# Symmetry-Based Disentangled Representation Learning requires Interaction with Environments

arXiv: https://arxiv.org/abs/1904.00243 · HTML: https://mlsanity.com/paper/1904.00243/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2019.

## Built on by (most cited first, 30 of 35)

- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Learning Disentangled Representations in the Imaging Domain](https://mlsanity.com/paper/2108.12043/) (2021)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Commutative Lie Group VAE for Disentanglement Learning](https://mlsanity.com/paper/2106.03375/) (2021)
- [Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamics](https://mlsanity.com/paper/2111.01365/) (2021)
- [Continuous MDP Homomorphisms and Homomorphic Policy Gradient](https://mlsanity.com/paper/2209.07364/) (2022)
- [Symmetry-Based Representations for Artificial and Biological General Intelligence](https://mlsanity.com/paper/2203.09250/) (2022)
- [Towards Building A Group-based Unsupervised Representation Disentanglement Framework](https://mlsanity.com/paper/2102.10303/) (2021)
- [Toward Compositional Generalization in Object-Oriented World Modeling](https://mlsanity.com/paper/2204.13661/) (2022)
- [Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitions](https://mlsanity.com/paper/2207.12067/) (2022)
- [Unsupervised Representation Learning in Deep Reinforcement Learning: A Review](https://mlsanity.com/paper/2208.14226/) (2022)
- [Addressing the Topological Defects of Disentanglement via Distributed Operators](https://mlsanity.com/paper/2102.05623/) (2021)
- [Policy Gradient Methods in the Presence of Symmetries and State Abstractions](https://mlsanity.com/paper/2305.05666/) (2023)
- [Hamiltonian latent operators for content and motion disentanglement in image sequences](https://mlsanity.com/paper/2112.01641/) (2021)
- [Topological Obstructions and How to Avoid Them](https://mlsanity.com/paper/2312.07529/) (2023)
- [SiT: Symmetry-Invariant Transformers for Generalisation in Reinforcement Learning](https://mlsanity.com/paper/2406.15025/) (2024)
- [What Drives Compositional Generalization in Visual Generative Models? The Importance of Continuous Training Objectives](https://mlsanity.com/paper/2510.03075/) (2025)
- [Enriching Disentanglement: From Logical Definitions to Quantitative Metrics](https://mlsanity.com/paper/2305.11512/) (2023)
- [Algebras of actions in an agent's representations of the world](https://mlsanity.com/paper/2310.01536/) (2023)
- [VECA : A Toolkit for Building Virtual Environments to Train and Test Human-like Agents](https://mlsanity.com/paper/2105.00762/) (2021)
- [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)
- [Groupoid-Based Internal State Representations for Reinforcement Learning with Local Symmetries](https://mlsanity.com/paper/2609.13035/) (2026)
- [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)
- [Learning Parsimonious Dynamics for Generalization in Reinforcement Learning](https://mlsanity.com/paper/2209.14781/) (2022)
- [A Short Survey of Systematic Generalization](https://mlsanity.com/paper/2211.11956/) (2022)
- [Symmetry Detection in Trajectory Data for More Meaningful Reinforcement Learning Representations](https://mlsanity.com/paper/2211.16381/) (2022)
- [Switchable Lightweight Anti-symmetric Processing (SLAP) with CNN Outspeeds Data Augmentation by Smaller Sample -- Application in Gomoku Reinforcement Learning](https://mlsanity.com/paper/2301.04746/) (2023)
- [Equivariant Representation Learning in the Presence of Stabilizers](https://mlsanity.com/paper/2301.05231/) (2023)

## Abstract (arXiv)

Finding a generally accepted formal definition of a disentangled representation in the context of an agent behaving in an environment is an important challenge towards the construction of data-efficient autonomous agents. Higgins et al. recently proposed Symmetry-Based Disentangled Representation Learning, a definition based on a characterization of symmetries in the environment using group theory. We build on their work and make observations, theoretical and empirical, that lead us to argue that Symmetry-Based Disentangled Representation Learning cannot only be based on static observations: agents should interact with the environment to discover its symmetries. Our experiments can be reproduced in Colab and the code is available on GitHub.