论文标题
基于耦合的白色收敛速率归一流流量
Whitening Convergence Rate of Coupling-based Normalizing Flows
论文作者
论文摘要
基于耦合的归一化流（例如，RealnVP）是一个流行的流量架构的家庭，在实践中出人意料地奏效。这需要理论理解。现有的工作表明，这种流动薄弱地融合到任意数据分布。但是，他们没有对实践中使用的更严格的收敛标准（最大似然损失）发表陈述。我们第一次就这种收敛性做出了定量陈述：我们证明，所有基于耦合的归一化流动都会对数据分布进行美白（即对角度化协方差矩阵），并得出相应的收敛界限，以表明流量深度的线性收敛速率。数值实验证明了我们的理论的含义，并指出了开放问题。
Coupling-based normalizing flows (e.g. RealNVP) are a popular family of normalizing flow architectures that work surprisingly well in practice. This calls for theoretical understanding. Existing work shows that such flows weakly converge to arbitrary data distributions. However, they make no statement about the stricter convergence criterion used in practice, the maximum likelihood loss. For the first time, we make a quantitative statement about this kind of convergence: We prove that all coupling-based normalizing flows perform whitening of the data distribution (i.e. diagonalize the covariance matrix) and derive corresponding convergence bounds that show a linear convergence rate in the depth of the flow. Numerical experiments demonstrate the implications of our theory and point at open questions.
