Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy

TL;DR

Fractal Flow introduces a hierarchical, interpretable normalizing flow architecture that combines topic modeling and recursive design to improve density estimation and generate controllable, semantically meaningful data representations.

Contribution

It integrates Kolmogorov-Arnold Networks and LDA into normalizing flows, creating a structured, interpretable latent space with a recursive modular design for enhanced expressiveness.

Findings

Achieves latent clustering and controllable generation.

Demonstrates superior density estimation accuracy.

Validates effectiveness on multiple datasets.

Abstract

Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing flow architecture that enhances both expressiveness and interpretability through two key innovations. First, we integrate Kolmogorov-Arnold Networks and incorporate Latent Dirichlet Allocation into normalizing flows to construct a structured, interpretable latent space and model hierarchical semantic clusters. Second, inspired by Fractal Generative Models, we introduce a recursive modular design into normalizing flows to improve transformation interpretability and estimation accuracy. Experiments on MNIST, FashionMNIST, CIFAR-10, and geophysical data demonstrate that the Fractal Flow achieves latent clustering, controllable generation, and superior estimation accuracy.