# Tensor-based Emotion Editing in the StyleGAN Latent Space

arXiv: https://arxiv.org/abs/2205.06102 · HTML: https://mlsanity.com/paper/2205.06102/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 12 May 2022.

## Builds on (most cited first, 30 of 31)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [MediaPipe: A Framework for Building Perception Pipelines](https://mlsanity.com/paper/1906.08172/) (2019)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [Pivotal Tuning for Latent-based Editing of Real Images](https://mlsanity.com/paper/2106.05744/) (2021)
- [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)
- [Image2StyleGAN++: How to Edit the Embedded Images?](https://mlsanity.com/paper/1911.11544/) (2019)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [StyleSpace Analysis: Disentangled Controls for StyleGAN Image Generation](https://mlsanity.com/paper/2011.12799/) (2020)
- [Challenges in Representation Learning: A report on three machine learning contests](https://mlsanity.com/paper/1307.0414/) (2013)
- [StyleRig: Rigging StyleGAN for 3D Control over Portrait Images](https://mlsanity.com/paper/2004.00121/) (2020)
- [ReStyle: A Residual-Based StyleGAN Encoder via Iterative Refinement](https://mlsanity.com/paper/2104.02699/) (2021)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [Py-Feat: Python Facial Expression Analysis Toolbox](https://mlsanity.com/paper/2104.03509/) (2021)
- [Multilinear Wavelets: A Statistical Shape Space for Human Faces](https://mlsanity.com/paper/1401.2818/) (2014)
- [Unconstrained Facial Expression Transfer using Style-based Generator](https://mlsanity.com/paper/1912.06253/) (2019)

## Built on by (most cited first, 7 of 7)

- [Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models](https://mlsanity.com/paper/2303.11073/) (2023)
- [PandA: Unsupervised Learning of Parts and Appearances in the Feature Maps of GANs](https://mlsanity.com/paper/2206.00048/) (2022)
- [Synthetic Face Datasets Generation via Latent Space Exploration from Brownian Identity Diffusion](https://mlsanity.com/paper/2405.00228/) (2024)
- [ReDirTrans: Latent-to-Latent Translation for Gaze and Head Redirection](https://mlsanity.com/paper/2305.11452/) (2023)
- [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)
- [Controllable GAN Synthesis Using Non-Rigid Structure-from-Motion](https://mlsanity.com/paper/2211.07195/) (2022)

## Abstract (arXiv)

In this paper, we use a tensor model based on the Higher-Order Singular Value Decomposition (HOSVD) to discover semantic directions in Generative Adversarial Networks. This is achieved by first embedding a structured facial expression database into the latent space using the e4e encoder. Specifically, we discover directions in latent space corresponding to the six prototypical emotions: anger, disgust, fear, happiness, sadness, and surprise, as well as a direction for yaw rotation. These latent space directions are employed to change the expression or yaw rotation of real face images. We compare our found directions to similar directions found by two other methods. The results show that the visual quality of the resultant edits are on par with State-of-the-Art. It can also be concluded that the tensor-based model is well suited for emotion and yaw editing, i.e., that the emotion or yaw rotation of a novel face image can be robustly changed without a significant effect on identity or other attributes in the images.