# Information Geometry for the Working Information Theorist

arXiv: https://arxiv.org/abs/2310.03884 · HTML: https://mlsanity.com/paper/2310.03884/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 74 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [The Information Geometry of Mirror Descent](https://mlsanity.com/paper/1310.7780/) (2013)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [A gradient descent perspective on Sinkhorn](https://mlsanity.com/paper/2002.03758/) (2020)
- [Sparse Continuous Distributions and Fenchel-Young Losses](https://mlsanity.com/paper/2108.01988/) (2021)
- [Quantum query complexity of entropy estimation](https://mlsanity.com/paper/1710.06025/) (2017)
- [When Optimal Transport Meets Information Geometry](https://mlsanity.com/paper/2206.14791/) (2022)
- [Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm](https://mlsanity.com/paper/2307.16421/) (2023)
- [Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover](https://mlsanity.com/paper/2008.10249/) (2020)
- [Clustering above Exponential Families with Tempered Exponential Measures](https://mlsanity.com/paper/2211.02765/) (2022)
- [Conformal Mirror Descent with Logarithmic Divergences](https://mlsanity.com/paper/2209.02938/) (2022)
- [Generalized Bayesian Cram'er-Rao Inequality via Information Geometry of Relative α-Entropy](https://mlsanity.com/paper/2002.04732/) (2020)
- [Cram'er-Rao Lower Bounds Arising from Generalized Csisz'ar Divergences](https://mlsanity.com/paper/2001.04769/) (2020)
- [Information Geometry and Classical Cram'er-Rao Type Inequalities](https://mlsanity.com/paper/2104.01061/) (2021)

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

- [The Spacetime of Diffusion Models: An Information Geometry Perspective](https://mlsanity.com/paper/2505.17517/) (2025)

## Abstract (arXiv)

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information, sufficient statistics, and efficient estimators. Today, information geometry has emerged as an interdisciplinary field that finds applications in diverse areas such as radar sensing, array signal processing, quantum physics, deep learning, and optimal transport. This article presents an overview of essential information geometry to initiate an information theorist, who may be unfamiliar with this exciting area of research. We explain the concepts of divergences on statistical manifolds, generalized notions of distances, orthogonality, and geodesics, thereby paving the way for concrete applications and novel theoretical investigations. We also highlight some recent information-geometric developments, which are of interest to the broader information theory community.