On the Effectiveness of Least Squares Generative Adversarial Networks

By Xudong Mao, Qing Li, Haoran Xie, Raymond Y. K. Lau, Zhen Wang, Stephen Paul Smolley. 2017

171 citations recorded by the source corpus.

Unsupervised learning with generative adversarial networks (GANs) has proven to be hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss for both the discriminator and the generator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson <inline-formula><tex-math notation="LaTeX">$\chi ^2$</tex-math><alternatives><mml:math><mml:msup><mml:mi>χ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="mao-ieq1-2872043.gif"/></alternatives></inline-formula> divergence. We also show that the derived objective function that yields minimizing the Pearson <inline-formula><tex-math notation="LaTeX">$\chi ^2$</tex-math><alternatives><mml:math><mml:msup><mml:mi>χ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="mao-ieq2-2872043.gif"/></alternatives></inline-formula> divergence performs better than the classical one of using least squares for classification. There are two benefits of LSGANs over regular GANs. First, LSGANs are able to generate higher quality images than regular GANs. Second, LSGANs perform more stably during the learning process. For evaluating the image quality, we conduct both qualitative and quantitative experiments, and the experimental results show that LSGANs can generate higher quality images than regular GANs. Furthermore, we evaluate the stability of LSGANs in two groups. One is to compare between LSGANs and regular GANs without gradient penalty. We conduct three experiments, including Gaussian mixture distribution, difficult architectures, and a newly proposed method — datasets with small variability, to illustrate the stability of LSGANs. The other one is to compare between LSGANs with gradient penalty (LSGANs-GP) and WGANs with gradient penalty (WGANs-GP). The experimental results show that LSGANs-GP succeed in training for all the difficult architectures used in WGANs-GP, including 101-layer ResNet.

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

Recent Progress on Generative Adversarial Networks (GANs): A Survey (2019, methodology): “References [22], [24], and [26] used different divergences to construct the objective function to enhance the GANs’ stability.”
RelGAN: Multi-Domain Image-to-Image Translation via Relative Attributes (2019, methodology): “For LReal (Equation 2) and LMatch (Equation 3), we use LSGANs-GP [22] for stabilizing the training process.”
A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications (2020, background): “GANs’ Representative variants InfoGAN [14], cGANs [15], CycleGAN [16], f -GAN [17], WGAN [18], WGAN-GP [19], LS-GAN [20] Objective function LSGANs [21], [22], hinge loss based GAN [23]–[25], MDGAN [26], unrolled GAN [27], SN-GANs [23], RGANs [28] Skills ImprovedGANs [29], AC-GAN [30] LAPGAN [31], DC”
Factorised spatial representation learning: application in semi-supervised myocardial segmentation (2018, unknown): “Both adversarial losses are based on [13].”
Confederated Machine Learning on Horizontally and Vertically Separated Medical Data for Large-Scale Health System Intelligence (2019, methodology): “A L1 matching loss between the generated data and real data was included that encourages the outputs to be close to observed data(Isola et al. 2017; Mao et al. 2019).”
Text-Guided Neural Image Inpainting (2020, background): “In the third term, D2 indicates whether Iд is a real word image, the term is based on the loss in LSGAN [21], which has been proven [44] to perform better than the original GAN loss in the inpainting scenario.”
Automatic Goal Generation for Reinforcement Learning Agents (2017, methodology): “Unlike in the original LSGAN paper (Mao et al., 2016), we have three terms in our value function V ( D ) rather than the original two.”