Information Geometry of Variational Bayes

Fuente: arXiv
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1. Verfasser: Khan, Mohammad Emtiyaz
Format: Preprint
Veröffentlicht: 2025
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author Khan, Mohammad Emtiyaz
author_facet Khan, Mohammad Emtiyaz
contents We highlight a fundamental connection between information geometry and variational Bayes (VB) and discuss its consequences for machine learning. Under certain conditions, a VB solution always requires estimation or computation of natural gradients. We show several consequences of this fact by using the natural-gradient descent algorithm of Khan and Rue (2023) called the Bayesian Learning Rule (BLR). These include (i) a simplification of Bayes' rule as addition of natural gradients, (ii) a generalization of quadratic surrogates used in gradient-based methods, and (iii) a large-scale implementation of VB algorithms for large language models. Neither the connection nor its consequences are new but we further emphasize the common origins of the two fields of information geometry and Bayes with a hope to facilitate more work at the intersection of the two fields.
format Preprint
id arxiv_https___arxiv_org_abs_2509_15641
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Information Geometry of Variational Bayes
Khan, Mohammad Emtiyaz
Machine Learning
Artificial Intelligence
We highlight a fundamental connection between information geometry and variational Bayes (VB) and discuss its consequences for machine learning. Under certain conditions, a VB solution always requires estimation or computation of natural gradients. We show several consequences of this fact by using the natural-gradient descent algorithm of Khan and Rue (2023) called the Bayesian Learning Rule (BLR). These include (i) a simplification of Bayes' rule as addition of natural gradients, (ii) a generalization of quadratic surrogates used in gradient-based methods, and (iii) a large-scale implementation of VB algorithms for large language models. Neither the connection nor its consequences are new but we further emphasize the common origins of the two fields of information geometry and Bayes with a hope to facilitate more work at the intersection of the two fields.
title Information Geometry of Variational Bayes
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2509.15641