From the 1 of 9 linked papers with an AI index.
12 papers
New Records for the Hadamard Maximal Determinant Problem in Dimensions , , and
Giorgi Butbaia, Pragatheeswaran Vipulanandan, Justin Tan +6
We compute new lower bounds for determinants of -matrices of orders , and , improving previous recorded bounds by , , and , r…
A Census of New Snake-in-the-Box Records
Paul Orland, Lucas Fagan, Michele Tarquini +7
The paper presents new longest induced (chordless) paths, called snakes, in hypercube graphs for dimensions 9 through 13, thereby improving the known lower bounds for the snake-in-…
Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra
Giorgi Butbaia, Paul Orland, Coco Huang +7
Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative exam…
The Two-Hump Problem: Bridging the Difficulty Gap in Mathematical Reinforcement Learning
Lucas Fagan, Michele Tarquini, Ali Shehper +6
Mathematical search problems present a unique challenge for Reinforcement Learning (RL) due to vast search spaces and sparse rewards. In previous works, the Andrews-Curtis (AC) con…
Learning Fricke signs from Maass form Coefficients
Joanna Bieri, Giorgi Butbaia, Edgar Costa +6
In this paper, we conduct a data-scientific investigation of Maass forms. We find that averaging the Fourier coefficients of Maass forms with the same Fricke sign reveals patterns…
Interpretable Machine Learning for Kronecker Coefficients
Giorgi Butbaia, Kyu-Hwan Lee, Fabian Ruehle
We analyze the saliency of neural networks and employ interpretable machine learning models to predict whether the Kronecker coefficients of the symmetric group are zero or not. Ou…