# Group Equivariant Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2005.01683 · HTML: https://mlsanity.com/paper/2005.01683/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2020.

## Built on by (most cited first, 19 of 19)

- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Multi-Agent MDP Homomorphic Networks](https://mlsanity.com/paper/2110.04495/) (2021)
- [Structure-preserving GANs](https://mlsanity.com/paper/2202.01129/) (2022)
- [Learning Infinitesimal Generators of Continuous Symmetries from Data](https://mlsanity.com/paper/2410.21853/) (2024)
- [Sample Complexity of Probability Divergences under Group Symmetry](https://mlsanity.com/paper/2302.01915/) (2023)
- [Sample Complexity Bounds for Estimating Probability Divergences under Invariances](https://mlsanity.com/paper/2311.02868/) (2023)
- [Three-dimensional microstructure generation using generative adversarial neural networks in the context of continuum micromechanics](https://mlsanity.com/paper/2206.01693/) (2022)
- [Efficient Equivariant Transfer Learning from Pretrained Models](https://mlsanity.com/paper/2305.09900/) (2023)
- [Flow Factorized Representation Learning](https://mlsanity.com/paper/2309.13167/) (2023)
- [Neural Approximate Mirror Maps for Constrained Diffusion Models](https://mlsanity.com/paper/2406.12816/) (2024)
- [Function-space regularized R'enyi divergences](https://mlsanity.com/paper/2210.04974/) (2022)
- [Statistical Guarantees of Group-Invariant GANs](https://mlsanity.com/paper/2305.13517/) (2023)
- [Autoequivariant Network Search via Group Decomposition](https://mlsanity.com/paper/2104.04848/) (2021)
- [Structure Preserving Diffusion Models](https://mlsanity.com/paper/2402.19369/) (2024)
- [Language Models and Cycle Consistency for Self-Reflective Machine Translation](https://mlsanity.com/paper/2411.02791/) (2024)
- [Symmetry-aware Neural Architecture for Embodied Visual Navigation](https://mlsanity.com/paper/2112.09515/) (2021)
- [Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions](https://mlsanity.com/paper/2512.06615/) (2025)

## Abstract (arXiv)

Recent improvements in generative adversarial visual synthesis incorporate real and fake image transformation in a self-supervised setting, leading to increased stability and perceptual fidelity. However, these approaches typically involve image augmentations via additional regularizers in the GAN objective and thus spend valuable network capacity towards approximating transformation equivariance instead of their desired task. In this work, we explicitly incorporate inductive symmetry priors into the network architectures via group-equivariant convolutional networks. Group-convolutions have higher expressive power with fewer samples and lead to better gradient feedback between generator and discriminator. We show that group-equivariance integrates seamlessly with recent techniques for GAN training across regularizers, architectures, and loss functions. We demonstrate the utility of our methods for conditional synthesis by improving generation in the limited data regime across symmetric imaging datasets and even find benefits for natural images with preferred orientation.