19 papers
Constraining the outputs of ReLU neural networks
Yulia Alexandr, Guido Montúfar
We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions i…
The Value Function Semi-Algebraic Set in Partially Observable Markov Decision Processes
Ryan A. Anderson, Guido Montufar
We study the geometry of feasible value functions in infinite-horizon partially observable Markov decision processes (POMDPs) under memoryless stochastic policies. Our main contrib…
TriSearch: Learning to Optimize Triangulations via Bistellar Flips
Yiran Wang, Guido Montúfar
We introduce TriSearch, a reinforcement learning framework for optimizing objectives over triangulations of a polytope via bistellar flips. The key idea is a circuit-supported subt…
Implicit Bias of Mirror Flow in Homogeneous Neural Networks: Sparse and Dense Feature Learning
Tom Jacobs, Guido Montufar
We study the max-margin solutions reached by mirror flow in deep neural networks with homogeneous activation functions. Extending classical results on gradient flow, we derive a no…
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…