Information Geometry of Message Passing
We show that the natural-gradient stationary condition of variational inference has an edge-local form on a Forney-style factor graph. We start from the Bethe free energy and constrain a selected edge marginal to an exponential family. At a stationary point, the natural parameter of that edge equals the sum of two projected messages, one from each incident factor. Each projected message is the natural-gradient projection of the exact belief-propagation log-message at the current receiving marginal, or equivalently, the gradient of its expectation in the so-called mean coordinates. We call the resulting scheme natural-gradient message passing (NGMP). The rule is local; each edge may carry ...
| Authors | Mykola Lukashchuk, Kyrylo Yemets, Alex Ledbetter et al. |
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| Primary category | cs.LG |
| Published | 16 August 2026 |
| Last updated at source | 21 August 2026 |
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