# Equivariant Representation Learning via Class-Pose Decomposition

arXiv: https://arxiv.org/abs/2207.03116 · HTML: https://mlsanity.com/paper/2207.03116/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 7 Jul 2022.

## Builds on (most cited first, 30 of 31)

- [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)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Habitat: A Platform for Embodied AI Research](https://mlsanity.com/paper/1904.01201/) (2019)
- [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)
- [A Survey on Contrastive Self-supervised Learning](https://mlsanity.com/paper/2011.00362/) (2020)
- [Gibson Env: Real-World Perception for Embodied Agents](https://mlsanity.com/paper/1808.10654/) (2018)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [On Learning Sets of Symmetric Elements](https://mlsanity.com/paper/2002.08599/) (2020)
- [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)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Interpretable Transformations with Encoder-Decoder Networks](https://mlsanity.com/paper/1710.07307/) (2017)
- [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)
- [Learning Group Structure and Disentangled Representations of Dynamical Environments](https://mlsanity.com/paper/2002.06991/) (2020)
- [Quantifying and Learning Linear Symmetry-Based Disentanglement](https://mlsanity.com/paper/2011.06070/) (2020)

## Built on by (most cited first, 17 of 17)

- [A Cookbook of Self-Supervised Learning](https://mlsanity.com/paper/2304.12210/) (2023)
- [Self-supervised learning of Split Invariant Equivariant representations](https://mlsanity.com/paper/2302.10283/) (2023)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [Latent Space Symmetry Discovery](https://mlsanity.com/paper/2310.00105/) (2023)
- [Steerers: A framework for rotation equivariant keypoint descriptors](https://mlsanity.com/paper/2312.02152/) (2023)
- [Back to the Manifold: Recovering from Out-of-Distribution States](https://mlsanity.com/paper/2207.08673/) (2022)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Topological Obstructions and How to Avoid Them](https://mlsanity.com/paper/2312.07529/) (2023)
- [Algebras of actions in an agent's representations of the world](https://mlsanity.com/paper/2310.01536/) (2023)
- [CFASL: Composite Factor-Aligned Symmetry Learning for Disentanglement in Variational AutoEncoder](https://mlsanity.com/paper/2401.08897/) (2024)
- [RECON: Robust symmetry discovery via Explicit Canonical Orientation Normalization](https://mlsanity.com/paper/2505.13289/) (2025)
- [Soft Equivariance Regularization for Invariant Self-Supervised Learning](https://mlsanity.com/paper/2603.06693/) (2026)
- [Equivariant Representation Learning in the Presence of Stabilizers](https://mlsanity.com/paper/2301.05231/) (2023)
- [Learning Geometric Representations of Objects via Interaction](https://mlsanity.com/paper/2309.05346/) (2023)
- [EquiCaps: Predictor-Free Pose-Aware Pre-Trained Capsule Networks](https://mlsanity.com/paper/2506.09895/) (2025)
- [Group-invariant Coresets for Data-efficient Active Learning](https://mlsanity.com/paper/2607.01089/) (2026)
- [Capturing Cardiac Cyclicity through Phase-Equivariant Self-Supervised Learning](https://mlsanity.com/paper/2608.21147/) (2026)

## Abstract (arXiv)

We introduce a general method for learning representations that are equivariant to symmetries of data. Our central idea is to decompose the latent space into an invariant factor and the symmetry group itself. The components semantically correspond to intrinsic data classes and poses respectively. The learner is trained on a loss encouraging equivariance based on supervision from relative symmetry information. The approach is motivated by theoretical results from group theory and guarantees representations that are lossless, interpretable and disentangled. We provide an empirical investigation via experiments involving datasets with a variety of symmetries. Results show that our representations capture the geometry of data and outperform other equivariant representation learning frameworks.