标题： 渐近精确变分流通过可逆MCMC核 显示英文标题

标题： Asymptotically exact variational flows via involutive MCMC kernels

摘要： 表达能力最强的变分族——例如归一化流（normalizing flows）——缺乏实用的收敛保证，因为它们的理论保障通常仅在不可行的全局最优解处成立。 在这项工作中，我们提出了一种通用的方法，用于从可逆马尔可夫链蒙特卡洛（involutory MCMC）核构建无需调参且渐近精确的变分流。 该方法的核心组成部分是一种新颖的表示，即将一般的可逆MCMC核视为可逆的保测度迭代随机函数系统，这些系统作为我们的变分流的流映射。 这导致了三个具有总变差收敛证明的新变分族的产生。 我们的框架解决了现有具有类似保证的变分族的关键实际限制（例如MixFlows），同时所需的理论假设显著减弱。 最后，我们在后验逼近、蒙特卡洛估计和规范化常数估计等任务中展示了我们流的竞争性能，超越或匹配了No-U-Turn采样器（NUTS）和黑盒归一化流。 显示英文摘要

摘要： Most expressive variational families -- such as normalizing flows -- lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present a general recipe for constructing tuning-free, asymptotically exact variational flows from involutive MCMC kernels. The core methodological component is a novel representation of general involutive MCMC kernels as invertible, measure-preserving iterated random function systems, which act as the flow maps of our variational flows. This leads to three new variational families with provable total variation convergence. Our framework resolves key practical limitations of existing variational families with similar guarantees (e.g., MixFlows), while requiring substantially weaker theoretical assumptions. Finally, we demonstrate the competitive performance of our flows across tasks including posterior approximation, Monte Carlo estimates, and normalization constant estimation, outperforming or matching No-U-Turn sampler (NUTS) and black-box normalizing flows.