Brief Review — SNGAN: Spectral Normalization for Generative Adversarial Networks

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

Sik-Ho Tsang
3 min readAug 4, 2023

Spectral Normalization for Generative Adversarial Networks
SNGAN, by Preferred Networks, Inc., Ritsumeikan University, and National Institute of Informatics
2018 ICLR, Over 4200 Citations (Sik-Ho Tsang @ Medium)

Generative Adversarial Network (GAN)
Image Synthesis: 20142019 [SAGAN]
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  • 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.


  1. SNGAN
  2. Results


The spectral normalization controls the Lipschitz constant of the discriminator function f by literally constraining the spectral norm of each layer g: hin hout.

  • σ(A) is the spectral norm of the matrix 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

Inception Score and FID on CIFAR-10

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

2.2. Visual Quality

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.



Sik-Ho Tsang

PhD, Researcher. I share what I learn. :) Linktree: for Twitter, LinkedIn, etc.