# Linear Disentangled Representations and Unsupervised Action Estimation

arXiv: https://arxiv.org/abs/2008.07922 · HTML: https://mlsanity.com/paper/2008.07922/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2020.

## Built on by (most cited first, 14 of 14)

- [Commutative Lie Group VAE for Disentanglement Learning](https://mlsanity.com/paper/2106.03375/) (2021)
- [Towards Building A Group-based Unsupervised Representation Disentanglement Framework](https://mlsanity.com/paper/2102.10303/) (2021)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [When are Post-hoc Conceptual Explanations Identifiable?](https://mlsanity.com/paper/2206.13872/) (2022)
- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [Equivariant Disentangled Transformation for Domain Generalization under Combination Shift](https://mlsanity.com/paper/2208.02011/) (2022)
- [Measuring Orthogonality in Representations of Generative Models](https://mlsanity.com/paper/2407.03728/) (2024)
- [Transformation Coding: Simple Objectives for Equivariant Representations](https://mlsanity.com/paper/2202.10930/) (2022)
- [On a Built-in Conflict between Deep Learning and Systematic Generalization](https://mlsanity.com/paper/2208.11633/) (2022)
- [A Short Survey of Systematic Generalization](https://mlsanity.com/paper/2211.11956/) (2022)
- [Equivariant Representation Learning in the Presence of Stabilizers](https://mlsanity.com/paper/2301.05231/) (2023)
- [Disentangled Representation Learning through Unsupervised Symmetry Group Discovery](https://mlsanity.com/paper/2603.11790/) (2026)
- [Commutator-Induced Uncertainty in VAEs](https://mlsanity.com/paper/2605.23449/) (2026)
- [Categorical Internalisation of Environmental Groupoids for Generalisable POMDP Solving](https://mlsanity.com/paper/2609.27745/) (2026)

## Abstract (arXiv)

Disentangled representation learning has seen a surge in interest over recent times, generally focusing on new models which optimise one of many disparate disentanglement metrics. Symmetry Based Disentangled Representation learning introduced a robust mathematical framework that defined precisely what is meant by a "linear disentangled representation". This framework determined that such representations would depend on a particular decomposition of the symmetry group acting on the data, showing that actions would manifest through irreducible group representations acting on independent representational subspaces. Caselles-Dupre et al [2019] subsequently proposed the first model to induce and demonstrate a linear disentangled representation in a VAE model. In this work we empirically show that linear disentangled representations are not generally present in standard VAE models and that they instead require altering the loss landscape to induce them. We proceed to show that such representations are a desirable property with regard to classical disentanglement metrics. Finally we propose a method to induce irreducible representations which forgoes the need for labelled action sequences, as was required by prior work. We explore a number of properties of this method, including the ability to learn from action sequences without knowledge of intermediate states and robustness under visual noise. We also demonstrate that it can successfully learn 4 independent symmetries directly from pixels.