# Brief Review — SNGAN: Spectral Normalization for Generative Adversarial Networks

## SNGAN, Spectual Normalization for Weight Matrix, Outperforms WGAN-GP

Spectral Normalization for Generative Adversarial NetworksSNGAN, by Preferred Networks, Inc., Ritsumeikan University, and National Institute of Informatics2018 ICLR, Over 4200 Citations(Sik-Ho Tsang @ Medium)

Generative Adversarial Network (GAN)Image Synthesis:2014…2019[SAGAN]

==== My Other Paper Readings Are Also Over Here ====

- A novel weight normalization technique,
**spectral normalization**, is proposed to**stabilize the training of the discriminator**. It is**computationally light**and**easy to incorporate into existing implementations.**

# Outline

**SNGAN****Results**

**1. SNGAN**

The spectral normalization controls the Lipschitz constant of the discriminator functionbyfliterally constraining the spectral norm of each layerg: hin→hout.

is the spectral norm of the matrix*σ*(*A*)*A*(L2 matrix norm of*A*), which is the maximum singular value.

- Then the
**weight matrix is normalized by***σ*(*A*):

- After normalized,
*σ*(.) will give the value of 1:

- For
**fast computation**,**power iteration method**is applied for spectual normalization:

- The change in
*W*at each update would be small, and hence the change in its largest singular value. The spectral norm of*W*is**approximated with the pair of so-approximated singular vectors:**

# 2. Results

## 2.1. Inception Score and FID

SNGANs performed better than almost all contemporaries on the optimal settings.SNGANs performed even better with hinge loss.

## 2.2. Visual Quality

- A-F: are different sets of Hyperparameter settings for GAN training.
**WGAN-GP****failed to train good GANs**with high learning rates and high momentums (D,E and F).

SN-GANs were consistently better than GANs with weight normalization in terms of the quality of generated images.