Scalable Normalizing Flows for Permutation Invariant Densities
This addresses set modeling in machine learning, which is incremental as it refines an existing method for better practicality.
The paper tackled the problem of modeling permutation invariant densities for sets using continuous normalizing flows, where calculating the trace caused issues in training and inference, and proposed an alternative with closed-form trace that improved performance.
Modeling sets is an important problem in machine learning since this type of data can be found in many domains. A promising approach defines a family of permutation invariant densities with continuous normalizing flows. This allows us to maximize the likelihood directly and sample new realizations with ease. In this work, we demonstrate how calculating the trace, a crucial step in this method, raises issues that occur both during training and inference, limiting its practicality. We propose an alternative way of defining permutation equivariant transformations that give closed form trace. This leads not only to improvements while training, but also to better final performance. We demonstrate the benefits of our approach on point processes and general set modeling.