# The Euclidean Distance Degree of Fermat Hypersurfaces

arXiv: https://arxiv.org/abs/1409.0684 · HTML: https://mlsanity.com/paper/1409.0684/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2014.

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

- [Robustness Verification of Polynomial Neural Networks](https://mlsanity.com/paper/2602.06105/) (2026)

## Abstract (arXiv)

Finding the point in an algebraic variety that is closest to a given point is an optimization problem with many applications. We study the case when the variety is a Fermat hypersurface. Our formula for its Euclidean distance degree is a piecewise polynomial whose pieces are defined by subtle congruence conditons.