reviews: 
Comments: This paper proposes a new loss function, zephyr loss, and applies it to the training of generative adversarial networks to stabilize the training and solve the problems of gradient vanishing and unstable training that existed in previous generative adversarial networks. Theoretical analysis and experiments are conducted to verify the effectiveness of this loss function.
Strengths: 1. The zephyr loss function is proposed to address common GAN issues (e.g., vanishing gradients, training instability). This is especially relevant given that the loss is smooth around zero, theoretically improving gradient stability and mitigating exploding/vanishing gradients.
2. The authors provide detailed proofs for the zephyr loss properties, including convexity, smoothness, and Lipschitz continuity, which contribute to ZGAN's stability.
3. The experiments on datasets (CIFAR-10, CIFAR-100, STL-10, SVHN) provide evidence that ZGAN outperforms traditional GANs (e.g., LSGAN, WGAN) in terms of inception scores, indicating higher quality and diversity in generated images.
Weaknesses: 1. My primary concern is the Inadequate experimental evaluation conducted in the paper.
  • The authors rely solely on the Inception Score (IS) to assess the performance of different GANs, which is insufficient for a comprehensive evaluation. Additional metrics, such as FID and KID, should be incorporated to provide a more reasonable comparison. The FID compares the distribution of generated images to that of real images in the feature space of the Inception model. It captures both the quality and diversity by measuring the distance between the two distributions. FID is particularly useful because it correlates well with human judgment of image quality, making it a more reliable indicator of GAN performance. KID is similar to FID but is based on a different statistical approach. It calculates the squared maximum mean discrepancy between the feature distributions of generated and real images. One of the advantages of KID is that it is unbiased and can be applied to small sample sizes, which makes it useful in scenarios where the number of generated images is limited. incorporating FID and KID alongside Inception Score enables a more nuanced evaluation of GAN performance, addressing the shortcomings of relying on a single metric and providing insights into both the realism and diversity of the generated outputs.
  • All experiments are conducted using relatively simple networks and datasets. To strengthen the validation of the proposed loss function, the authors are suggested to employ the proposed loss function to some more advanced architectures like StyleGAN2 and StyleGAN-XL, and test them on more challenging datasets such as FFHQ and AFHQ. StyleGAN2 and StyleGAN-XL are the most popular and advanced GANs. It is necessary to verify the proposed loss function based on these advanced models and challenging datasets.
  • Since the paper focuses on the stable training of GANs, it is well known that GANs are even more unstable when trained on a small amount of data. Authors are suggested to conduct experiments with a small dataset to verify whether the proposed loss function can also stabilize GAN training on small amount of training data. Obama-100, Sketch-100, and FFHQ-Sunglasses are three common few-shot image generation datasets. By focusing on these aspects, you can get a clearer picture of the model's stability and robustness.
  • The authors only compare the proposed method with WGAN and LSGAN. More comparison with WGAN-GP, WGAN-LP are expected.
  • Note that the proposed loss function contains two variables, the authors should conduct ablation experiments on these two variables and list the experimental results in the form of figures or lists, rather than just briefly mentioning them in the main text. Given the current experiment setup, it is difficult for me to be fully convinced of the performance advantages claimed for the proposed method.

2. This paper provides a proof of the Lipschitz continuity for the proposed loss function. However, as far as I am aware, other loss functions commonly used in GANs also share this property. Ensuring the continuity of the discriminator is fundamental to achieving stable GAN training.

3. The 5th section of the paper seems to be redundant, and is not supported by any experimental results. It might be better to place it in the analysis of experimental results in 6th section.
Recommendation: 3
Reviewer confidence: 5
Soundness/correctness: 2
Clarity: 2