aiqbench analysis
This research applies reinforcement learning to solve complex problems in geometric topology by automating the simplification of knot diagrams through Reidemeister moves. By training agents to navigate these mathematical structures, the study demonstrates a novel intersection where machine learning techniques advance theoretical bounds on unknotting numbers for prime knots and links. This work represents a significant step in using AI to tackle non-trivial challenges within pure mathematics rather than just optimizing standard datasets.
RL unknotter, hard unknots and unknotting number
arXiv:2603.07955v4 Announce Type: replace-cross Abstract: We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on ``very hard'' unknot diagrams and, using diagram inflation, on $4_1\#9_{10}$ where we investigate the recently established and surprising upper bound of three for the unknotting number. In addition, we explain a self-improving workbook-driven extension of the pipeline that systematically improves unknotting number upper bounds on the prime knots.
Abstract:We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on ``very hard'' unknot diagrams and, using diagram inflation, on $4_1\#9_{10}$ where we investigate the recently established and surprising upper bound of three for the unknotting number. In addition, we explain a self-improving workbook-driven extension of the pipeline that systematically improves unknotting number upper bounds on the prime knots.
Geometric Topology (math.GT); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2603.07955 [math.GT]
(or arXiv:2603.07955v4 [math.GT] for this version)
https://doi.org/10.48550/arXiv.2603.07955 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 182 words
