{"slug": "direct-message-approximation-dma-a-consistency-based-framework-for-tractable-on", "title": "Direct Message Approximation (DMA): A Consistency-Based Framework for Tractable Approximate Inference on Factor Graphs", "summary": "Researchers introduced Direct Message Approximation (DMA), a consistency-based framework that approximates factor-to-variable messages directly on factor graphs rather than approximating marginals as expectation propagation (EP) and variational message passing (VMP) do. The authors prove a master theorem bounding marginal KL divergence from message KL divergence for any graph, with corollaries eliminating EP-style inner-loop iteration and negative-precision messages, plus an O(1/r^2) guarantee for the product factor's improper backward message. They derive explicit DMA messages for the product and leaky-ReLU factors and assemble a Bayesian neural network inference algorithm requiring one forward/backward sweep per training example and no gradient learning-rate hyperparameter, with predictive uncertainty widening in data-sparse regions under model mismatch.", "body_md": "arXiv:2609.29466v1 Announce Type: new \nAbstract: Approximate message passing on factor graphs underlies two dominant families of probabilistic inference algorithms: expectation propagation (EP) and variational message passing (VMP). Both methods approximate the marginal at each factor edge, forcing an iterative round-robin schedule, risking negative-precision messages, and, for VMP, collapsing to point estimates at Dirac-delta factors. We introduce Direct Message Approximation (DMA), which approximates factor-to-variable messages directly rather than the marginal. For normalisable factors, we define a consistency condition (requiring exactness when all other incoming messages are Dirac deltas) to guide message construction. We prove a master theorem (proper messages, any graph) bounding marginal KL from message KL, with three structural corollaries: Dirac-input consistency, no EP-style inner-loop iteration, and no negative-precision messages. Further, we prove a complementary $O(1/r^2)$ guarantee for the inherently improper backward message of the product factor, whose closed-form treatment has resisted prior work. As a concrete instantiation, we derive explicit DMA messages for the product and leaky-ReLU factors and assemble a Bayesian neural network (BNN) inference algorithm with one forward/backward sweep per training example and no gradient learning-rate hyperparameter, validating that the structural guarantees translate to predictive uncertainty that widens in data-sparse regions, including under model mismatch.", "url": "https://wpnews.pro/news/direct-message-approximation-dma-a-consistency-based-framework-for-tractable-on", "canonical_source": "https://www.machinebrief.com/news/direct-message-approximation-dma-a-consistency-based-framewo-nv8u", "published_at": "2026-09-25 04:00:00+00:00", "updated_at": "2026-09-25 05:00:59.201374+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "neural-networks", "artificial-intelligence"], "entities": ["Direct Message Approximation", "expectation propagation", "variational message passing", "Bayesian neural network", "leaky-ReLU", "arXiv"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/direct-message-approximation-dma-a-consistency-based-framework-for-tractable-on", "markdown": "https://wpnews.pro/news/direct-message-approximation-dma-a-consistency-based-framework-for-tractable-on.md", "text": "https://wpnews.pro/news/direct-message-approximation-dma-a-consistency-based-framework-for-tractable-on.txt", "jsonld": "https://wpnews.pro/news/direct-message-approximation-dma-a-consistency-based-framework-for-tractable-on.jsonld"}}