Accelerating Continuous Normalizing Flow with Trajectory Polynomial Regularization

TL;DR

This paper introduces a polynomial regularization method to accelerate continuous normalizing flows by reducing ODE solving errors, significantly decreasing function evaluations without compromising training quality.

Contribution

The authors propose a novel regularization technique that enforces polynomial-like trajectories in CNF, leading to faster computations and lower NFEs while maintaining performance.

Findings

42.3% to 71.3% reduction in NFE for density estimation

19.3% to 32.1% reduction in NFE for variational auto-encoders

Training loss remains unaffected by the regularization

Abstract

In this paper, we propose an approach to effectively accelerating the computation of continuous normalizing flow (CNF), which has been proven to be a powerful tool for the tasks such as variational inference and density estimation. The training time cost of CNF can be extremely high because the required number of function evaluations (NFE) for solving corresponding ordinary differential equations (ODE) is very large. We think that the high NFE results from large truncation errors of solving ODEs. To address the problem, we propose to add a regularization. The regularization penalizes the difference between the trajectory of the ODE and its fitted polynomial regression. The trajectory of ODE will approximate a polynomial function, and thus the truncation error will be smaller. Furthermore, we provide two proofs and claim that the additional regularization does not harm training quality. Experimental results show that our proposed method can result in 42.3% to 71.3% reduction of NFE on the task of density estimation, and 19.3% to 32.1% reduction of NFE on variational auto-encoder, while the testing losses are not affected.