5 papers · 1 filter
Removing spurious minima for planar features by skip connections
Jakob Paul Zimmermann, Moritz Grillo, Andrei Balakin +1
Understanding loss landscapes is central to explaining neural-network training, yet their structure remains only partially understood even in simple models. We study the Gaussian p…
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…
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.…
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…