# Disentangled Representation Learning through Unsupervised Symmetry Group Discovery

arXiv: https://arxiv.org/abs/2603.11790 · HTML: https://mlsanity.com/paper/2603.11790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Conditional Object-Centric Learning from Video](https://mlsanity.com/paper/2111.12594/) (2021)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Learning Deep Disentangled Embeddings with the F-Statistic Loss](https://mlsanity.com/paper/1802.05312/) (2018)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [Automatic Symmetry Discovery with Lie Algebra Convolutional Network](https://mlsanity.com/paper/2109.07103/) (2021)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Unsupervised Model Selection for Variational Disentangled Representation Learning](https://mlsanity.com/paper/1905.12614/) (2019)
- [BISCUIT: Causal Representation Learning from Binary Interactions](https://mlsanity.com/paper/2306.09643/) (2023)
- [DRANet: Disentangling Representation and Adaptation Networks for Unsupervised Cross-Domain Adaptation](https://mlsanity.com/paper/2103.13447/) (2021)
- [Symmetry-Based Disentangled Representation Learning requires Interaction with Environments](https://mlsanity.com/paper/1904.00243/) (2019)
- [Disentangling by Subspace Diffusion](https://mlsanity.com/paper/2006.12982/) (2020)
- [Towards Building A Group-based Unsupervised Representation Disentanglement Framework](https://mlsanity.com/paper/2102.10303/) (2021)
- [Evaluating the Disentanglement of Deep Generative Models through Manifold Topology](https://mlsanity.com/paper/2006.03680/) (2020)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [Object-Oriented Dynamics Predictor](https://mlsanity.com/paper/1806.07371/) (2018)

## Abstract (arXiv)

Symmetry-based disentangled representation learning leverages the group structure of environment transformations to uncover the latent factors of variation. Prior approaches to symmetry-based disentanglement have required strong prior knowledge of the symmetry group's structure, or restrictive assumptions about the subgroup properties. In this work, we remove these constraints by proposing a method whereby an embodied agent autonomously discovers the group structure of its action space through unsupervised interaction with the environment. We prove the identifiability of the true symmetry group decomposition under minimal assumptions, and derive two algorithms: one for discovering the group decomposition from interaction data, and another for learning Linear Symmetry-Based Disentangled (LSBD) representations without assuming specific subgroup properties. Our method is validated on three environments exhibiting different group decompositions, where it outperforms existing LSBD approaches.