# An overview of uniformity tests on the hypersphere

arXiv: https://arxiv.org/abs/1804.00286 · HTML: https://mlsanity.com/paper/1804.00286/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2018.

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

- [Generalizing and Decoupling Neural Collapse via Hyperspherical Uniformity Gap](https://mlsanity.com/paper/2303.06484/) (2023)
- [Self-supervised learning with rotation-invariant kernels](https://mlsanity.com/paper/2208.00789/) (2022)
- [Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds](https://mlsanity.com/paper/2607.06696/) (2026)
- [Shared Gaussianization: What Gaussian Regularizers Certify About Contrastive Learning, and What They Miss](https://mlsanity.com/paper/2610.10299/) (2026)

## Abstract (arXiv)

When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different from uniformity. We review in this article a reasonably exhaustive collection of uniformity tests for assessing uniformity in the hypersphere. Specifically, we review the classical circular-specific tests, the large class of Sobolev tests with its many notable particular cases, some recent alternative tests, and novel results in the high-dimensional low-sample size case. A reasonably comprehensive bibliography on the topic is provided.