发表机构
Cisco Research; The University of Texas at Austin（思科研究院; 德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对掩码扩散语言模型约束解码中的轨迹偏差问题，提出TWISTER解码器，利用自动机扭曲序贯蒙特卡洛与Feynman-Kac校正，实现无偏的Doob h变换路径采样。
AI 中文摘要
掩码扩散语言模型（MDLMs）的约束解码旨在确保生成的输出满足指定的结构或语法约束。MDLMs通过反复解掩码当前状态中的掩码位置来生成输出。最近的约束解码策略通过使用自动机强制执行所需约束，来约束模型的每步平均场后验（该后验在掩码位置上分解）。由此产生的链式结构因子图允许通过动态规划进行精确的约束采样。然而，尽管每次抽取都是精确且满足约束的，我们证明它们的组合通常会在有效轨迹上偏离模型的相对概率，从而导致轨迹偏差。我们推导出该偏差的精确表达式，作为衡量当去噪器被重新条件化时有效延续质量如何变化的比率乘积，并刻画了偏差消失的条件。然后，我们通过引入TWISTER——首个用于MDLMs的自动机扭曲序贯蒙特卡洛解码器——来纠正偏差，使用逐步精确解码器作为提议分布。我们证明，对于正则语言约束，Feynman-Kac校正可以精确计算，其中扭曲利用为逐步精确采样预计算的数量高效获得。我们证明所得的Feynman-Kac模型以无偏的Doob h变换路径律为目标，该路径律以约束满足为条件。
英文摘要
Constrained decoding for Masked Diffusion Language Models (MDLMs) aims to ensure that generated outputs satisfy a specified structure or syntax constraint. MDLMs generate outputs by repeatedly unmasking masked positions present in their current state. Recent strategies for constrained decoding constrain the model's per-step mean-field posterior (which factorizes over masked positions) by enforcing the desired constraint with an automaton. The resulting chain-structured factor graph allows exact constrained sampling via dynamic programming. However, despite each draw being exact and constraint-satisfying, we prove that their composition, in general, tilts away from the model's relative probabilities over valid trajectories, thus leading to trajectory bias. We derive an exact expression for this bias as a product of ratios measuring how valid continuation mass changes when the denoiser is reconditioned, and characterize when the bias vanishes. We then correct the bias by introducing TWISTER, the first automaton-twisted Sequential Monte Carlo decoder for MDLMs, using the step-exact decoder as the proposal. We show that for regular language constraints, the Feynman-Kac correction is exactly computable, with the twists obtained efficiently using quantities pre-computed for step-exact sampling. We prove that the resulting Feynman-Kac model targets the unbiased Doob h-transformed path law conditioned on constraint satisfaction.
CommentsPreprint under review
