arXiv Machine Learning
Computations of the slice genus and the unknotting number of links via machine learning
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Related stories
arXiv Statistics ML
Sep 10
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 n...
arXiv Machine Learning
Jun 11
Minimal surfaces, Knots, and Neural Networks
arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.
arXiv Machine Learning
Aug 19
On detection probabilities of link invariants
The paper proves that for many standard link invariants, the proportion of distinct invariant values and the detection probability among prime alternating links with at most n crossings decay exponentially in n, with an explicit universal rate. It shows that almost every such link lies in an invariant fiber whose size is itself exponential in n, a phenomenon that applies broadly, including to the Jones and HOMFLYPT polynomials and integral Khovanov homology. The companion website provides detailed data, including complete distributions of fiber sizes, separate alternating and non-alternating data, and topological data analysis.
arXiv AI
Sep 4
AutoGraphForge: Towards Automated Graph Theory Discovery
AutoGraphForge is a computational pipeline designed to automate the discovery, refutation, formalization, and proving of graph-theoretic conjectures. It generates conjectures using a Graffiti3 generator, filters out known results with a novelty filter, tests candidates against a large dataset of graphs, and refines surviving conjectures through counterexample search. The pipeline then translates each conjecture into Lean 4, verifies proofs with neural provers, and integrates the results into a formal library.
arXiv Machine Learning
Sep 25
A New Gap Sequence for Shellsort: RL-Driven Algorithm Discovery Beyond $N^{4/3}$
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
arXiv AI
Oct 2
New Snake-in-the-Box Records via Snakepit Surgery and Learned Construction
The paper reports a new record for the snake-in-the-box problem, presenting a length‑191 snake in the 9‑dimensional hypercube, surpassing the previous 190‑length record that had stood for 14 years. It also establishes new lower bounds for dimensions 10 through 13. The authors introduce a novel search technique called snakepits, which expands the search space by considering collections of disjoint snakes, and propose a new benchmark, Snakepit‑in‑the‑Box, that evaluates maximal edge counts across multiple components. Additionally, they present Beam Anchor, a learned construction algorithm that generates 100 inequivalent length‑190 snakes in dimension 9.