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…
Decomposition Polyhedra of Piecewise Linear Functions
Marie-Charlotte Brandenburg, Moritz Grillo, Christoph Hertrich
In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions. Eve…
Most ReLU Networks Admit Identifiable Parameters
Moritz Grillo, Guido Montúfar
We study the realization map of deep ReLU networks, focusing on when a function determines its parameters up to scaling and permutation. To analyze hidden redundancies beyond these…
The Symmetries of Three-Layer ReLU Networks
Johanna Marie Gegenfurtner, Moritz Grillo, Guido Montúfar
We develop a framework for analyzing parameter symmetries in deep ReLU networks and obtain a complete characterization of the generic parameter fibers for three-layer bottleneck ar…
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…
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…