论文标题
卷积指数和广义的Sylvester流动
The Convolution Exponential and Generalized Sylvester Flows
论文作者
论文摘要
本文通过采取线性转换的指数来介绍一种构建线性流的新方法。这种线性转换不需要可逆本身，并且指数具有以下理想的属性：保证它是可逆的，它的逆逆向计算很简单，而log jacobian决定因素等于线性转换的痕迹。一个重要的见解是可以隐式计算指数，从而允许使用卷积层。利用这种见解，我们开发了名为“卷积指数”和“图形卷积指数”的新的可逆变换，该指数保留了其基本转换的均衡。此外，我们概括了Sylvester流量，并提出了基于概括和卷积指数为基础变化的卷积Sylvester流。从经验上讲，我们表明卷积指数优于CIFAR10上生成流中的其他线性变换，图形卷积指数提高了图归一化流的性能。此外，我们表明卷积的西尔维斯特流动可以改善残留流的性能，因为在对数似然测得的生成流程模型中，卷积流动流动。
This paper introduces a new method to build linear flows, by taking the exponential of a linear transformation. This linear transformation does not need to be invertible itself, and the exponential has the following desirable properties: it is guaranteed to be invertible, its inverse is straightforward to compute and the log Jacobian determinant is equal to the trace of the linear transformation. An important insight is that the exponential can be computed implicitly, which allows the use of convolutional layers. Using this insight, we develop new invertible transformations named convolution exponentials and graph convolution exponentials, which retain the equivariance of their underlying transformations. In addition, we generalize Sylvester Flows and propose Convolutional Sylvester Flows which are based on the generalization and the convolution exponential as basis change. Empirically, we show that the convolution exponential outperforms other linear transformations in generative flows on CIFAR10 and the graph convolution exponential improves the performance of graph normalizing flows. In addition, we show that Convolutional Sylvester Flows improve performance over residual flows as a generative flow model measured in log-likelihood.
