# Householder Projector for Unsupervised Latent Semantics Discovery arXiv: https://arxiv.org/abs/2307.08012 · HTML: https://mlsanity.com/paper/2307.08012/ ## Key facts - Cited by 5 papers in the map (data through 14 Oct 2026). - Builds on 62 of its 74 references that are in the map. - First posted on arXiv 16 Jul 2023. ## Builds on (most cited first, 30 of 62) - [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018) - [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) - [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) - [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021) - [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) - [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019) - [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021) - [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016) - [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019) - [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020) - [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022) - [StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis](https://mlsanity.com/paper/2110.08985/) (2021) - [Pivotal Tuning for Latent-based Editing of Real Images](https://mlsanity.com/paper/2106.05744/) (2021) - [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) - [StyleSpace Analysis: Disentangled Controls for StyleGAN Image Generation](https://mlsanity.com/paper/2011.12799/) (2020) - [StyleGAN-V: A Continuous Video Generator with the Price, Image Quality and Perks of StyleGAN2](https://mlsanity.com/paper/2112.14683/) (2021) - [Unsupervised Discovery of Interpretable Directions in the GAN Latent Space](https://mlsanity.com/paper/2002.03754/) (2020) - [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021) - [On the "steerability" of generative adversarial networks](https://mlsanity.com/paper/1907.07171/) (2019) - [Disentangled and Controllable Face Image Generation via 3D Imitative-Contrastive Learning](https://mlsanity.com/paper/2004.11660/) (2020) - [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) - [EditGAN: High-Precision Semantic Image Editing](https://mlsanity.com/paper/2111.03186/) (2021) ## Built on by (most cited first, 5 of 5) - [Closed-Loop Unsupervised Representation Disentanglement with β-VAE Distillation and Diffusion Probabilistic Feedback](https://mlsanity.com/paper/2402.02346/) (2024) - [Identity-preserving Editing of Multiple Facial Attributes by Learning Global Edit Directions and Local Adjustments](https://mlsanity.com/paper/2309.14267/) (2023) - [Unsupervised Representation Learning from Sparse Transformation Analysis](https://mlsanity.com/paper/2410.05564/) (2024) - [Discovering Intersectional Bias via Directional Alignment in Face Recognition Embeddings](https://mlsanity.com/paper/2510.15520/) (2025) - [Unsupervised Panoptic Interpretation of Latent Spaces in GANs Using Space-Filling Vector Quantization](https://mlsanity.com/paper/2410.20573/) (2024) ## Abstract (arXiv) Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only 1% of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity.