11 citations · 20 across the 16 of their papers we have counts for
17 papers
Boundaries of logarithmic Voronoi cells can be transcendental
Yulia Alexandr
We show that logarithmic Voronoi boundaries for one-dimensional algebraic models in the probability simplex need not be algebraic. We give two explicit examples. For a union of two…
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…
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…
Decomposing Determinantal Varieties from Statistics via Matroid Theory
Per Alexandersson, Yulia Alexandr, Emiliano Liwski +2
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases. E…
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…