# Finding the global semantic representation in GAN through Frechet Mean

arXiv: https://arxiv.org/abs/2210.05509 · HTML: https://mlsanity.com/paper/2210.05509/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 27 of 27)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [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)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Closed-Form Factorization of Latent Semantics in GANs](https://mlsanity.com/paper/2007.06600/) (2020)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [On the "steerability" of generative adversarial networks](https://mlsanity.com/paper/1907.07171/) (2019)
- [GANalyze: Toward Visual Definitions of Cognitive Image Properties](https://mlsanity.com/paper/1906.10112/) (2019)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Controlling generative models with continuous factors of variations](https://mlsanity.com/paper/2001.10238/) (2020)
- [Deep Feature Interpolation for Image Content Changes](https://mlsanity.com/paper/1611.05507/) (2016)
- [Differentiating through the Fr'echet Mean](https://mlsanity.com/paper/2003.00335/) (2020)
- [Low-Rank Subspaces in GANs](https://mlsanity.com/paper/2106.04488/) (2021)
- [A Spectral Regularizer for Unsupervised Disentanglement](https://mlsanity.com/paper/1812.01161/) (2018)
- [Do Not Escape From the Manifold: Discovering the Local Coordinates on the Latent Space of GANs](https://mlsanity.com/paper/2106.06959/) (2021)
- [Analyzing the Latent Space of GAN through Local Dimension Estimation](https://mlsanity.com/paper/2205.13182/) (2022)

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

- [Enabling Local Editing in Diffusion Models by Joint and Individual Component Analysis](https://mlsanity.com/paper/2408.16845/) (2024)

## Abstract (arXiv)

The ideally disentangled latent space in GAN involves the global representation of latent space with semantic attribute coordinates. In other words, considering that this disentangled latent space is a vector space, there exists the global semantic basis where each basis component describes one attribute of generated images. In this paper, we propose an unsupervised method for finding this global semantic basis in the intermediate latent space in GANs. This semantic basis represents sample-independent meaningful perturbations that change the same semantic attribute of an image on the entire latent space. The proposed global basis, called Fr'echet basis, is derived by introducing Fr'echet mean to the local semantic perturbations in a latent space. Fr'echet basis is discovered in two stages. First, the global semantic subspace is discovered by the Fr'echet mean in the Grassmannian manifold of the local semantic subspaces. Second, Fr'echet basis is found by optimizing a basis of the semantic subspace via the Fr'echet mean in the Special Orthogonal Group. Experimental results demonstrate that Fr'echet basis provides better semantic factorization and robustness compared to the previous methods. Moreover, we suggest the basis refinement scheme for the previous methods. The quantitative experiments show that the refined basis achieves better semantic factorization while constrained on the same semantic subspace given by the previous method.