# Low-Rank Subspaces in GANs

arXiv: https://arxiv.org/abs/2106.04488 · HTML: https://mlsanity.com/paper/2106.04488/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 45 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 29 of 29)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [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)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [In-Domain GAN Inversion for Real Image Editing](https://mlsanity.com/paper/2004.00049/) (2020)
- [Closed-Form Factorization of Latent Semantics in GANs](https://mlsanity.com/paper/2007.06600/) (2020)
- [InterFaceGAN: Interpreting the Disentangled Face Representation Learned by GANs](https://mlsanity.com/paper/2005.09635/) (2020)
- [Video-to-Video Synthesis](https://mlsanity.com/paper/1808.06601/) (2018)
- [StyleSpace Analysis: Disentangled Controls for StyleGAN Image Generation](https://mlsanity.com/paper/2011.12799/) (2020)
- [Unsupervised Discovery of Interpretable Directions in the GAN Latent Space](https://mlsanity.com/paper/2002.03754/) (2020)
- [On the "steerability" of generative adversarial networks](https://mlsanity.com/paper/1907.07171/) (2019)
- [Large Scale Adversarial Representation Learning](https://mlsanity.com/paper/1907.02544/) (2019)
- [GANalyze: Toward Visual Definitions of Cognitive Image Properties](https://mlsanity.com/paper/1906.10112/) (2019)
- [Editing in Style: Uncovering the Local Semantics of GANs](https://mlsanity.com/paper/2004.14367/) (2020)
- [Semantic Photo Manipulation with a Generative Image Prior](https://mlsanity.com/paper/2005.07727/) (2020)
- [Semantic Hierarchy Emerges in Deep Generative Representations for Scene Synthesis](https://mlsanity.com/paper/1911.09267/) (2019)
- [Controlling generative models with continuous factors of variations](https://mlsanity.com/paper/2001.10238/) (2020)
- [Generative Hierarchical Features from Synthesizing Images](https://mlsanity.com/paper/2007.10379/) (2020)
- [GAN "Steerability" without optimization](https://mlsanity.com/paper/2012.05328/) (2020)
- [The Geometry of Deep Generative Image Models and its Applications](https://mlsanity.com/paper/2101.06006/) (2021)
- [A Spectral Regularizer for Unsupervised Disentanglement](https://mlsanity.com/paper/1812.01161/) (2018)
- [Spatially Controllable Image Synthesis with Internal Representation Collaging](https://mlsanity.com/paper/1811.10153/) (2018)
- [Decorating Your Own Bedroom: Locally Controlling Image Generation with Generative Adversarial Networks](https://mlsanity.com/paper/2105.08222/) (2021)

## Built on by (most cited first, 30 of 53)

- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [3D-aware Image Synthesis via Learning Structural and Textural Representations](https://mlsanity.com/paper/2112.10759/) (2021)
- [Arc2Face: A Foundation Model for ID-Consistent Human Faces](https://mlsanity.com/paper/2403.11641/) (2024)
- [Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models](https://mlsanity.com/paper/2303.11073/) (2023)
- [Rank Diminishing in Deep Neural Networks](https://mlsanity.com/paper/2206.06072/) (2022)
- [3D-Aware Indoor Scene Synthesis with Depth Priors](https://mlsanity.com/paper/2202.08553/) (2022)
- [User-Controllable Latent Transformer for StyleGAN Image Layout Editing](https://mlsanity.com/paper/2208.12408/) (2022)
- [Unsupervised Discovery of Semantic Latent Directions in Diffusion Models](https://mlsanity.com/paper/2302.12469/) (2023)
- [Do Not Escape From the Manifold: Discovering the Local Coordinates on the Latent Space of GANs](https://mlsanity.com/paper/2106.06959/) (2021)
- [High-fidelity GAN Inversion with Padding Space](https://mlsanity.com/paper/2203.11105/) (2022)
- [Region-Based Semantic Factorization in GANs](https://mlsanity.com/paper/2202.09649/) (2022)
- [PandA: Unsupervised Learning of Parts and Appearances in the Feature Maps of GANs](https://mlsanity.com/paper/2206.00048/) (2022)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [VToonify: Controllable High-Resolution Portrait Video Style Transfer](https://mlsanity.com/paper/2209.11224/) (2022)
- [Attributing Image Generative Models using Latent Fingerprints](https://mlsanity.com/paper/2304.09752/) (2023)
- [StyleGANEX: StyleGAN-Based Manipulation Beyond Cropped Aligned Faces](https://mlsanity.com/paper/2303.06146/) (2023)
- [Discovering Low-rank Subspaces for Language-agnostic Multilingual Representations](https://mlsanity.com/paper/2401.05792/) (2024)
- [Latent Traversals in Generative Models as Potential Flows](https://mlsanity.com/paper/2304.12944/) (2023)
- [GAN-based Facial Attribute Manipulation](https://mlsanity.com/paper/2210.12683/) (2022)
- [LinkGAN: Linking GAN Latents to Pixels for Controllable Image Synthesis](https://mlsanity.com/paper/2301.04604/) (2023)
- [Exploring Low-Dimensional Subspaces in Diffusion Models for Controllable Image Editing](https://mlsanity.com/paper/2409.02374/) (2024)
- [Exploring Sparse MoE in GANs for Text-conditioned Image Synthesis](https://mlsanity.com/paper/2309.03904/) (2023)
- [Flow Factorized Representation Learning](https://mlsanity.com/paper/2309.13167/) (2023)
- [PaRa: Personalizing Text-to-Image Diffusion via Parameter Rank Reduction](https://mlsanity.com/paper/2406.05641/) (2024)
- [Masked-Attention Diffusion Guidance for Spatially Controlling Text-to-Image Generation](https://mlsanity.com/paper/2308.06027/) (2023)
- [Existence and Estimation of Critical Batch Size for Training Generative Adversarial Networks with Two Time-Scale Update Rule](https://mlsanity.com/paper/2201.11989/) (2022)
- [IA-FaceS: A Bidirectional Method for Semantic Face Editing](https://mlsanity.com/paper/2203.13097/) (2022)
- [Content-Based Search for Deep Generative Models](https://mlsanity.com/paper/2210.03116/) (2022)
- [Optimizing Latent Space Directions For GAN-based Local Image Editing](https://mlsanity.com/paper/2111.12583/) (2021)
- [Orthogonal SVD Covariance Conditioning and Latent Disentanglement](https://mlsanity.com/paper/2212.05599/) (2022)

## Abstract (arXiv)

The latent space of a Generative Adversarial Network (GAN) has been shown to encode rich semantics within some subspaces. To identify these subspaces, researchers typically analyze the statistical information from a collection of synthesized data, and the identified subspaces tend to control image attributes globally (i.e., manipulating an attribute causes the change of an entire image). By contrast, this work introduces low-rank subspaces that enable more precise control of GAN generation. Concretely, given an arbitrary image and a region of interest (e.g., eyes of face images), we manage to relate the latent space to the image region with the Jacobian matrix and then use low-rank factorization to discover steerable latent subspaces. There are three distinguishable strengths of our approach that can be aptly called LowRankGAN. First, compared to analytic algorithms in prior work, our low-rank factorization of Jacobians is able to find the low-dimensional representation of attribute manifold, making image editing more precise and controllable. Second, low-rank factorization naturally yields a null space of attributes such that moving the latent code within it only affects the outer region of interest. Therefore, local image editing can be simply achieved by projecting an attribute vector into the null space without relying on a spatial mask as existing methods do. Third, our method can robustly work with a local region from one image for analysis yet well generalize to other images, making it much easy to use in practice. Extensive experiments on state-of-the-art GAN models (including StyleGAN2 and BigGAN) trained on various datasets demonstrate the effectiveness of our LowRankGAN.