{"ID":2921624,"CreatedAt":"2026-06-02T02:42:49.606572591Z","UpdatedAt":"2026-06-03T05:56:00.181519634Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.01078","arxiv_id":"2606.01078","title":"Non-Vacuous Certification of Transport MCMC via Oscillation-Controlled Normalizing Flows","abstract":"Transport MCMC trains a normalizing flow to precondition Metropolis--Hastings proposals, achieving high empirical efficiency on challenging posteriors; yet no prior work produces a numerically non-vacuous, rigorous spectral-gap bound for such samplers. We establish the first such bounds. For independence MH on the banana family we certify (γ^\\ast = 0.828) at (D = 2) (covering in the original space) and (γ^\\ast \\ge 7.6\\times 10^{-4}) at (D = 5) (covering in an analytically unwarped Gaussian space with a grid-certified gradient bound under the stated numerical Lipschitz certification), both rigorous at 95% confidence. The framework rests on three pillars: (i) spectral normalization with reduced scale clips constrains the flow Lipschitz constant from (10^{47}) to (10^4); (ii) a coverage-based empirical oscillation bound replaces the vacuous analytical bound with a data-dependent certificate; and (iii) oscillation-regularised training cuts the empirical oscillation by 60--90% at no cost to density fit, extending practical certificates through (D = 20) ((γ^\\ast \\ge 1.7\\times 10^{-4})). Tests on four further targets (Gaussian mixture, shear-building, Neal's funnel, Bayesian logistic regression) identify three precise barriers: boundary curvature, target stiffness, and tail-coverage mismatch. An affine-vs-spline comparison shows that simpler architectures yield tighter certificates at identical NLL, inverting the usual expressiveness hierarchy.","short_abstract":"Transport MCMC trains a normalizing flow to precondition Metropolis--Hastings proposals, achieving high empirical efficiency on challenging posteriors; yet no prior work produces a numerically non-vacuous, rigorous spectral-gap bound for such samplers. We establish the first such bounds. For independence MH on the bana...","url_abs":"https://arxiv.org/abs/2606.01078","url_pdf":"https://arxiv.org/pdf/2606.01078v1","authors":"[\"Jun Hu\"]","published":"2026-05-31T07:46:48Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.CO\",\"stat.ME\"]","methods":"[]","has_code":false}