On detection probabilities of link invariants
Read the original on arXiv Machine Learning →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.
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