# On the Effectiveness of Least Squares Generative Adversarial Networks

**Authors:** Xudong Mao, Qing Li, Haoran Xie, Raymond Y. K. Lau, Zhen Wang, Stephen Paul Smolley  
**arXiv:** [1712.06391](https://arxiv.org/abs/1712.06391)  
**Date:** 2017-12-18  
**Summary page:** https://www.summarizepaper.com/en/paper/1712.06391v2/

## Key points

- Unsupervised learning with generative adversarial networks (GANs) has seen significant success in recent years.
- Traditional GANs use the discriminator as a classifier with the sigmoid cross entropy loss function, which can lead to vanishing gradients during training.
- LSGANs employ the least squares loss for both the discriminator and generator, resulting in improved stability during training.
- Minimizing the objective function of LSGAN leads to minimizing the Pearson $\chi^2$ divergence.
- LSGANs offer higher quality image generation and more stable performance compared to regular GANs.
- Experimental evaluations by Mao et al. confirmed LSGANs' superior image quality over conventional GAN models.
- Stability of LSGANs was evaluated through comparisons against regular GANs without gradient penalty and against WGANs with gradient penalty, showcasing successful training on challenging architectures like the 101-layer ResNet.
- Least Squares Generative Adversarial Networks effectively address issues related to vanishing gradients and instability in traditional GAN frameworks, leading to improved image generation quality and enhanced training stability.

## Summary

Unsupervised learning with generative adversarial networks (GANs) has seen significant success in recent years. Traditional GANs utilize the discriminator as a classifier with the sigmoid cross entropy loss function. However, this approach can sometimes lead to vanishing gradients during training. To address this issue, LSGANs employ the least squares loss for both the discriminator and generator, resulting in improved stability during training. The authors demonstrated that minimizing the objective function of LSGAN leads to minimizing the Pearson $\chi^2$ divergence. This approach outperforms traditional least squares classification methods and offers two main advantages over regular GANs: higher quality image generation and more stable performance throughout the learning process. Experimental evaluations conducted by Mao et al. included qualitative and quantitative assessments that confirmed LSGANs' ability to produce superior image quality compared to conventional GAN models. Furthermore, the researchers evaluated the stability of LSGANs through various experiments. One set of comparisons involved testing LSGANs against regular GANs without gradient penalty across scenarios like Gaussian mixture distribution and challenging architectures with datasets exhibiting small variability. Another comparison was made between LSGANs with gradient penalty (LSGANs-GP) and WGANs with gradient penalty (WGANs-GP), showcasing LSGANs-GP's successful training on difficult architectures such as the 101-layer ResNet. Overall, Mao et al. 's study highlights the effectiveness of Least Squares Generative Adversarial Networks in addressing issues related to vanishing gradients and instability commonly encountered in traditional GAN frameworks. Their findings underscore how adopting a least squares approach can lead to improved image generation quality and enhanced training stability in generative adversarial networks.