Invertible Generative Modeling using Linear Rational Splines

01/15/2020
by   Hadi M. Dolatabadi, et al.
34

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.

READ FULL TEXT

page 7

page 12

page 14

page 15

07/19/2015

A concise parametrisation of affine transformation

Good parametrisations of affine transformations are essential to interpo...
11/30/2020

General Invertible Transformations for Flow-based Generative Modeling

In this paper, we present a new class of invertible transformations. We ...
10/22/2020

Exploring the Impact of Affine Loop Transformations in Qubit Allocation

Most quantum compiler transformations and qubit allocation techniques to...
06/01/2020

You say Normalizing Flows I see Bayesian Networks

Normalizing flows have emerged as an important family of deep neural net...
02/06/2018

Polynomial Invariants for Affine Programs

We exhibit an algorithm to compute the strongest polynomial (or algebrai...
07/07/2021

Universal Approximation for Log-concave Distributions using Well-conditioned Normalizing Flows

Normalizing flows are a widely used class of latent-variable generative ...
04/02/2022

Dually affine Information Geometry modeled on a Banach space

In this chapter, we study Information Geometry from a particular non-par...

Code Repositories

LRS_NF

[AISTATS2020] The official repository of "Invertible Generative Modling using Linear Rational Splines (LRS)".


view repo