Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the fundamental domain of the symmetry group. The quotient proposal is formed by symmetrising a learned normalising flow over the group orbits. We prove that the LCNF oscillation-based certification framework transfers to the quotient metric with a stabiliser-corrected ball-mass bound and improved covering radius, and that the quantile-core certified lower bound improves whenever the unfolded flow exhibits cross-mode proposal deficiency. On Gaussian mixtures (d = 2 - 20), label-switching targets (up to 24 equivalent modes), and a standard Bayesian three-component mixture posterior, the quantile-core certified improvement ratio ranges from 2x to 145x, with the folded certificate empirically nearly dimension-free. On real accelerometer data from a supertall building during Typhoon Mangkhut, FolT-MCMC yields a non-vacuous quantile-core certificate where the unfolded certificate is vacuous.

翻译：有限对称性的贝叶斯模型——如具有可交换成分的混合模型、存在紧邻模态的结构识别问题——定义了在标签置换群作用下不变的后验分布，由此产生冗余的多模态性，降低了MCMC收敛诊断的有效性。本文提出折叠运输MCMC（Folded Transport MCMC, FolT-MCMC），该方法通过在对称群的基本域上构建独立采样器，直接对商后验进行推断。商提议分布通过对群轨道上的学习归一化流进行对称化处理而生成。我们证明了基于LCNF振荡的验证框架可迁移至商度量空间，并具有稳定子修正的球质量界与改进的覆盖半径；同时，当未折叠流存在跨模态提议缺陷时，分位数核验证下界将获得改善。在高斯混合模型（d=2-20）、标签交换目标（多达24个等价模态）以及标准贝叶斯三成分混合后验实验中，分位数核验证改进比从2倍到145倍不等，且折叠验证经验上几乎具有维度无关性。在对台风"山竹"期间超高层建筑实测加速度数据的处理中，FolT-MCMC生成了非平凡的分位数核验证结果，而对应的未折叠验证结果为无效。