分形流：通过主题建模与递归策略构建的层次化可解释归一化流
Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
AI总结：
本文提出分形流，通过结合Kolmogorov-Arnold网络、Latent Dirichlet Allocation和递归模块化设计，构建层次化可解释的归一化流，在多个数据集上实现潜在聚类、可控生成和更高估计精度。
摘要：
归一化流通过构造具有可计算雅可比行列式的可逆变换，为高维密度估计和生成建模提供了一个有原则的框架。我们提出分形流（Fractal Flow），这是一种新颖的归一化流架构，通过两项关键创新同时提升表达能力和可解释性。第一，我们将Kolmogorov-Arnold网络集成到归一化流中，并引入Latent Dirichlet Allocation，以构建结构化的、可解释的潜在空间，并对层次化语义簇进行建模。第二，受分形生成模型（Fractal Generative Models）启发，我们在归一化流中引入递归模块化设计，以提高变换的可解释性和估计精度。在MNIST、FashionMNIST、CIFAR-10和地球物理数据上的实验表明，分形流实现了潜在聚类、可控生成以及更优的估计精度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
