用高阶代数构建生成流模型，提升生成效果
Higher Gauge Flow Models
- 基于L∞代数扩展传统流模型框架
- 在高斯混合数据集上显著优于传统流模型
- 适合研究高阶对称性与生成模型的学者
本文提出一类新型生成流模型——高阶规范流模型（Higher Gauge Flow Models）。该模型在普通规范流模型（arXiv:2507.13414）基础上，引入L∞-代数，有效拓展了李代数结构。这一扩展使模型能够整合高阶群所对应的高阶几何与高阶对称性，从而丰富生成模型的数学基础。在高斯混合模型数据集上的实验表明，该模型相较传统流模型表现出显著性能提升。
原文摘要 · Abstract (English)
This paper introduces Higher Gauge Flow Models, a novel class of Generative Flow Models. Building upon ordinary Gauge Flow Models (arXiv:2507.13414), these Higher Gauge Flow Models leverage an L$_{\infty}$-algebra, effectively extending the Lie Algebra. This expansion allows for the integration of the higher geometry and higher symmetries associated with higher groups into the framework of Generative Flow Models. Experimental evaluation on a Gaussian Mixture Model dataset revealed substantial performance improvements compared to traditional Flow Models.
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