# Learning Group Structure and Disentangled Representations of Dynamical Environments

arXiv: https://arxiv.org/abs/2002.06991 · HTML: https://mlsanity.com/paper/2002.06991/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2020.

## Built on by (most cited first, 13 of 13)

- [Commutative Lie Group VAE for Disentanglement Learning](https://mlsanity.com/paper/2106.03375/) (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)
- [Structuring Representation Geometry with Rotationally Equivariant Contrastive Learning](https://mlsanity.com/paper/2306.13924/) (2023)
- [Towards Building A Group-based Unsupervised Representation Disentanglement Framework](https://mlsanity.com/paper/2102.10303/) (2021)
- [Equivariant Representation Learning via Class-Pose Decomposition](https://mlsanity.com/paper/2207.03116/) (2022)
- [Group Equivariant Conditional Neural Processes](https://mlsanity.com/paper/2102.08759/) (2021)
- [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)
- [GEM: Group Enhanced Model for Learning Dynamical Control Systems](https://mlsanity.com/paper/2104.02844/) (2021)
- [Who Said Neural Networks Aren't Linear?](https://mlsanity.com/paper/2510.08570/) (2025)
- [Learning Abstract World Models with a Group-Structured Latent Space](https://mlsanity.com/paper/2506.01529/) (2025)
- [Transformation Coding: Simple Objectives for Equivariant Representations](https://mlsanity.com/paper/2202.10930/) (2022)

## Abstract (arXiv)

Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of symmetry preserving transformations. Inspired by this formalism, we propose a framework, built upon the theory of group representation, for learning representations of a dynamical environment structured around the transformations that generate its evolution. Experimentally, we learn the structure of explicitly symmetric environments without supervision from observational data generated by sequential interactions. We further introduce an intuitive disentanglement regularisation to ensure the interpretability of the learnt representations. We show that our method enables accurate long-horizon predictions, and demonstrate a correlation between the quality of predictions and disentanglement in the latent space.