用神经网络自动判断采样何时停止，提升马尔可夫链采样效率
Stop the Sampler! Classifier-Based Adaptive Stopping for Sampling Kernels
- 训练神经分类器动态判断采样是否到达高密度区域并终止
- 平均轨迹长度显著缩短，模式覆盖和混合效果优于传统MCMC
- 适合需要高效采样的复杂概率模型场景
从复杂的未归一化概率密度中采样是贝叶斯推断与概率建模中的基础挑战。尽管马尔可夫链蒙特卡洛（MCMC）方法具有渐近保证，但其常因固定或手动调参的轨迹长度导致混杂慢、计算成本高。本文提出一种新框架，将轨迹终止视为采样动态的可学习组件。通过将MCMC置于非循环生成流网络（GFlowNets）理论框架下，训练状态相关的神经分类器以判断轨迹是否已进入高密度区域并应终止。我们理论上建立了最优分类器与目标密度之间的联系，基于细致平衡条件，并引入多级训练策略以促进复杂几何结构中的探索。在多个基准密度上的实验结果表明，该方法显著减少了平均轨迹长度，同时提升了模式覆盖与混杂性能，优于标准MCMC基线。
原文摘要 · Abstract (English)
Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling. While Markov chain Monte Carlo (MCMC) methods provide asymptotic guarantees, they often suffer from slow mixing and high computational costs due to fixed or manually tuned trajectory lengths. In this work, we propose a novel framework that treats trajectory termination as a learnable component of the sampling dynamics. By framing MCMC within the theory of non-acyclic generative flow networks (GFlowNets), we train state-dependent neural classifiers to decide when a trajectory has reached a high-density region and should terminate. We theoretically establish the connection between optimal classifiers and the target density via detailed balance conditions and introduce a multilevel training scheme to facilitate exploration in complex geometries. Experimental results across various benchmark densities demonstrate that our approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。