# Tensor-based Subspace Factorization for StyleGAN

arXiv: https://arxiv.org/abs/2111.04554 · HTML: https://mlsanity.com/paper/2111.04554/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [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)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [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)
- [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)
- [Closed-Form Factorization of Latent Semantics in GANs](https://mlsanity.com/paper/2007.06600/) (2020)
- [StyleRig: Rigging StyleGAN for 3D Control over Portrait Images](https://mlsanity.com/paper/2004.00121/) (2020)
- [Disentangled and Controllable Face Image Generation via 3D Imitative-Contrastive Learning](https://mlsanity.com/paper/2004.11660/) (2020)
- [Arbitrary Style Transfer with Style-Attentional Networks](https://mlsanity.com/paper/1812.02342/) (2018)
- [Adversarial Latent Autoencoders](https://mlsanity.com/paper/2004.04467/) (2020)
- [Multilinear Wavelets: A Statistical Shape Space for Human Faces](https://mlsanity.com/paper/1401.2818/) (2014)

## Built on by (most cited first, 3 of 3)

- [PandA: Unsupervised Learning of Parts and Appearances in the Feature Maps of GANs](https://mlsanity.com/paper/2206.00048/) (2022)
- [Tensor-based Emotion Editing in the StyleGAN Latent Space](https://mlsanity.com/paper/2205.06102/) (2022)
- [Controllable GAN Synthesis Using Non-Rigid Structure-from-Motion](https://mlsanity.com/paper/2211.07195/) (2022)

## Abstract (arXiv)

In this paper, we propose τGAN a tensor-based method for modeling the latent space of generative models. The objective is to identify semantic directions in latent space. To this end, we propose to fit a multilinear tensor model on a structured facial expression database, which is initially embedded into latent space. We validate our approach on StyleGAN trained on FFHQ using BU-3DFE as a structured facial expression database. We show how the parameters of the multilinear tensor model can be approximated by Alternating Least Squares. Further, we introduce a tacked style-separated tensor model, defined as an ensemble of style-specific models to integrate our approach with the extended latent space of StyleGAN. We show that taking the individual styles of the extended latent space into account leads to higher model flexibility and lower reconstruction error. Finally, we do several experiments comparing our approach to former work on both GANs and multilinear models. Concretely, we analyze the expression subspace and find that the expression trajectories meet at an apathetic face that is consistent with earlier work. We also show that by changing the pose of a person, the generated image from our approach is closer to the ground truth than results from two competing approaches.