Normalizing flows are deep generative models that allow efficient likelihood calculation and sampling. The core requirement for this advantage is that they are constructed using functions that can be efficiently inverted and for which the determinant of the function's Jacobian can be efficiently computed. Researchers have introduced various such flow operations, but few of these allow rich interactions among variables without incurring significant computational costs. In this paper, we introduce Woodbury transformations, which achieve efficient invertibility via the Woodbury matrix identity and efficient determinant calculation via Sylvester's determinant identity. In contrast with other operations used in state-of-the-art normalizing flows, Woodbury transformations enable (1) high-dimensional interactions, (2) efficient sampling, and (3) efficient likelihood evaluation. Other similar operations, such as 1x1 convolutions, emerging convolutions, or periodic convolutions allow at most two of these three advantages. In our experiments on multiple image datasets, we find that Woodbury transformations allow learning of higher-likelihood models than other flow architectures while still enjoying their efficiency advantages.

翻译：这种优势的核心要求是,在构建这些功能时,可以高效率地进行反转,并且可以有效地计算函数Jacobian的决定因素。研究人员已经引入了各种这种流动操作,但其中很少有人允许在不产生大量计算成本的情况下在变量之间进行丰富的互动。在本文中,我们引入了Woodbury变异,通过Woodbury矩阵特性和通过Sylvester的决定因素特性进行高效的决定因素计算,从而实现高效的可视性。与在最先进的正常流动中使用的其他操作相比,Woodbury变异使得(1) 高维互动,(2) 高效取样和(3) 高效的可能性评估。其他类似的操作,如1x1演进、新兴演进或周期演进,最多允许这三种优势中的两种。在我们关于多个图像数据集的实验中,我们发现Woodbury变异允许学习比其他流动结构更相似的模型,同时仍然享有效率优势。