832 citations · 1.3k across the 79 of their papers we have counts for
11 papers · 1 filter
Polyhedral Geometry of Time-to-First-Spike Neural Networks
Manjot Singh, Guido Montúfar, Gitta Kutyniok
We study the expressivity of spiking neural networks, which provide a natural framework for asynchronous, event-driven computation complementary to conventional feedforward neural…
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…
Stress-Testing Neural Network Verifiers with Provably Robust Instances
David Troxell, Yulia Alexandr, Sofia Hunt +2
Neural network verifiers aim to provide formal guarantees on model behavior, but existing verification benchmarks are fundamentally limited by their lack of ground-truth labels. As…
Differentiable Optimization Layers for Guaranteed Fairness in Deep Learning
David Troxell, Noah Roemer, Guido Montúfar
Differentiable optimization layers are traditionally integrated in predict-then-optimize frameworks where a neural model estimates parameters that subsequently serve as fixed input…
Algebraic Invariants of Lightning Self-Attention
Yulia Alexandr, Hao Duan, Guido Montúfar
We study the polynomial coefficients of lightning self-attention as coordinates of an algebraic variety. In the single-token case, we characterize the coefficient variety as a rank…
Robustness Verification of Polynomial Neural Networks
Yulia Alexandr, Hao Duan, Guido Montúfar
We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance…
Harmful Overfitting in Sobolev Spaces
Kedar Karhadkar, Alexander Sietsema, Deanna Needell +1
Motivated by recent work on benign overfitting in overparameterized machine learning, we study the generalization behavior of functions in Sobolev spaces t…