Direct Bethe Free Energy Minimization for Bayesian Neural Networks

תקציר מקורי באנגליתarXiv:2605.08446v4 Announce Type: replace Abstract: Bayesian neural networks are typically trained on the evidence lower bound (ELBO), which keeps the joint likelihood but pays a Jensen gap at every observation. We train by local consistency instead: direct minimisation of the Bethe free energy, whose data term pays no gap-it scores each observation exactly by its predictive density, a strictly proper rule, for any likelihood with a tractable predictive convolution. Our departure is free routing: the beliefs are trained as free parameters of this objective, jointly with the backbone, rather than bound to the conjugate posterior computed in closed form (closed routing). Instantiated with a Gaussian last layer over a deterministic backbone, exact inference appears as the known, closed-routed