Tensor Gauge Flow Models

TL;DR

Tensor Gauge Flow Models are a novel class of generative models that incorporate higher-order tensor gauge fields, enhancing expressiveness and geometric encoding, with improved performance demonstrated on Gaussian mixture data.

Contribution

This work introduces Tensor Gauge Flow Models, extending gauge flow models with higher-order tensor gauge fields for richer geometric representation.

Findings

Achieve better generative performance on Gaussian mixtures

Encode richer geometric and gauge-theoretic structures

Generalize existing gauge flow models

Abstract

This paper introduces Tensor Gauge Flow Models, a new class of Generative Flow Models that generalize Gauge Flow Models and Higher Gauge Flow Models by incorporating higher-order Tensor Gauge Fields into the Flow Equation. This extension allows the model to encode richer geometric and gauge-theoretic structure in the data, leading to more expressive flow dynamics. Experiments on Gaussian mixture models show that Tensor Gauge Flow Models achieve improved generative performance compared to both standard and gauge flow baselines.