Rethinking Multidimensional Discriminator Output for Generative Adversarial Networks

TL;DR

This paper extends Wasserstein GANs to multidimensional critic outputs, introducing a new transformation and discrepancy measure that improve training stability, convergence speed, and diversity of generated samples.

Contribution

It generalizes the Wasserstein GAN framework to multidimensional critic outputs and proposes a novel SRVT block and maximal p-centrality discrepancy.

Findings

High-dimensional critic output enhances real-fake distribution discrimination.

The proposed discrepancy equals 1-Wasserstein distance when n=1 and p=1.

Empirical results show faster convergence and increased diversity.

Abstract

The study of multidimensional discriminator (critic) output for Generative Adversarial Networks has been underexplored in the literature. In this paper, we generalize the Wasserstein GAN framework to take advantage of multidimensional critic output and explore its properties. We also introduce a square-root velocity transformation (SRVT) block which favors training in the multidimensional setting. Proofs of properties are based on our proposed maximal p-centrality discrepancy, which is bounded above by p-Wasserstein distance and fits the Wasserstein GAN framework with multidimensional critic output n. Especially when n = 1 and p = 1, the proposed discrepancy equals 1-Wasserstein distance. Theoretical analysis and empirical evidence show that high-dimensional critic output has its advantage on distinguishing real and fake distributions, and benefits faster convergence and diversity of results.