# Unsupervised Disentanglement with Tensor Product Representations on the Torus

arXiv: https://arxiv.org/abs/2202.06201 · HTML: https://mlsanity.com/paper/2202.06201/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 13 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [Theory and Evaluation Metrics for Learning Disentangled Representations](https://mlsanity.com/paper/1908.09961/) (2019)

## Built on by (most cited first, 4 of 4)

- [Evaluating Disentanglement in Generative Models Without Knowledge of Latent Factors](https://mlsanity.com/paper/2210.01760/) (2022)
- [TC-VAE: Uncovering Out-of-Distribution Data Generative Factors](https://mlsanity.com/paper/2304.04103/) (2023)
- [Gradient Adjusting Networks for Domain Inversion](https://mlsanity.com/paper/2302.11413/) (2023)
- [Twincher: Bijective Representation Learning for Robust Inversion of Continuous Systems](https://mlsanity.com/paper/2605.13470/) (2026)

## Abstract (arXiv)

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained representations are naturally disentangled. In contrast to the conventional variations methods, which are targeted toward normally distributed features, the latent space in our representation is distributed uniformly over a set of unit circles. We argue that the torus structure of the latent space captures the generative factors effectively. We employ recent tools for measuring unsupervised disentanglement, and in an extensive set of experiments demonstrate the advantage of our method in terms of disentanglement, completeness, and informativeness. The code for our proposed method is available at https://github.com/rotmanmi/Unsupervised-Disentanglement-Torus.