# Tensor Component Analysis for Interpreting the Latent Space of GANs

arXiv: https://arxiv.org/abs/2111.11736 · HTML: https://mlsanity.com/paper/2111.11736/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 40 references that are in the map.
- First posted on arXiv 23 Nov 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [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)
- [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)
- [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)
- [GANalyze: Toward Visual Definitions of Cognitive Image Properties](https://mlsanity.com/paper/1906.10112/) (2019)
- [TensorLy: Tensor Learning in Python](https://mlsanity.com/paper/1610.09555/) (2016)
- [Controlling generative models with continuous factors of variations](https://mlsanity.com/paper/2001.10238/) (2020)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [WarpedGANSpace: Finding non-linear RBF paths in GAN latent space](https://mlsanity.com/paper/2109.13357/) (2021)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Factorized Higher-Order CNNs with an Application to Spatio-Temporal Emotion Estimation](https://mlsanity.com/paper/1906.06196/) (2019)
- [Pi-nets: Deep Polynomial Neural Networks](https://mlsanity.com/paper/2003.03828/) (2020)
- [High-Fidelity Synthesis with Disentangled Representation](https://mlsanity.com/paper/2001.04296/) (2020)
- [Incremental multi-domain learning with network latent tensor factorization](https://mlsanity.com/paper/1904.06345/) (2019)
- [Multilinear Latent Conditioning for Generating Unseen Attribute Combinations](https://mlsanity.com/paper/2009.04075/) (2020)
- [An Adversarial Neuro-Tensorial Approach For Learning Disentangled Representations](https://mlsanity.com/paper/1711.10402/) (2017)

## Built on by (most cited first, 13 of 13)

- [HyperReenact: One-Shot Reenactment via Jointly Learning to Refine and Retarget Faces](https://mlsanity.com/paper/2307.10797/) (2023)
- [Attribute-preserving Face Dataset Anonymization via Latent Code Optimization](https://mlsanity.com/paper/2303.11296/) (2023)
- [Finding Directions in GAN's Latent Space for Neural Face Reenactment](https://mlsanity.com/paper/2202.00046/) (2022)
- [PandA: Unsupervised Learning of Parts and Appearances in the Feature Maps of GANs](https://mlsanity.com/paper/2206.00048/) (2022)
- [StyleMask: Disentangling the Style Space of StyleGAN2 for Neural Face Reenactment](https://mlsanity.com/paper/2209.13375/) (2022)
- [Improving Fairness using Vision-Language Driven Image Augmentation](https://mlsanity.com/paper/2311.01573/) (2023)
- [ContraCLIP: Interpretable GAN generation driven by pairs of contrasting sentences](https://mlsanity.com/paper/2206.02104/) (2022)
- [One-shot Neural Face Reenactment via Finding Directions in GAN's Latent Space](https://mlsanity.com/paper/2402.03553/) (2024)
- [Householder Projector for Unsupervised Latent Semantics Discovery](https://mlsanity.com/paper/2307.08012/) (2023)
- [Cluster-guided Image Synthesis with Unconditional Models](https://mlsanity.com/paper/2112.12911/) (2021)
- [Deep Curvilinear Editing: Commutative and Nonlinear Image Manipulation for Pretrained Deep Generative Model](https://mlsanity.com/paper/2211.14573/) (2022)
- [Compressing Image-to-Image Translation GANs Using Local Density Structures on Their Learned Manifold](https://mlsanity.com/paper/2312.14776/) (2023)
- [Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models](https://mlsanity.com/paper/2510.05509/) (2025)

## Abstract (arXiv)

This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) to facilitate controllable image synthesis. Such interpretable directions correspond to transformations that can affect both the style and geometry of the synthetic images. However, existing approaches that utilise linear techniques to find these transformations often fail to provide an intuitive way to separate these two sources of variation. To address this, we propose to a) perform a multilinear decomposition of the tensor of intermediate representations, and b) use a tensor-based regression to map directions found using this decomposition to the latent space. Our scheme allows for both linear edits corresponding to the individual modes of the tensor, and non-linear ones that model the multiplicative interactions between them. We show experimentally that we can utilise the former to better separate style- from geometry-based transformations, and the latter to generate an extended set of possible transformations in comparison to prior works. We demonstrate our approach's efficacy both quantitatively and qualitatively compared to the current state-of-the-art.