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.

本文提出了一种新方法——Woodbury变换，使用Woodbury矩阵恒等式实现高效可逆性和Sylvester行列式恒等式实现高效行列式计算，使得高维交互在计算成本不高的情况下变得可能。实验结果表明，相比其他流架构，Woodbury变换可以学习到更高可能性的模型，同时仍保持它们的高效优势。

深度生成流的伍德伯里变换