# Equivariant Representation Learning in the Presence of Stabilizers

arXiv: https://arxiv.org/abs/2301.05231 · HTML: https://mlsanity.com/paper/2301.05231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 31 references that are in the map.
- First posted on arXiv 12 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [Explorations in Homeomorphic Variational Auto-Encoding](https://mlsanity.com/paper/1807.04689/) (2018)
- [Plannable Approximations to MDP Homomorphisms: Equivariance under Actions](https://mlsanity.com/paper/2002.11963/) (2020)
- [Learning Symmetric Embeddings for Equivariant World Models](https://mlsanity.com/paper/2204.11371/) (2022)
- [Equivariant Neural Rendering](https://mlsanity.com/paper/2006.07630/) (2020)
- [Learning the Irreducible Representations of Commutative Lie Groups](https://mlsanity.com/paper/1402.4437/) (2014)
- [Symmetry-Based Disentangled Representation Learning requires Interaction with Environments](https://mlsanity.com/paper/1904.00243/) (2019)
- [Interpretable Transformations with Encoder-Decoder Networks](https://mlsanity.com/paper/1710.07307/) (2017)
- [Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning](https://mlsanity.com/paper/2110.15796/) (2021)
- [Symmetry-Based Representations for Artificial and Biological General Intelligence](https://mlsanity.com/paper/2203.09250/) (2022)
- [Equivariant Representation Learning via Class-Pose Decomposition](https://mlsanity.com/paper/2207.03116/) (2022)
- [Linear Disentangled Representations and Unsupervised Action Estimation](https://mlsanity.com/paper/2008.07922/) (2020)
- [Quantifying and Learning Linear Symmetry-Based Disentanglement](https://mlsanity.com/paper/2011.06070/) (2020)
- [Efficient conversion from rotating matrix to rotation axis and angle by extending Rodrigues' formula](https://mlsanity.com/paper/1810.02999/) (2018)

## Abstract (arXiv)

We introduce Equivariant Isomorphic Networks (EquIN) -- a method for learning representations that are equivariant with respect to general group actions over data. Differently from existing equivariant representation learners, EquIN is suitable for group actions that are not free, i.e., that stabilize data via nontrivial symmetries. EquIN is theoretically grounded in the orbit-stabilizer theorem from group theory. This guarantees that an ideal learner infers isomorphic representations while trained on equivariance alone and thus fully extracts the geometric structure of data. We provide an empirical investigation on image datasets with rotational symmetries and show that taking stabilizers into account improves the quality of the representations.