复正则化流可以几乎成为信息凯勒-里奇流
Complex normalizing flows can almost be information Kähler-Ricci flows
AI总结：
本文探讨复正则化流与近凯勒-里奇流之间的联系，通过log determinant与里奇曲率的关联，揭示了统计行为与几何特征的桥梁。
摘要：
我们建立了复正则化流与近凯勒-里奇流之间的联系，复正则化流通过复变量变换将初始和目标实化密度联系起来，需要恩索特集合的log determinant。凯勒流形的里奇曲率是局部体积形式密度log的二次混合Wirtinger偏导数。因此，我们通过log determinant与里奇曲率项的联系，揭示了复正则化流与凯勒-里奇流的关系。通过此框架，我们建立了其他相关结果，试图将复正则化流的统计行为与几何特征联系起来。
英文摘要：
We develop interconnections between the complex normalizing flow for data drawn from Borel probability measures on the twofold realification of the complex manifold and a nonlinear flow nearly Kähler-Ricci. The complex normalizing flow relates the initial and target realified densities under the complex change of variables, necessitating the log determinant of the ensemble of Wirtinger Jacobians. The Ricci curvature of a Kähler manifold is the second order mixed Wirtinger partial derivative of the log of the local density of the volume form. Therefore, we reconcile these two facts by drawing forth the connection that the log determinant used in the complex normalizing flow matches a Ricci curvature term under differentiation and conditions. The log density under the normalizing flow is kindred to a spatial information metric under an augmented Jacobian and a Bayesian perspective to the parameter, thus under the continuum limit the log likelihood matches a Fisher metric, or more closely a Kähler cross-entropy Hessian. This recovers a Kähler-Ricci flow variation up to a time derivative and expectation, or an average-valued Kähler-Einstein flow. Using this framework, we establish other relevant results, attempting to bridge the statistical and ordinary behaviors of the complex normalizing flow to the geometric features of our derived Kähler flow.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
