Amortized quadrature for posterior expectations in inverse problems

תקציר מקורי באנגליתarXiv:2606.15871v2 Announce Type: replace-cross Abstract: Uncertainty in the solution of an inverse problem and in the tasks performed on it is quantified by posterior expectations, each an average of an integrand over $M$ posterior samples. While designed quadratures improve on the $O(M^{-1/2})$ error of Monte-Carlo estimation, they solve an optimization problem, often against the posterior density, for every new observation, which can be computationally costly. To address this limitation, we introduce the quadrature field, a set-equivariant network that maps an observation and its $M$ posterior samples to an $M$-node signed-weight quadrature in one forward pass. Trained once on a family of posteriors to minimize the worst-case integration error over a class of functions, it serves any ob