4 papers
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. We identify linear and nonlinear families of algebraic invariants, includin…
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…
Understanding Learning Invariance in Deep Linear Networks
Hao Duan, Guido Montúfar
Equivariant and invariant machine learning models exploit symmetries and structural patterns in data to improve sample efficiency. While empirical studies suggest that data-driven…
Rapfi: Distilling Efficient Neural Network for the Game of Gomoku
Zhanggen Jin, Haobin Duan, Zhiyang Hang
Games have played a pivotal role in advancing artificial intelligence, with AI agents using sophisticated techniques to compete. Despite the success of neural network based game AI…