# A Generalization of Amari's Bayesian Duality

arXiv: https://arxiv.org/abs/2609.09126 · HTML: https://mlsanity.com/paper/2609.09126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 5 of 5)

- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [SAM as an Optimal Relaxation of Bayes](https://mlsanity.com/paper/2210.01620/) (2022)
- [Dual Parameterization of Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2111.03412/) (2021)
- [Knowledge Adaptation as Posterior Correction](https://mlsanity.com/paper/2506.14262/) (2025)
- [Federated ADMM from Bayesian Duality](https://mlsanity.com/paper/2506.13150/) (2025)

## Abstract (arXiv)

Amari's contributions to information geometry and machine learning are well known. Here, we revisit Amari's work on Bayesian duality which has not received as much attention. We connect Amari's Bayesian duality to a convex duality of Bayes' rule. Using this connection, we present a generalization of Amari's Bayesian duality and discuss its relevance for modern artificial intelligence.