mlsanityData to 7 Oct 2026

Learning Symmetric Embeddings for Equivariant World Models

arXiv 2204.11371 ↗First posted 24 Apr 2022cs.LGcited by 54

On the map: World models → Latent predictive world models

Abstract (arXiv)

Incorporating symmetries can lead to highly data-efficient and generalizable models by defining equivalence classes of data samples related by transformations. However, characterizing how transformations act on input data is often difficult, limiting the applicability of equivariant models. We propose learning symmetric embedding networks (SENs) that encode an input space (e.g. images), where we do not know the effect of transformations (e.g. rotations), to a feature space that transforms in a known manner under these operations. This network can be trained end-to-end with an equivariant task network to learn an explicitly symmetric representation. We validate this approach in the context of equivariant transition models with 3 distinct forms of symmetry. Our experiments demonstrate that SENs facilitate the application of equivariant networks to data with complex symmetry representations. Moreover, doing so can yield improvements in accuracy and generalization relative to both fully-equivariant and non-equivariant baselines.

Key facts. Cited by 54 papers in the map (data through 7 Oct 2026). Placed in Latent predictive world models, one of 11 directions in World models. Builds on 36 of its 53 references that are in the map. First posted on arXiv 24 Apr 2022.

Builds on

36 of 53 references.

Closest ancestors · 2

Same direction, newest first

  1. 2019Contrastive Learning of Structured World Models27 Nov
  2. 2018Learning Latent Dynamics for Planning from Pixels12 Nov

Other references · 34

  1. 2020A Simple Framework for Contrastive Learning of Visual Representationscited by 11,979
  2. 2018Representation Learning with Contrastive Predictive Codingcited by 7,662
  3. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  4. 2016Layer Normalizationcited by 5,579
  5. 2018World Modelscited by 1,444
  6. 2016Group Equivariant Convolutional Networkscited by 1,154
  7. 2020Mastering Atari with Discrete World Modelscited by 990
  8. 2020CURL: Contrastive Unsupervised Representations for Reinforcement Learningcited by 745
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  10. 2018Spherical CNNscited by 452
  11. 2019General E(2)-Equivariant Steerable CNNscited by 441
  12. 2016End-to-end Sequence Labeling via Bi-directional LSTM-CNNs-CRFcited by 341
22 more
  1. 2016Steerable CNNscited by 298
  2. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  3. 2018Towards a Definition of Disentangled Representationscited by 294
  4. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  5. 2015Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Imagescited by 266
  6. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  7. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  8. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  9. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  10. 2019Unsupervised State Representation Learning in Ataricited by 144
  11. 2020MDP Homomorphic Networks: Group Symmetries in Reinforcement Learningcited by 133
  12. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  13. 2020On Learning Sets of Symmetric Elementscited by 97
  14. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  15. 2017Polar Transformer Networkscited by 81
  16. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  17. 2020Meta-Learning Symmetries by Reparameterizationcited by 75
  18. 2018Explorations in Homeomorphic Variational Auto-Encodingcited by 65
  19. 2020Plannable Approximations to MDP Homomorphisms: Equivariance under Actionscited by 61
  20. 2020Learning Invariances in Neural Networkscited by 52
  21. 2020Trajectory Prediction using Equivariant Continuous Convolutioncited by 26
  22. 2021Reasoning-Modulated Representationscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 6; 2023: 18; 2024: 10; 2025: 9; 2026: 11.

54 papers.

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  1. 2023A Cookbook of Self-Supervised Learningcited by 248
  2. 2023GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformerscited by 75
  3. 2024Learning and Leveraging World Models in Visual Representation Learningcited by 71
  4. 2023Invariant Slot Attention: Object Discovery with Slot-Centric Reference Framescited by 51
  5. 2023Self-supervised learning of Split Invariant Equivariant representationscited by 41
  6. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
  7. 2023Latent Space Symmetry Discoverycited by 29
  8. 2022Continuous MDP Homomorphisms and Homomorphic Policy Gradientcited by 24
  9. 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
  10. 2022Equivariant Representation Learning via Class-Pose Decompositioncited by 17
  11. 2023Image to Sphere: Learning Equivariant Features for Efficient Pose Predictioncited by 17
  12. 2023One-shot Imitation Learning via Interaction Warpingcited by 16
38 more
  1. 2023Neurosymbolic Grounding for Compositional World Modelscited by 14
  2. 2023Neural Fourier Transform: A General Approach to Equivariant Representation Learningcited by 12
  3. 2025Four Principles for Physically Interpretable World Modelscited by 10
  4. 2026OneVision-Encoder: Codec-Aligned Sparsity as a Foundational Principle for Multimodal Intelligencecited by 10
  5. 2024Approximate Equivariance in Reinforcement Learningcited by 9
  6. 2023Policy Gradient Methods in the Presence of Symmetries and State Abstractionscited by 8
  7. 2024Pose-Aware Self-Supervised Learning with Viewpoint Trajectory Regularizationcited by 7
  8. 2024Collapse-Proof Non-Contrastive Self-Supervised Learningcited by 7
  9. 2024Understanding the Role of Equivariance in Self-supervised Learningcited by 7
  10. 2025seq-JEPA: Autoregressive Predictive Learning of Invariant-Equivariant World Modelscited by 7
  11. 2022Integrating Symmetry into Differentiable Planning with Steerable Convolutionscited by 6
  12. 2023Equivariant Single View Pose Prediction Via Induced and Restricted Representationscited by 6
  13. 2023E(2)-Equivariant Graph Planning for Navigationcited by 6
  14. 2024Affine steerers for structured keypoint descriptioncited by 6
  15. 2026Flow Equivariant World Models: Memory for Partially Observed Dynamic Environmentscited by 6
  16. 2024In-Context Symmetries: Self-Supervised Learning through Contextual World Modelscited by 5
  17. 2023Topological Obstructions and How to Avoid Themcited by 4
  18. 2024Equivariant Action Sampling for Reinforcement Learning and Planningcited by 4
  19. 2022Image to Icosahedral Projection for SO(3) Object Reasoning from Single-View Imagescited by 3
  20. 2023Equivariant MuZerocited by 3
  21. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  22. 2023Algebras of actions in an agent's representations of the worldcited by 2
  23. 2024Capsule Network Projectors are Equivariant and Invariant Learnerscited by 2
  24. 2025MatrixNet: Learning over symmetry groups using learned group representationscited by 2
  25. 2025Learning Equivariant Functions via Quadratic Formscited by 2
  26. 2025Equivariance by Contrast: Identifiable Equivariant Embeddings from Unlabeled Finite Group Actionscited by 2
  27. 2023Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?cited by 1
  28. 2024Contrastive Learning Via Equivariant Representationcited by 1
  29. 2025Self-Supervised Learning Based on Transformed Image Reconstruction for Equivariance-Coherent Feature Representationcited by 1
  30. 2025Learning Abstract World Models with a Group-Structured Latent Spacecited by 1
  31. 2026Self-Supervised Learning from Structural Invariancecited by 1
  32. 2026Soft Equivariance Regularization for Invariant Self-Supervised Learningcited by 1
  33. 2026Equivariant Multi-agent Reinforcement Learning for Multimodal Vehicle-to-Infrastructure Systemscited by 1
  34. 2023Equivariant Representation Learning in the Presence of Stabilizerscited by 0
  35. 2023Learning Geometric Representations of Objects via Interactioncited by 0
  36. 2025EquiCaps: Predictor-Free Pose-Aware Pre-Trained Capsule Networkscited by 0
  37. 2026Geometric Priors for Generalizable World Models via Vector Symbolic Architecturecited by 0
  38. 2026Disentangled Representation Learning through Unsupervised Symmetry Group Discoverycited by 0

50 most cited of 54 All 54 (JSON)

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  1. 2025Improving Equivariant Networks with Probabilistic Symmetry Breaking
  2. 2025Training Dynamics of Learning 3D-Rotational Equivariance
  3. 2026Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group
  4. 2025Symmetry-Aware Generative Modeling through Learned Canonicalization
  5. 2026Preserving Continuous Symmetry in Discrete Spaces: Geometric-Aware Quantization for SO(3)-Equivariant GNNs
  6. 2026Balancing Symmetry and Efficiency in Graph Flow Matching
  7. 2025A Practical Guide for Incorporating Symmetry in Diffusion Policy
  8. 2024Learning on LoRAs: GL-Equivariant Processing of Low-Rank Weight Spaces for Large Finetuned Models