类别生成的流对偶性与源几何
Flow Duality and Source Geometry for Categorical Generation
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中文总结 AI 辅助
本文发现连续与离散流匹配间的对偶性，通过argmax投影将连续凸插值转为离散，并揭示源分布几何对类别生成质量的影响。
中文摘要 AI 辅助
连续和离散的流匹配通常被视为两种独立的构造。本文揭示了它们之间的对偶性：将具有独热目标点的连续凸插值路径通过逐位置的argmax投影，可得到离散凸插值路径。这一结果要求源分布具有适当的坐标对称性和边界正则性，并使连续源分布成为类别生成中的一个显式设计选择。我们推导了高斯、有界均匀和中心负指数源所诱导的离散插值行为，表明不同的源几何会导致定性的不同的转换时序和词汇表大小依赖性。小型视觉诊断和一个简短的语言建模试点表明，这些源设计效应也可能出现在学习到的变换和早期生成质量中。
英文摘要
Continuous and discrete flow matching are usually treated as separate constructions. This paper identifies a duality between them: projecting continuous convex-interpolant flows with one-hot targets through a position-wise argmax yields discrete convex-interpolant flows. The result requires source laws with appropriate coordinate symmetry and regularity, and it makes the continuous source distribution an explicit design choice for categorical generation. We derive the induced discrete interpolation behavior for Gaussian, bounded-uniform, and centered negative-exponential sources, showing that different source geometries lead to qualitatively different transition timing and vocabulary-size dependence. Small visual diagnostics and a short language-modeling pilot suggest that these source-design effects can also appear in learned transports and early generative quality.
