11 citations · 20 across the 16 of their papers we have counts for
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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…