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Full-Covariance Smoothing of Bayesian Neural Networks for Online Adaptation

arXiv · AI, language, vision and robotics · article · Sep 23, 2026 · UTC

A neural network's layers can be treated as time steps of a state-space model, turning Bayesian training into a smoothing problem: a forward pass propagates Gaussian moments through the network, and a backward Rauch--Tung--Striebel pass updates the weight posteriors in closed form. Such methods learn from each observation in a single pass, in an uncertainty-aware manner, and without gradient-based iterations or replay, which makes them well suited for online adaptation and data-efficient learning. Existing smoothing-based methods, however, are restricted to diagonal covariances across activati

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