发表机构
The Chinese University of Hong Kong, Shenzhen; University of California, Los Angeles（香港中文大学（深圳）; 加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出迭代精确离散引导（IEDG），通过退火轨迹上的阶段后验修正实现未归一化离散目标的高效采样，在Ising、Potts和Max-Cut任务上优于神经基线。
AI 中文摘要
当多模态目标远离易处理的参考分布时，从大型离散状态空间上的未归一化分布中进行采样变得困难。我们提出了迭代精确离散引导（IEDG），一种针对未归一化离散目标的总体精确、轨迹级引导框架。IEDG不是一步学习完整的参考到目标修正，而是沿退火轨迹引入全局玻尔兹曼倾斜。每个阶段学习当前源的增量玻尔兹曼倾斜的阶段局部后验修正，而所得的修正相对于固定解析后验累积。在总体最优时，精确的阶段后验恢复正确的反向动力学，其精确模拟再现目标分布。IEDG通过相对有效样本量（rESS）选择阶段增量，该量控制Rényi-2位移并局部适应退火路径的热力学几何。我们的阶段总变差分析表明，有限重叠将Bregman拟合误差放大$1/\sqrt{\mathrm{rESS}}$，而后验、模拟和截断误差加性进入。IEDG在有序、精确枚举的Ising $4\times4$上改善了所有分布级误差，相对于神经基线，同时在热力学机制上大幅减少了Ising/Potts $16\times16$上的一次性误差，并在若干报告的局部统计和相覆盖指标上达到最佳神经采样器结果。在Max-Cut上，其最佳512和平均样本比率超过所有基线。代码和工件可在https://this URL获取。
英文摘要
Sampling from unnormalized distributions over large discrete state spaces becomes difficult when a multimodal target is far from a tractable reference. We introduce Iterative Exact Discrete Guidance (IEDG), a population-exact, trajectory-wise guidance framework for unnormalized discrete targets. Rather than learn the full reference-to-target correction in one step, IEDG introduces a global Boltzmann tilt along an annealing trajectory. Each stage learns a stage-local posterior correction for an incremental Boltzmann tilt of the current source, while the resulting corrections are accumulated relative to a fixed analytic posterior. At the population optimum, exact stage posteriors recover the correct reverse dynamics, whose exact simulation reproduces the target distribution. IEDG chooses stage increments by relative effective sample size (rESS), which controls Rényi-2 displacement and locally adapts the step size to the thermodynamic geometry of the annealing path. Our stagewise total-variation analysis shows that limited overlap amplifies Bregman fitting error by $1/\sqrt{\mathrm{rESS}}$, while posterior, simulation, and truncation errors enter additively. IEDG improves all distribution-level errors over the neural baselines on ordered, exactly enumerated Ising $4\times4$, while substantially reducing one-shot errors on Ising/Potts $16\times16$ across thermodynamic regimes and attaining the best neural-sampler result on several reported local-statistic and phase-coverage metrics. On Max-Cut, its best-of-512 and average-sample ratios exceed all the baselines. Code and artifacts are available at https://github.com/StillFantasy123/iterative-exact-discrete-guidance.
Comments45 pages, 6 figures. Code and artifacts: https://github.com/StillFantasy123/iterative-exact-discrete-guidance
