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

2025-08-27

AI Summary

Normalizing flows suffer from limited expressiveness and poor interpretability in high-dimensional density estimation and generative modeling. To address this, we propose Fractal Flow—a reversible generative model that integrates topic modeling with a fractal-inspired recursive architecture. Methodologically, we couple Latent Dirichlet Allocation (LDA) with a Kolmogorov–Arnold network to construct a semantically interpretable latent space; additionally, we design a fractal-motivated recursive invertible module that enhances modeling capacity via hierarchical Jacobian transformations. Experiments on MNIST, Fashion-MNIST, CIFAR-10, and geophysical datasets demonstrate significant improvements in density estimation accuracy. Moreover, the model enables semantic clustering in latent space and fine-grained controllable generation. By unifying expressive power with structural transparency, Fractal Flow achieves both state-of-the-art performance and intrinsic interpretability—advancing the frontier of principled, human-understandable deep generative modeling.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Large language models for search

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.

Problem

• Enhancing expressiveness and interpretability in normalizing flows
• Modeling hierarchical semantic clusters through structured latent space
• Improving transformation interpretability and estimation accuracy recursively

Innovation

• Integrates Kolmogorov-Arnold Networks and Latent Dirichlet Allocation
• Uses recursive modular design inspired by Fractal Generative Models
• Constructs structured interpretable latent space for hierarchical clustering