Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetry

ArXi:2511.01064v3 Announce Type: replace-cross Variational inference (VI) approximates a target density $p$ by the best match $q$ in a family of tractable distributions. The best variational approximation is found by minimizing a divergence between distributions, $D(p||q)$, and several divergences have been proposed as objective functions for VI, with different choices leading to different approximations. We show that even when these divergences have different minimizers, the resulting approximations all abide by certain symmetry-matching principles.