# Deep Learning Gauss-Manin Connections

arXiv: https://arxiv.org/abs/2007.13786 · HTML: https://mlsanity.com/paper/2007.13786/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Is deep learning a useful tool for the pure mathematician?](https://mlsanity.com/paper/2304.12602/) (2023)
- [Cluster Algebras: Network Science and Machine Learning](https://mlsanity.com/paper/2203.13847/) (2022)
- [Machine Learning Clifford invariants of ADE Coxeter elements](https://mlsanity.com/paper/2310.00041/) (2023)
- [Learning proofs for the classification of nilpotent semigroups](https://mlsanity.com/paper/2106.03015/) (2021)

## Abstract (arXiv)

The Gauss-Manin connection of a family of hypersurfaces governs the change of the period matrix along the family. This connection can be complicated even when the equations defining the family look simple. When this is the case, it is computationally expensive to compute the period matrices of varieties in the family via homotopy continuation. We train neural networks that can quickly and reliably guess the complexity of the Gauss-Manin connection of a pencil of hypersurfaces. As an application, we compute the periods of 96% of smooth quartic surfaces in projective 3-space whose defining equation is a sum of five monomials; from the periods of these quartic surfaces, we extract their Picard numbers and the endomorphism fields of their transcendental lattices.