发表机构
University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
受掩码离散扩散启发，研究高斯随机场模型单步选择，用局部相关非负分数场表示不确定性，通过距离相关高斯模型衡量所选位置相关性，建立两个互补结果，为理解相关因素对掩码离散扩散中基于置信度一步选择的影响提供基线。
AI 中文摘要
受掩码离散扩散中置信度引导的并行解掩码的启发，我们研究了一个简化的高斯随机场模型中的单个选择步骤。一个局部相关的非负分数场表示位置上的不确定性，调度器选择分数最小的K个位置。通过距离相关的高斯相关模型来衡量所选位置之间的相关性。这种分离为量化低分位置的几何结构如何影响因式分解并行解码的相关成本提供了一个易于处理的框架。我们建立了两个互补的结果。在保守的亚平方根区域，所选块的条件高斯总相关性概率消失。在平方根尺度上，它以正渐近概率保持不可忽略，并允许一个严格正的期望下界。合成实验支持预测的有限尺寸行为。这些结果为理解预算大小、分数相关性和空间相关性如何共同塑造掩码离散扩散中基于置信度的一步选择提供了一个严格的随机几何基线。
英文摘要
Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model. A locally dependent nonnegative score field represents position wise uncertainty, and the scheduler selects the K positions with the smallest scores. Dependence among the selected positions is measured through a distance-dependent Gaussian correlation model. This separation provides a tractable framework for quantifying how the geometry of low-score locations affects the dependence cost of factorized parallel decoding. We establish two complementary results. In a conservative sub-square-root regime, the conditional Gaussian total correlation of the selected block vanishes in probability. At the square-root scale, it remains non-negligible with positive asymptotic probability and admits a strictly positive expectation lower bound. Synthetic experiments support the predicted finite-size behavior. These results provide a rigorous stochastic-geometry baseline for understanding how budget size, score dependence, and spatial correlation jointly shape one-step confidence-based selection in masked discrete diffusion.
Comments27 pages; welcome comments
