4 papers
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…
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…
A large color -matrix for
Angus Gruen, Lara San Martín Suárez
We construct the invariant for any positive braid knot , whose existence was conjectured by Park, building on earlier work…
What makes math problems hard for reinforcement learning: a case study
Ali Shehper, Anibal M. Medina-Mardones, Lucas Fagan +6
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high…