Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive Strategy
This work addresses the need for more interpretable and accurate generative models in machine learning, though it appears incremental by combining existing techniques like Kolmogorov-Arnold Networks and Latent Dirichlet Allocation.
The paper tackled the problem of enhancing expressiveness and interpretability in normalizing flows for density estimation and generative modeling by proposing Fractal Flow, which integrates topic modeling and a recursive design, resulting in improved latent clustering, controllable generation, and superior estimation accuracy as demonstrated on datasets like MNIST, FashionMNIST, CIFAR-10, and geophysical data.
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.