Higher Gauge Flow Models

2025/07/22 by Strunk, Alexander, Assam, Roland
#Artificial Intelligence (cs.AI) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2507.16334

Abstract

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_∞-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.

Citations

• Gauge Flow Models
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• Position: Categorical Deep Learning is an Algebraic Theory of All Architectures
• Higher geometry in physics
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• Flow Matching for Generative Modeling
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• Category Theory in Machine Learning
• Categorical Foundations of Gradient-Based Learning
• Homotopy Theoretic and Categorical Models of Neural Information Networks
• L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism
• Neural Ordinary Differential Equations
• Differential cohomology in a cohesive infinity-topos
• Differentiable Stacks and Gerbes
• Higher Gauge Theory
• From Loop Groups to 2-Groups
• Strongly homotopy Lie algebras

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