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

• URL: http://arxiv.org/abs/2508.19750v1
• Date: Wed, 27 Aug 2025 10:25:15 GMT
• Title: Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
• Authors: Binhui Zhang, Jianwei Ma,
• Abstract summary: We propose Fractal Flow, a novel normalizing flow architecture that enhances both expressiveness and interpretability.<n> Experiments on MNIST, FashionMNIST, CIFAR-10, and geophysical data demonstrate that the Fractal Flow achieves latent clustering, controllable generation, and superior estimation accuracy.
• Score: 3.648417123399582
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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