Invertible normalizing flow neural networks by JKO scheme

Chen Xu, Xiuyuan Cheng, Yao Xie

Keywords: Normalizing flow, invertible neural networks, JKO scheme

TL;DR: We propose JKO-Flow to train normalizing flow neural ODE model block-wise with time reparametrization, and experimentally show JKO-Flow reaches competitive performance while greatly reduce computation

Abstract:

Normalizing flow is a class of deep generative models for efficient sampling and density estimation. In practice, the flow often appears as a chain of invertible neural network blocks. To facilitate training, past works have regularized flow trajectories and designed special network architectures. The current paper develops a neural ODE flow network inspired by the Jordan-Kinderleherer-Otto (JKO) scheme, which allows an efficient \textit{block-wise} training procedure: as the JKO scheme unfolds the dynamic of gradient flow, the proposed model naturally stacks residual network blocks one-by-one and reduces the memory load as well as the difficulty of training deep networks. We also develop an adaptive time-reparametrization of the flow network with a progressive refinement of the trajectory in probability space, which improves the optimization efficiency and model accuracy in practice.
On high-dimensional generative tasks for tabular data, JKO-Flow can process larger data batches and perform competitively as or better than continuous and discrete flow models, using 10X less number of iterations (e.g., batches) and significantly less time per iteration.

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