5 papers
New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction
Paul Orland, Lucas Fagan, Michele Tarquini +7
The snake-in-the-box problem asks for a longest induced path in the hypercube graph . We find a length-191 snake in dimension , the lowest dimension where the maximum 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…
Going to the Other Side via the Resurgent Bridge
Ovidiu Costin, Gerald V. Dunne, Angus Gruen +1
Using resurgent analysis we offer a novel mathematical perspective on a curious bijection (duality) that has many potential applications ranging from the theory of vertex algebras…