constants are a standard way to quantify the sensitivity of neural networks to small input perturbations, but computing them is difficult even for shallow ReLU networks.…
Tropical Circuits with Scalar Multiplication Gates
Christoph Hertrich, Moritz Stargalla
We study tropical circuits with scalar multiplication gates, that is, algebraic circuits whose gates implement , , or multiplication with a positive constant. For such cir…
An Adaptive Variable Neighborhood Search for a Family of Set Covering Routing Problems with an Application in Disaster Relief Operations
Andreas Hagn, Jan Krause, Moritz Stargalla +1
This paper studies a variant of the Set Covering Routing Problem (SCRP) motivated by post-disaster humanitarian logistics. We consider a hybrid distribution concept in which the ma…
Parameterized Hardness of Zonotope Containment and Neural Network Verification
Vincent Froese, Moritz Grillo, Christoph Hertrich +1
Neural networks with ReLU activations are a widely used model in machine learning. It is thus important to have a profound understanding of the properties of the functions computed…
Optimized Qubit Routing for Commuting Gates via Integer Programming
Moritz Stargalla, Friedrich Wagner
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective com…
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,…
An Adaptive Variable Neighborhood Search for a Family of Set Covering Routing Problems with an Application in Disaster Relief Operations
Andreas Hagn, Jan Krause, Moritz Stargalla +1
This paper studies a variant of the Set Covering Routing Problem (SCRP) motivated by post-disaster humanitarian logistics. We consider a hybrid distribution concept in which the ma…