Accelerating Continuous Normalizing Flow with Trajectory Polynomial Regularization

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 at all.

Attribute-aware Collaborative Filtering: Survey and Classification

Attribute-aware CF models aims at rating prediction given not only the historical rating from users to items, but also the information associated with users (e.g. age), items (e.g. price), or even ratings (e.g. rating time). This paper surveys works in the past decade developing attribute-aware CF systems, and discovered that mathematically they can be classified into four different categories. We provide the readers not only the high level mathematical interpretation of the existing works in this area but also the mathematical insight for each category of models. Finally we provide in-depth experiment results comparing the effectiveness of the major works in each category.