用主题模型和递归结构提升生成模型的可解释性与精度
Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
- 结合主题模型构建分层可解释的潜在空间
- 递归模块设计使变换过程更清晰，生成可控
- 在多个数据集上实现更好密度估计和聚类效果
正则化流提供了一种高维密度估计和生成建模的严谨框架，通过构建可逆变换并计算可处理的雅可比行列式。我们提出Fractal Flow，一种新型正则化流架构，通过两项关键创新提升表达能力和可解释性：首先，将Kolmogorov-Arnold网络与潜在狄利克雷分配（LDA）结合，构建结构化、可解释的潜在空间，并建模分层语义簇；其次，受分形生成模型启发，引入递归模块化设计，增强变换的可解释性与估计准确性。在MNIST、FashionMNIST、CIFAR-10及地球物理数据上的实验表明，Fractal Flow实现了潜在聚类、可控生成与更优的估计精度。
原文摘要 · Abstract (English)
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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