Glow: Generative Flow with Invertible 1x1 Convolutions_glow: generative flow with invertible 1 x 1 convol

Glow: Generative Flow with Invertible 1$\times$1 Convolutions

Diederik P. Kingma, Prafulla Dhariwal

Abstract

flow-based generative models: tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis
Glow: a simple type of generative flow using an invertible 1 $\times$ 1 convolution
capable of efficient realistic-looking synthesis and manipulation of large images
code:https://github.com/openai/glow

Introduction

two major unsolved problems of machine learning:
(1) data-efficiency: the ability to learn from few datapoints, like humans;
(2) generalization: robustness to changes of the task or its context

generative models:
(1) learning realistic world models
(2) learning meaningful features of the input while requiring little or no human supervision or labeling

$$\text{generative model}\begin{cases}\text{likelihood-based methods}\begin{cases} \text{autoregressive model}\\ \text{VAE} \\ \text{flow-based generative model} \end{cases} \\ \text{GAN} \end{cases}$$

merits of flow-based generative models:
1. Exact latent-variable inference and log-likelihood evaluation
2. Efficient inference and efficient synthesis
3. Useful latent space for downstream tasks
4. Significant potential for memory savings

Background: Flow-based Generative Models

$x$: high dimensional random vector with unknown true distribution $p(x)$
$D$: i.i.d dataset from $p(x)$
$p_\theta(x)$: model
log-likelihood objective(the expected compression cost):

$$\min_\theta \quad L(D)=E(-\log p_\theta(x))=\frac{1}{\lvert D \rvert} \sum_{x \in D} -\log p_\theta(x)$$

$z$: latent variable with tractable/simple pdf