# Closed-Form Factorization of Latent Semantics in GANs

arXiv: https://arxiv.org/abs/2007.06600 · HTML: https://mlsanity.com/paper/2007.06600/

## Key facts

- Cited by 408 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

## Built on by (most cited first, 30 of 408)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Paint by Example: Exemplar-based Image Editing with Diffusion Models](https://mlsanity.com/paper/2211.13227/) (2022)
- [Pivotal Tuning for Latent-based Editing of Real Images](https://mlsanity.com/paper/2106.05744/) (2021)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [SVDiff: Compact Parameter Space for Diffusion Fine-Tuning](https://mlsanity.com/paper/2303.11305/) (2023)
- [DragDiffusion: Harnessing Diffusion Models for Interactive Point-based Image Editing](https://mlsanity.com/paper/2306.14435/) (2023)
- [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021)
- [ReStyle: A Residual-Based StyleGAN Encoder via Iterative Refinement](https://mlsanity.com/paper/2104.02699/) (2021)
- [Drag Your GAN: Interactive Point-based Manipulation on the Generative Image Manifold](https://mlsanity.com/paper/2305.10973/) (2023)
- [HyperStyle: StyleGAN Inversion with HyperNetworks for Real Image Editing](https://mlsanity.com/paper/2111.15666/) (2021)
- [Encoder-based Domain Tuning for Fast Personalization of Text-to-Image Models](https://mlsanity.com/paper/2302.12228/) (2023)
- [Latent Image Animator: Learning to Animate Images via Latent Space Navigation](https://mlsanity.com/paper/2203.09043/) (2022)
- [A Good Image Generator Is What You Need for High-Resolution Video Synthesis](https://mlsanity.com/paper/2104.15069/) (2021)
- [EditGAN: High-Precision Semantic Image Editing](https://mlsanity.com/paper/2111.03186/) (2021)
- [CIPS-3D: A 3D-Aware Generator of GANs Based on Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2110.09788/) (2021)
- [StyleGAN-Human: A Data-Centric Odyssey of Human Generation](https://mlsanity.com/paper/2204.11823/) (2022)
- [Uncertainty Modeling for Out-of-Distribution Generalization](https://mlsanity.com/paper/2202.03958/) (2022)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Explaining in Style: Training a GAN to explain a classifier in StyleSpace](https://mlsanity.com/paper/2104.13369/) (2021)
- [Interpretable Deep Learning: Interpretation, Interpretability, Trustworthiness, and Beyond](https://mlsanity.com/paper/2103.10689/) (2021)
- [Uncovering the Disentanglement Capability in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2212.08698/) (2022)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [3D-aware Image Synthesis via Learning Structural and Textural Representations](https://mlsanity.com/paper/2112.10759/) (2021)
- [Talk-to-Edit: Fine-Grained Facial Editing via Dialog](https://mlsanity.com/paper/2109.04425/) (2021)

## Abstract (arXiv)

A rich set of interpretable dimensions has been shown to emerge in the latent space of the Generative Adversarial Networks (GANs) trained for synthesizing images. In order to identify such latent dimensions for image editing, previous methods typically annotate a collection of synthesized samples and train linear classifiers in the latent space. However, they require a clear definition of the target attribute as well as the corresponding manual annotations, limiting their applications in practice. In this work, we examine the internal representation learned by GANs to reveal the underlying variation factors in an unsupervised manner. In particular, we take a closer look into the generation mechanism of GANs and further propose a closed-form factorization algorithm for latent semantic discovery by directly decomposing the pre-trained weights. With a lightning-fast implementation, our approach is capable of not only finding semantically meaningful dimensions comparably to the state-of-the-art supervised methods, but also resulting in far more versatile concepts across multiple GAN models trained on a wide range of datasets.