# A Gauss-Newton Approach for Min-Max Optimization in Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2404.07172 · HTML: https://mlsanity.com/paper/2404.07172/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 10 Apr 2024.

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

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1709.01953/) (2017)
- [Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution](https://mlsanity.com/paper/1711.10467/) (2017)
- [Competitive Gradient Descent](https://mlsanity.com/paper/1905.12103/) (2019)
- [Implicit competitive regularization in GANs](https://mlsanity.com/paper/1910.05852/) (2019)
- [Riemannian Hamiltonian methods for min-max optimization on manifolds](https://mlsanity.com/paper/2204.11418/) (2022)
- [Adaptive Consensus Optimization Method for GANs](https://mlsanity.com/paper/2304.10317/) (2023)
- [Angle based dynamic learning rate for gradient descent](https://mlsanity.com/paper/2304.10457/) (2023)

## Built on by (most cited first, 1 of 1)

- [SignMuon: Communication-Efficient Distributed Muon Optimization](https://mlsanity.com/paper/2605.16311/) (2026)

## Abstract (arXiv)

A novel first-order method is proposed for training generative adversarial networks (GANs). It modifies the Gauss-Newton method to approximate the min-max Hessian and uses the Sherman-Morrison inversion formula to calculate the inverse. The method corresponds to a fixed-point method that ensures necessary contraction. To evaluate its effectiveness, numerical experiments are conducted on various datasets commonly used in image generation tasks, such as MNIST, Fashion MNIST, CIFAR10, FFHQ, and LSUN. Our method is capable of generating high-fidelity images with greater diversity across multiple datasets. It also achieves the highest inception score for CIFAR10 among all compared methods, including state-of-the-art second-order methods. Additionally, its execution time is comparable to that of first-order min-max methods.