Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
Binhui Zhang, Jianwei Ma

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…
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