In this paper, we present a new class of invertible transformations with an
application to flow-based generative models. We indicate that many well-known
invertible transformations in reversible logic and reversible neural networks
could be derived from our proposition. Next, we propose two new coupling layers
that are important building blocks of flow-based generative models. In the
experiments on digit data, we present how these new coupling layers could be
used in Integer Discrete Flows (IDF), and that they achieve better results than
standard coupling layers used in IDF and RealNVP.

本文提出了一种新的可逆变换类别，并将其应用于基于流的生成模型，提出两种新的耦合层并在数字数据实验中验证，表明这些新的耦合层能够在 Integer Discrete Flows（IDF）中取得比标准耦合层更好的效果，并能导出一些已知的可逆转换。

基于流的生成建模的通用可逆变换

General Invertible Transformations for Flow-based Generative Modeling

In this paper we analyse and improve integer discrete flows for lossless
compression. Integer discrete flows are a recently proposed class of models
that learn invertible transformations for integer-valued random variables.
Their discrete nature makes them particularly suitable for lossless compression
with entropy coding schemes. We start by investigating a recent theoretical
claim that states that invertible flows for discrete random variables are less
flexible than their continuous counterparts. We demonstrate with a proof that
this claim does not hold for integer discrete flows due to the embedding of
data with finite support into the countably infinite integer lattice.
Furthermore, we zoom in on the effect of gradient bias due to the
straight-through estimator in integer discrete flows, and demonstrate that its
influence is highly dependent on architecture choices and less prominent than
previously thought. Finally, we show how different architecture modifications
improve the performance of this model class for lossless compression, and that
they also enable more efficient compression: a model with half the number of
flow layers performs on par with or better than the original integer discrete
flow model.

本文研究和改进针对无损压缩的整数离散流。我们通过探究离散随机变量的可逆流是否比连续随机变量的更为灵活来开始分析，并通过证明发现此理论不适用于整数离散流。此外，我们研究了整数离散流中的梯度偏差效应，并通过实验证明其对模型的性能影响高度依赖于架构选择并不像先前想象的那样突出。最后，我们展示了不同架构修改如何改进该模型类别的性能并使其更加高效：我们发现具有一半数量流层的模型性能不亚于或者比原始整数离散流模型更好。