Unsupervised learning with generative adversarial networks (GANs) has proven 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 function for the discriminator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson $\chi^2$ divergence. We also present a theoretical analysis about the properties of LSGANs and $\chi^2$ divergence. 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 stable during the learning process. For evaluating the image quality, we train LSGANs on several datasets including LSUN and a cat dataset, and the experimental results show that the images generated by LSGANs are of better quality than the ones generated by 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 new proposed method --- datasets with small variance, to illustrate the stability of LSGANs. The other one is to compare between LSGANs with gradient penalty and WGANs with gradient penalty (WGANs-GP). The experimental results show that LSGANs with gradient penalty succeed in training for all the difficult architectures used in WGANs-GP, including 101-layer ResNet.

本文提出了最小二乘生成对抗网络（LSGANs），采用了最小二乘损失函数来提高稳定性并生成高质量图像，并通过定性和定量实验进行了比较评估。

最小二乘生成对抗网络的有效性