From the 1 of 5 linked papers with an AI index.
5 papers
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…
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…
Classification of Cellular Fake Surfaces
Lucas Fagan, Yang Qiu, Zhenghan Wang
Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye…