Accelerating Continuous Normalizing Flow with Trajectory Polynomial Regularization
This work provides a method to accelerate the training of continuous normalizing flows, which is beneficial for researchers and practitioners using CNFs for tasks like variational inference and density estimation, by significantly reducing computational time.
This paper addresses the high computational cost of continuous normalizing flows (CNF) by proposing a regularization method that penalizes the difference between the ODE trajectory and a fitted polynomial regression. This approach reduces the number of function evaluations (NFE) by 42.3% to 71.3% for density estimation and 19.3% to 32.1% for variational auto-encoders, without impacting testing losses.
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.