Despite their popularity, to date, the application of normalizing flows on
categorical data stays limited. The current practice of using dequantization to
map discrete data to a continuous space is inapplicable as categorical data has
no intrinsic order. Instead, categorical data have complex and latent relations
that must be inferred, like the synonymy between words. In this paper, we
investigate \emph{Categorical Normalizing Flows}, that is normalizing flows for
categorical data. By casting the encoding of categorical data in continuous
space as a variational inference problem, we jointly optimize the continuous
representation and the model likelihood. Using a factorized decoder, we
introduce an inductive bias to model any interactions in the normalizing flow.
As a consequence, we do not only simplify the optimization compared to having a
joint decoder, but also make it possible to scale up to a large number of
categories that is currently impossible with discrete normalizing flows. Based
on Categorical Normalizing Flows, we propose GraphCNF a permutation-invariant
generative model on graphs. GraphCNF implements a three step approach modeling
the nodes, edges and adjacency matrix stepwise to increase efficiency. On
molecule generation, GraphCNF outperforms both one-shot and autoregressive
flow-based state-of-the-art.

本文介绍一种针对分类数据的正则化流方法，利用可变推理将分类数据的编码转换为连续空间，并使用分解器解决正则化流中包含的潜在关系和相互作用。基于这种方法提出了 GraphCNF，是一种置换不变的图形生成模型，并在分子生成上表现优于现有方法。