7 papers
Shallower ReLU Network Representations via Exact Linear Algebra
Kilian RueÃ, Gennadiy Averkov, Florestan Brunck +7
We prove that the maximum of real numbers is exactly representable by a ReLU network with two hidden layers for every . The constructions are obtained by reducing the…
Neural Networks and (Virtual) Extended Formulations
Christoph Hertrich, Georg Loho
Neural networks with piecewise linear activation functions, such as rectified linear units (ReLU) or maxout, are among the most fundamental models in modern machine learning. We ma…
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…
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…
Exact Characterization of Aggregate Flexibility via Generalized Polymatroids
Karan Mukhi, Georg Loho, Alessandro Abate
It is well established that the aggregate flexibility inherent in populations of distributed energy resources (DERs) can be leveraged to mitigate the intermittency and uncertainty…
Beyond Value Iteration for Parity Games: Strategy Iteration with Universal Trees
Zhuan Khye Koh, Georg Loho
Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (STOC 2017). The combinatorial object underlying these approaches…