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Higher Gauge Flow Models

arXiv 2507.16334 ↗First posted 22 Jul 2025cs.AI cs.LG math.DGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 14 of its 45 references that are in the map. First posted on arXiv 22 Jul 2025.

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References · 14

  1. 2022Flow Matching for Generative Modelingcited by 5,702
  2. 2018Neural Ordinary Differential Equationscited by 3,779
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2023Flow Matching on General Geometriescited by 265
  5. 2017Backprop as Functor: A compositional perspective on supervised learningcited by 44
  6. 2021Categorical Foundations of Gradient-Based Learningcited by 44
  7. 2021Category Theory in Machine Learningcited by 36
  8. 2024Position: Categorical Deep Learning is an Algebraic Theory of All Architecturescited by 32
  9. 2019Lenses and Learnerscited by 11
  10. 2024Fundamental Components of Deep Learning: A category-theoretic approachcited by 5
  11. 2020Homotopy Theoretic and Categorical Models of Neural Information Networkscited by 4
  12. 2022Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Marketscited by 2
2 more
  1. 2024Towards a Categorical Foundation of Deep Learning: A Surveycited by 2
  2. 2025Gauge Flow Modelscited by 2

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