mlsanityData to 7 Oct 2026

Commutative Lie Group VAE for Disentanglement Learning

arXiv 2106.03375 ↗First posted 7 Jun 2021cs.LG cs.CVcited by 27

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Abstract (arXiv)

We view disentanglement learning as discovering an underlying structure that equivariantly reflects the factorized variations shown in data. Traditionally, such a structure is fixed to be a vector space with data variations represented by translations along individual latent dimensions. We argue this simple structure is suboptimal since it requires the model to learn to discard the properties (e.g. different scales of changes, different levels of abstractness) of data variations, which is an extra work than equivariance learning. Instead, we propose to encode the data variations with groups, a structure not only can equivariantly represent variations, but can also be adaptively optimized to preserve the properties of data variations. Considering it is hard to conduct training on group structures, we focus on Lie groups and adopt a parameterization using Lie algebra. Based on the parameterization, some disentanglement learning constraints are naturally derived. A simple model named Commutative Lie Group VAE is introduced to realize the group-based disentanglement learning. Experiments show that our model can effectively learn disentangled representations without supervision, and can achieve state-of-the-art performance without extra constraints.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). Builds on 36 of its 53 references that are in the map. First posted on arXiv 7 Jun 2021.

Builds on

36 of 53 references.

References · 36

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
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  3. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  4. 2016Group Equivariant Convolutional Networkscited by 1,154
  5. 2016InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Netscited by 858
  6. 2018Disentangling by Factorisingcited by 614
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  8. 2014Semi-Supervised Learning with Deep Generative Modelscited by 494
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  10. 2018Towards a Definition of Disentangled Representationscited by 294
  11. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  12. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
24 more
  1. 2017Variational Inference of Disentangled Latent Concepts from Unlabeled Observationscited by 240
  2. 2015Deep Convolutional Inverse Graphics Networkcited by 121
  3. 2017Fader Networks: Manipulating Images by Sliding Attributescited by 118
  4. 2019Deep Scale-spaces: Equivariance Over Scalecited by 113
  5. 2019Scale-Equivariant Steerable Networkscited by 110
  6. 2019B-Spline CNNs on Lie Groupscited by 97
  7. 2015Attribute2Image: Conditional Image Generation from Visual Attributescited by 93
  8. 2016Exploiting Cyclic Symmetry in Convolutional Neural Networkscited by 91
  9. 2020The Hessian Penalty: A Weak Prior for Unsupervised Disentanglementcited by 90
  10. 2018Learning Disentangled Joint Continuous and Discrete Representationscited by 83
  11. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  12. 2019Theory and Evaluation Metrics for Learning Disentangled Representationscited by 57
  13. 2014Learning the Irreducible Representations of Commutative Lie Groupscited by 41
  14. 2019Symmetry-Based Disentangled Representation Learning requires Interaction with Environmentscited by 35
  15. 2020Progressive Learning and Disentanglement of Hierarchical Representationscited by 30
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  18. 2021Where and What? Examining Interpretable Disentangled Representationscited by 27
  19. 2014Learning to Generate Chairs, Tables and Cars with Convolutional Networkscited by 26
  20. 2019Learning Discrete and Continuous Factors of Data via Alternating Disentanglementcited by 23
  21. 2020Learning Disentangled Representations with Latent Variation Predictabilitycited by 19
  22. 2019InfoGAN-CR and ModelCentrality: Self-supervised Model Training and Selection for Disentangling GANscited by 16
  23. 2020Linear Disentangled Representations and Unsupervised Action Estimationcited by 14
  24. 2020Learning Group Structure and Disentangled Representations of Dynamical Environmentscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 8; 2024: 2; 2025: 8; 2026: 6.

27 papers.

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  1. 2022Disentangled Representation Learningcited by 111
  2. 2022Lost in Latent Space: Disentangled Models and the Challenge of Combinatorial Generalisationcited by 11
  3. 2023VTAE: Variational Transformer Autoencoder with Manifolds Learningcited by 10
  4. 2023Scalable Infomin Learningcited by 8
  5. 2023Learning Lie Group Symmetry Transformations with Neural Networkscited by 6
  6. 2023Topological Obstructions and How to Avoid Themcited by 4
  7. 2024Sequential Representation Learning via Static-Dynamic Conditional Disentanglementcited by 4
  8. 2025Identifying Metric Structures of Deep Latent Variable Modelscited by 3
  9. 2025Learning Conditionally Independent Transformations using Normal Subgroups in Group Theorycited by 3
  10. 2023Algebras of actions in an agent's representations of the worldcited by 2
  11. 2024CFASL: Composite Factor-Aligned Symmetry Learning for Disentanglement in Variational AutoEncodercited by 2
  12. 2023Concept-free Causal Disentanglement with Variational Graph Auto-Encodercited by 1
15 more
  1. 2025DiViD: Disentangled Video Diffusion for Static-Dynamic Factorizationcited by 1
  2. 2025Disentangled Representation Learning via Modular Compositional Biascited by 1
  3. 2026Discovering Data Manifold Geometry through Geometric Propertiescited by 1
  4. 2026Refining the Information Bottleneck via Adversarial Information Separationcited by 1
  5. 2026Generative Modeling in Protein Design: Neural Representations, Conditional Generation, and Evaluation Standardscited by 1
  6. 2022ContraFeat: Contrasting Deep Features for Semantic Discoverycited by 0
  7. 2023ProtoVAE: Prototypical Networks for Unsupervised Disentanglementcited by 0
  8. 2023Independent Modular Networkscited by 0
  9. 2025Multiple Invertible and Partial-Equivariant Function for Latent Vector Transformation to Enhance Disentanglement in VAEscited by 0
  10. 2025Harmonizing Generalization and Personalization in Ring-topology Decentralized Federated Learningcited by 0
  11. 2025Knowledge Abstraction for Knowledge-based Semantic Communication: A Generative Causality Invariant Approachcited by 0
  12. 2025Causal Representation Learning from Network Datacited by 0
  13. 2026Commutator-Induced Uncertainty in VAEscited by 0
  14. 2026Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiabilitycited by 0
  15. 2026Decafs: Disentangled Conditional adversarial Flowscited by 0