# Big data comparison of quantum invariants

arXiv: https://arxiv.org/abs/2503.15810 · HTML: https://mlsanity.com/paper/2503.15810/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 70 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 4 of 4)

- [Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial](https://mlsanity.com/paper/1912.10086/) (2019)
- [Big data approach to Kazhdan-Lusztig polynomials](https://mlsanity.com/paper/2412.01283/) (2024)
- [Mapper-type algorithms for complex data and relations](https://mlsanity.com/paper/2109.00831/) (2021)
- [Monoidal categories, representation gap and cryptography](https://mlsanity.com/paper/2201.01805/) (2022)

## Built on by (most cited first, 3 of 3)

- [On detection probabilities of link invariants](https://mlsanity.com/paper/2509.05574/) (2025)
- [On knot detection via picture recognition](https://mlsanity.com/paper/2510.06284/) (2025)
- [RL unknotter, hard unknots and unknotting number](https://mlsanity.com/paper/2603.07955/) (2026)

## Abstract (arXiv)

We apply big data techniques, including exploratory and topological data analysis, to investigate quantum invariants. More precisely, our study explores the Jones polynomial's structural properties and contrasts its behavior under four principal methods of enhancement: coloring, rank increase, categorification, and leaving the realm of Lie algebras.