arXiv Machine Learning By Oren Wright, Haoming Jing, Qiaoan Shen, Koichiro Niinuma, Yorie Nakahira, Jos\'e M. F. Moura

Full-Covariance Smoothing of Bayesian Neural Networks for Online Adaptation

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The paper proposes treating a neural network’s layers as time steps in a state‑space model, converting Bayesian training into a smoothing problem. By propagating Gaussian moments forward and applying a Rauch–Tung–Striebel backward pass, weight posteriors are updated in closed form without gradient iterations or replay. The authors extend prior work by introducing a cross‑covariance identity that allows full‑covariance propagation through nonlinear activations, enabling more accurate online adaptation in non‑stationary classification, dynamics learning, and vision‑language‑action policy adaptation.

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