标题： 分形流：通过主题建模和递归策略实现的分层且可解释的归一化流 显示英文标题

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

摘要： 归一化流通过构建可逆变换并具有易于处理的雅可比行列式，为高维密度估计和生成建模提供了一个系统的方法框架。 我们提出了一种名为分形流的新归一化流架构，通过两个关键创新提高了表达能力和可解释性。 首先，我们整合了柯尔莫哥洛夫-阿诺德网络，并将潜在狄利克雷分布引入归一化流，以构建结构化、可解释的潜在空间并建模层次语义聚类。 其次，受分形生成模型的启发，我们在归一化流中引入了递归模块化设计，以提高变换的可解释性和估计准确性。 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、可控生成和优越的估计准确性。 显示英文摘要

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.