Least Squares Generative Adversarial Networks (1611.04076v3)

Abstract: 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. 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. We evaluate LSGANs on five scene datasets and the experimental results show that the images generated by LSGANs are of better quality than the ones generated by regular GANs. We also conduct two comparison experiments between LSGANs and regular GANs to illustrate the stability of LSGANs.

• The paper introduces LSGANs, replacing the GAN discriminator's sigmoid cross entropy loss with a least squares loss to mitigate vanishing gradients.
• It establishes that minimizing the LSGAN objective equates to minimizing the Pearson χ2 divergence, providing a robust theoretical foundation.
• Empirical results show that LSGANs generate higher-quality images with improved training stability and reduced mode collapse across various datasets.

Least Squares Generative Adversarial Networks: A Formal Overview

The paper "Least Squares Generative Adversarial Networks," authored by Xudong Mao et al., presents an innovative approach in the field of unsupervised learning through generative models, specifically addressing the pervasive vanishing gradient problem in Generative Adversarial Networks (GANs). This work introduces the Least Squares Generative Adversarial Networks (LSGANs), offering a solution by replacing the sigmoid cross entropy loss function typically used in GAN discriminators with a least squares loss function.

Key Contributions

The primary contributions of this paper are twofold:

1. Introduction of LSGANs: The paper proposes LSGANs, which uses a least squares loss function to enhance the performance of the discriminator in GANs. The authors argue that this leads to higher-quality image generation and improves the stability of the GAN training process. This is because the least squares loss penalizes samples based on their distance to the decision boundary, providing non-saturating gradients and reducing the risk of mode collapse.
2. Theoretical Insight and Empirical Validation: The authors theoretically demonstrate that minimizing the objective function of LSGAN equates to minimizing the Pearson $\chi^2$ divergence. Empirical evaluations were conducted across a series of datasets—five scene datasets and one dataset containing handwritten Chinese characters. In all scenarios, LSGANs outperformed traditional GANs, producing more realistic images with improved stability during training.

Experimental Results

The experimental results underscore the effectiveness of LSGANs. The paper rigorously tests the presented models on well-known datasets, including various scene datasets from LSUN and a large dataset of Chinese characters. Notably, LSGANs not only produced images of superior quality compared to traditional GANs but also exhibited a reduced propensity for mode collapse, a common issue in GAN architectures.

The analysis demonstrated that LSGANs can generate images that are not only quantitatively better but also qualitatively more diverse and closer to the manifold of real data. The findings are evidenced by side-by-side comparisons with DCGANs and EBGANs, where LSGANs show marked improvement.

Theoretical Implications

The theoretical implication of the paper is significant. By establishing a relation between the LSGAN loss and the Pearson $\chi^2$ divergence, the paper provides a robust mathematical foundation for the empirical observations of improved performance and stability. This offers a novel perspective for future research in the development of alternative loss functions for GANs.

Practical Implications and Future Directions

Practically, LSGANs present an advancement in the design of generative models that require less arduous hyperparameter tuning and exhibit more stable convergence behavior. These characteristics have strong practical implications, particularly when applied to complex real-world tasks such as image generation at high resolutions or across diverse datasets with numerous classes, as demonstrated with the Chinese character dataset.

For future research, the paper suggests extending LSGANs to address more complex datasets like ImageNet, potentially integrating mechanisms to move generated samples directly toward real data, which remains an open area of research.

In summary, the paper on Least Squares Generative Adversarial Networks makes significant strides in addressing the limitations of traditional GANs. The introduction of the least squares loss function for the discriminator not only improves image quality and stability but also opens new avenues for theoretical exploration and application in complex generative tasks.