# CHAIN: Enhancing Generalization in Data-Efficient GANs via lipsCHitz continuity constrAIned Normalization

arXiv: https://arxiv.org/abs/2404.00521 · HTML: https://mlsanity.com/paper/2404.00521/

## Key facts

- Cited by 2 papers in the map (data through 7 Oct 2026).
- Builds on 90 of its 127 references that are in the map.
- First posted on arXiv 31 Mar 2024.

## Builds on (most cited first, 30 of 90)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Zero-shot Image-to-Image Translation](https://mlsanity.com/paper/2302.03027/) (2023)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Differentiable Augmentation for Data-Efficient GAN Training](https://mlsanity.com/paper/2006.10738/) (2020)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [MAGVIT: Masked Generative Video Transformer](https://mlsanity.com/paper/2212.05199/) (2022)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Revisiting Batch Normalization For Practical Domain Adaptation](https://mlsanity.com/paper/1603.04779/) (2016)

## Built on by (most cited first, 2 of 2)

- [PACE: Marrying generalization in PArameter-efficient fine-tuning with Consistency rEgularization](https://mlsanity.com/paper/2409.17137/) (2024)
- [Noise Consistency Regularization for Improved Subject-Driven Image Synthesis](https://mlsanity.com/paper/2506.06483/) (2025)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) significantly advanced image generation but their performance heavily depends on abundant training data. In scenarios with limited data, GANs often struggle with discriminator overfitting and unstable training. Batch Normalization (BN), despite being known for enhancing generalization and training stability, has rarely been used in the discriminator of Data-Efficient GANs. Our work addresses this gap by identifying a critical flaw in BN: the tendency for gradient explosion during the centering and scaling steps. To tackle this issue, we present CHAIN (lipsCHitz continuity constrAIned Normalization), which replaces the conventional centering step with zero-mean regularization and integrates a Lipschitz continuity constraint in the scaling step. CHAIN further enhances GAN training by adaptively interpolating the normalized and unnormalized features, effectively avoiding discriminator overfitting. Our theoretical analyses firmly establishes CHAIN's effectiveness in reducing gradients in latent features and weights, improving stability and generalization in GAN training. Empirical evidence supports our theory. CHAIN achieves state-of-the-art results in data-limited scenarios on CIFAR-10/100, ImageNet, five low-shot and seven high-resolution few-shot image datasets. Code: https://github.com/MaxwellYaoNi/CHAIN