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Higher Gauge Flow Models

Alexander Strunk, Roland Assam

TL;DR

This paper introduces Higher Gauge Flow Models, a novel class of Generative Flow Models that leverage an L$_{\infty}$-algebra, effectively extending the Lie Algebra, which allows for the integration of the higher geometry and higher symmetries associated with higher groups into the framework of Generative Flow Models.

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$_{\infty}$-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.

Higher Gauge Flow Models

TL;DR

This paper introduces Higher Gauge Flow Models, a novel class of Generative Flow Models that leverage an L-algebra, effectively extending the Lie Algebra, which allows for the integration of the higher geometry and higher symmetries associated with higher groups into the framework of Generative Flow Models.

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.

Paper Structure

This paper contains 14 sections, 15 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Mathematical Background
  3. Graded Vector Space
  4. L$_{\infty}$-algebra
  5. Higher Gauge Flow Model
  6. Experiments
  7. Model
  8. Dataset
  9. Results
  10. Train Loss
  11. Test Loss
  12. Number of Parameters
  13. Related Work
  14. Outlook

Figures (3)

  • Figure 1: Train Loss Comparison (lower is better): The train loss was normalized to the loss of the Higher Gauge Model. Loss values are shown for several dimensions $N$.
  • Figure 2: Test Loss Comparison (lower is better): The test loss was normalized to the loss of the Higher Gauge Model. The test loss values are shown for several dimensions $N$.
  • Figure 3: Number of Parameters