# Colored Jones Polynomials and the Volume Conjecture

arXiv: https://arxiv.org/abs/2502.18575 · HTML: https://mlsanity.com/paper/2502.18575/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 59 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Is deep learning a useful tool for the pure mathematician?](https://mlsanity.com/paper/2304.12602/) (2023)
- [Disentangling a Deep Learned Volume Formula](https://mlsanity.com/paper/2012.03955/) (2020)
- [Learning knot invariants across dimensions](https://mlsanity.com/paper/2112.00016/) (2021)
- [Rigor with Machine Learning from Field Theory to the Poincar'e Conjecture](https://mlsanity.com/paper/2402.13321/) (2024)
- [Big Data Approaches to Knot Theory: Understanding the Structure of the Jones Polynomial](https://mlsanity.com/paper/1912.10086/) (2019)
- [Learning BPS Spectra and the Gap Conjecture](https://mlsanity.com/paper/2405.09993/) (2024)

## Abstract (arXiv)

Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-colored Jones polynomials or adjoint Jones polynomials. Training a subset of the data using a fully connected feedforward neural network, we predict the volume of the knot complement of hyperbolic knots from the adjoint Jones polynomial or its evaluations with 99.34% accuracy. A function of the adjoint Jones polynomial evaluated at the phase q=e 8 π i / 15  predicts the volume with nearly the same accuracy as the neural network. From an analysis of 2-colored and 3-colored Jones polynomials, we conjecture the best phase for n-colored Jones polynomials, and use this hypothesis to motivate an improved statement of the volume conjecture. This is tested for knots for which closed form expressions for the n-colored Jones polynomial are known, and we show improved convergence to the volume.