mlsanityData to 14 Oct 2026

A Category-theoretical Meta-analysis of Definitions of Disentanglement

arXiv 2305.06886 ↗First posted 11 May 2023cs.LG cs.CV math.CTcited by 3

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Abstract (arXiv)

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 25 of its 45 references that are in the map. First posted on arXiv 11 May 2023.

Builds on

25 of 45 references.

References · 25

  1. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  2. 2018Towards a Definition of Disentangled Representationscited by 296
  3. 2017Variational Inference of Disentangled Latent Concepts from Unlabeled Observationscited by 241
  4. 2018Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustnesscited by 108
  5. 2018Learning Deep Disentangled Embeddings with the F-Statistic Losscited by 101
  6. 2020On Disentangled Representations Learned From Correlated Datacited by 94
  7. 2019Weakly Supervised Disentanglement with Guaranteescited by 82
  8. 2020Measuring Disentanglement: A Review of Metricscited by 70
  9. 2020On the Transfer of Disentangled Representations in Realistic Settingscited by 63
  10. 2018Leveraging Unlabeled Data for Crowd Counting by Learning to Rankcited by 57
  11. 2019Theory and Evaluation Metrics for Learning Disentangled Representationscited by 57
  12. 2019A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statisticscited by 56
13 more
  1. 2022Graph Neural Networks are Dynamic Programmerscited by 55
  2. 2021Self-Supervised Learning Disentangled Group Representation as Featurecited by 47
  3. 2019Unsupervised Model Selection for Variational Disentangled Representation Learningcited by 46
  4. 2014Learning the Irreducible Representations of Commutative Lie Groupscited by 41
  5. 2021Category Theory in Machine Learningcited by 36
  6. 2020Natural Graph Networkscited by 35
  7. 2017Disintegration and Bayesian Inversion via String Diagramscited by 32
  8. 2020Progressive Learning and Disentanglement of Hierarchical Representationscited by 30
  9. 2014Transformation Properties of Learned Visual Representationscited by 18
  10. 2021Disentanglement Analysis with Partial Information Decompositioncited by 9
  11. 2019Compositional Deep Learningcited by 7
  12. 2017Knowledge Representation in Bicategories of Relationscited by 4
  13. 2019How to Not Measure Disentanglementcited by 2

Built on by

Cited by year

Citing papers per year: 2023: 1; 2024: 1; 2025: 1.

3 papers.

  1. 2023Enriching Disentanglement: From Logical Definitions to Quantitative Metricscited by 2
  2. 2024Disentangled Representations for Causal Cognitioncited by 0
  3. 2025Disentangling Hyperedges through the Lens of Category Theorycited by 0