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# Invertible Generative Modeling using Linear Rational Splines

*Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics*, PMLR 108:4236-4246, 2020.

#### Abstract

Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine transformations. The significant advantage of such models is their easy-to-compute inverse. Nevertheless, making use of affine transformations may limit the expressiveness of such models. Recently, invertible piecewise polynomial functions as a replacement for affine transformations have attracted attention. However, these methods require solving a polynomial equation to calculate their inverse. In this paper, we explore using linear rational splines as a replacement for affine transformations used in coupling layers. Besides having a straightforward inverse, inference and generation have similar cost and architecture in this method. Moreover, simulation results demonstrate the competitiveness of this approach’s performance compared to existing methods.