# A Spectral Regularizer for Unsupervised Disentanglement

arXiv: https://arxiv.org/abs/1812.01161 · HTML: https://mlsanity.com/paper/1812.01161/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2018.

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

- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry](https://mlsanity.com/paper/2307.12868/) (2023)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [Low-Rank Subspaces in GANs](https://mlsanity.com/paper/2106.04488/) (2021)
- [WarpedGANSpace: Finding non-linear RBF paths in GAN latent space](https://mlsanity.com/paper/2109.13357/) (2021)
- [Orthogonal Jacobian Regularization for Unsupervised Disentanglement in Image Generation](https://mlsanity.com/paper/2108.07668/) (2021)
- [EigenGAN: Layer-Wise Eigen-Learning for GANs](https://mlsanity.com/paper/2104.12476/) (2021)
- [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)
- [Symmetry-Based Representations for Artificial and Biological General Intelligence](https://mlsanity.com/paper/2203.09250/) (2022)
- [Region-Based Semantic Factorization in GANs](https://mlsanity.com/paper/2202.09649/) (2022)
- [Personalized Image Generation with Deep Generative Models: A Decade Survey](https://mlsanity.com/paper/2502.13081/) (2025)
- [When are Post-hoc Conceptual Explanations Identifiable?](https://mlsanity.com/paper/2206.13872/) (2022)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Generative Adversarial Networks Unlearning](https://mlsanity.com/paper/2308.09881/) (2023)
- [In-Domain GAN Inversion for Faithful Reconstruction and Editability](https://mlsanity.com/paper/2309.13956/) (2023)
- [Analyzing the Latent Space of GAN through Local Dimension Estimation](https://mlsanity.com/paper/2205.13182/) (2022)
- [Supervised Attribute Information Removal and Reconstruction for Image Manipulation](https://mlsanity.com/paper/2207.06555/) (2022)
- [Local Manifold Augmentation for Multiview Semantic Consistency](https://mlsanity.com/paper/2211.02798/) (2022)
- [Deep Curvilinear Editing: Commutative and Nonlinear Image Manipulation for Pretrained Deep Generative Model](https://mlsanity.com/paper/2211.14573/) (2022)
- [Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models](https://mlsanity.com/paper/2510.05509/) (2025)
- [Mechanistically Eliciting Latent Behaviors in Language Models](https://mlsanity.com/paper/2606.29604/) (2026)
- [Varying Manifolds in Diffusion: From Time-varying Geometries to Visual Saliency](https://mlsanity.com/paper/2406.18588/) (2024)
- [A Survey on Leveraging Pre-trained Generative Adversarial Networks for Image Editing and Restoration](https://mlsanity.com/paper/2207.10309/) (2022)
- [Finding the global semantic representation in GAN through Frechet Mean](https://mlsanity.com/paper/2210.05509/) (2022)
- [How Video Meetings Change Your Expression](https://mlsanity.com/paper/2406.00955/) (2024)
- [(Deep) Generative Geodesics](https://mlsanity.com/paper/2407.11244/) (2024)
- [Trained Latent Space Navigation to Prevent Lack of Photorealism in Generated Images on Style-based Models](https://mlsanity.com/paper/2310.00936/) (2023)
- [Unsupervised Panoptic Interpretation of Latent Spaces in GANs Using Space-Filling Vector Quantization](https://mlsanity.com/paper/2410.20573/) (2024)
- [Generative Fields: Uncovering Hierarchical Feature Control for StyleGAN via Inverted Receptive Fields](https://mlsanity.com/paper/2504.17712/) (2025)

## Abstract (arXiv)

A generative model with a disentangled representation allows for independent control over different aspects of the output. Learning disentangled representations has been a recent topic of great interest, but it remains poorly understood. We show that even for GANs that do not possess disentangled representations, one can find curved trajectories in latent space over which local disentanglement occurs. These trajectories are found by iteratively following the leading right-singular vectors of the Jacobian of the generator with respect to its input. Based on this insight, we describe an efficient regularizer that aligns these vectors with the coordinate axes, and show that it can be used to induce disentangled representations in GANs, in a completely unsupervised manner.