5 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 , $0.44\…
A Census of New Snake-in-the-Box Records
Paul Orland, Lucas Fagan, Michele Tarquini +7
The snake-in-the-box problem, introduced by Kautz in 1958, asks for the longest induced (chordless) path, called a snake, in the hypercube graph . The maximum length is…
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…
Stable Andrews-Curtis Conjecture via Fake Surfaces and Zeeman Conjecture
Lucas Fagan, Yang Qiu, Zhenghan Wang
We propose an induction scheme that aims at establishing the stable Andrews-Curtis conjecture in the affirmative. The stable Andrews-Curtis conjecture is equivalent to the conjectu…