# Gibbs Manifolds

arXiv: https://arxiv.org/abs/2211.15490 · HTML: https://mlsanity.com/paper/2211.15490/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Entropic covariance models](https://mlsanity.com/paper/2306.03590/) (2023)
- [Prediction Is Not a Sufficient Memory State](https://mlsanity.com/paper/2610.13881/) (2026)

## Abstract (arXiv)

Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety is the zero locus of all polynomials that vanish on the Gibbs manifold. We compute these polynomials and show that the Gibbs variety is low-dimensional. Our theory is applied to a wide range of scenarios, including matrix pencils and quantum optimal transport.