# Latent Space Factorisation and Manipulation via Matrix Subspace Projection

arXiv: https://arxiv.org/abs/1907.12385 · HTML: https://mlsanity.com/paper/1907.12385/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2019.

## Built on by (most cited first, 9 of 9)

- [LinkGAN: Linking GAN Latents to Pixels for Controllable Image Synthesis](https://mlsanity.com/paper/2301.04604/) (2023)
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- [Discovering Novel Biological Traits From Images Using Phylogeny-Guided Neural Networks](https://mlsanity.com/paper/2306.03228/) (2023)
- [DuelGAN: A Duel Between Two Discriminators Stabilizes the GAN Training](https://mlsanity.com/paper/2101.07524/) (2021)
- [Flow Plugin Network for conditional generation](https://mlsanity.com/paper/2110.04081/) (2021)
- [TRIP: Refining Image-to-Image Translation via Rival Preferences](https://mlsanity.com/paper/2111.13411/) (2021)
- [Robust Deep Learning Models Against Semantic-Preserving Adversarial Attack](https://mlsanity.com/paper/2304.03955/) (2023)
- [SAFA-SNN: Sparsity-Aware On-Device Few-Shot Class-Incremental Learning with Fast-Adaptive Structure of Spiking Neural Network](https://mlsanity.com/paper/2510.03648/) (2025)

## Abstract (arXiv)

We tackle the problem disentangling the latent space of an autoencoder in order to separate labelled attribute information from other characteristic information. This then allows us to change selected attributes while preserving other information. Our method, matrix subspace projection, is much simpler than previous approaches to latent space factorisation, for example not requiring multiple discriminators or a careful weighting among their loss functions. Furthermore our new model can be applied to autoencoders as a plugin, and works across diverse domains such as images or text. We demonstrate the utility of our method for attribute manipulation in autoencoders trained across varied domains, using both human evaluation and automated methods. The quality of generation of our new model (e.g. reconstruction, conditional generation) is highly competitive to a number of strong baselines.