# Search for Z/2 eigenfunctions on the sphere using machine learning

arXiv: https://arxiv.org/abs/2507.13122 · HTML: https://mlsanity.com/paper/2507.13122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 2 of 2)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)

## Built on by (most cited first, 1 of 1)

- [A Machine Learning Approach to the Nirenberg Problem](https://mlsanity.com/paper/2602.12368/) (2026)

## Abstract (arXiv)

We use machine learning to search for examples of Z/2 eigenfunctions on the 2-sphere. For this we created a multivalued version of a feedforward deep neural network, and we implemented it using the JAX library. We found Z/2 eigenfunctions for three cases: In the first two cases we fixed the branch points at the vertices of a tetrahedron and at a cube respectively. In a third case, we allowed the AI to move the branch points around and, in the end, it positioned the branch points at the vertices of a squashed tetrahedron.