Generative adversarial training can be generally understood as minimizing
certain moment matching loss defined by a set of discriminator functions,
typically neural networks. The discriminator set should be large enough to be
able to uniquely identify the true distribution (discriminative), and also be
small enough to go beyond memorizing samples (generalizable). In this paper, we
show that a discriminator set is guaranteed to be discriminative whenever its
linear span is dense in the set of bounded continuous functions. This is a very
mild condition satisfied even by neural networks with a single neuron. Further,
we develop generalization bounds between the learned distribution and true
distribution under different evaluation metrics. When evaluated with neural
distance, our bounds show that generalization is guaranteed as long as the
discriminator set is small enough, regardless of the size of the generator or
hypothesis set. When evaluated with KL divergence, our bound provides an
explanation on the counter-intuitive behaviors of testing likelihood in GAN
training. Our analysis sheds lights on understanding the practical performance
of GANs.
Description
On the Discrimination-Generalization Tradeoff in GANs
%0 Generic
%1 zhang2017discriminationgeneralization
%A Zhang, Pengchuan
%A Liu, Qiang
%A Zhou, Dengyong
%A Xu, Tao
%A He, Xiaodong
%D 2017
%K GAN seminar
%T On the Discrimination-Generalization Tradeoff in GANs
%U http://arxiv.org/abs/1711.02771
%X Generative adversarial training can be generally understood as minimizing
certain moment matching loss defined by a set of discriminator functions,
typically neural networks. The discriminator set should be large enough to be
able to uniquely identify the true distribution (discriminative), and also be
small enough to go beyond memorizing samples (generalizable). In this paper, we
show that a discriminator set is guaranteed to be discriminative whenever its
linear span is dense in the set of bounded continuous functions. This is a very
mild condition satisfied even by neural networks with a single neuron. Further,
we develop generalization bounds between the learned distribution and true
distribution under different evaluation metrics. When evaluated with neural
distance, our bounds show that generalization is guaranteed as long as the
discriminator set is small enough, regardless of the size of the generator or
hypothesis set. When evaluated with KL divergence, our bound provides an
explanation on the counter-intuitive behaviors of testing likelihood in GAN
training. Our analysis sheds lights on understanding the practical performance
of GANs.
@misc{zhang2017discriminationgeneralization,
abstract = {Generative adversarial training can be generally understood as minimizing
certain moment matching loss defined by a set of discriminator functions,
typically neural networks. The discriminator set should be large enough to be
able to uniquely identify the true distribution (discriminative), and also be
small enough to go beyond memorizing samples (generalizable). In this paper, we
show that a discriminator set is guaranteed to be discriminative whenever its
linear span is dense in the set of bounded continuous functions. This is a very
mild condition satisfied even by neural networks with a single neuron. Further,
we develop generalization bounds between the learned distribution and true
distribution under different evaluation metrics. When evaluated with neural
distance, our bounds show that generalization is guaranteed as long as the
discriminator set is small enough, regardless of the size of the generator or
hypothesis set. When evaluated with KL divergence, our bound provides an
explanation on the counter-intuitive behaviors of testing likelihood in GAN
training. Our analysis sheds lights on understanding the practical performance
of GANs.},
added-at = {2018-02-27T08:12:31.000+0100},
author = {Zhang, Pengchuan and Liu, Qiang and Zhou, Dengyong and Xu, Tao and He, Xiaodong},
biburl = {https://www.bibsonomy.org/bibtex/2b7d42da150e5aedbd06bb389073ab9f1/jk_itwm},
description = {On the Discrimination-Generalization Tradeoff in GANs},
interhash = {ef39c100dcf108601c6d471afbd179f3},
intrahash = {b7d42da150e5aedbd06bb389073ab9f1},
keywords = {GAN seminar},
note = {cite arxiv:1711.02771Comment: ICLR 2018},
timestamp = {2018-02-27T08:12:31.000+0100},
title = {On the Discrimination-Generalization Tradeoff in GANs},
url = {http://arxiv.org/abs/1711.02771},
year = 2017
}