Mode Collapse of Mean-Field Variational Inference

arXiv:2510.17063v2 Announce Type: replace-cross Abstract: Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. It has been empirically observed that MFVI optimizers often suffer from mode collapse. For example, when the target measure pi is a mixture pi = w P_0 + (1 - w) P_1, the MFVI optimizer tends to place most of its mass near a single component of the mixture. This work provides the first theoretical explanation of mode collapse in MFVI. Starting from two-component mixtures, we introduce the notion of arepsilon-separateness to quantify the separation of the mixture components. We derive explicit bounds on the mass that any MFVI optimizer assigns to each component, when P_0 and P_1 are arepsilon-separated for sufficiently small arepsilon. We further extend this analysis to mixture target distributions with multiple components. Our results reveal that the occurrence of mode collapse crucially depends on the relative position of the components. To address this issue, we propose rotational variational inference (RoVI), which augments MFVI with a rotation matrix. The numerical studies support our theoretical findings and illustrate improved mode coverage with RoVI in Bayesian mixture posteriors, including a real-data example.

Source: arXiv cs.LG | 2026-10-14