mlsanityData to 14 Oct 2026

Mechanistic Independence: A Principle for Identifiable Disentangled Representations

arXiv 2509.22196 ↗First posted 26 Sep 2025cs.LG stat.MLcited by 3

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Abstract (arXiv)

Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through mechanistic independence, which characterizes latent factors by how they act on observed variables rather than by their latent distribution. This perspective is invariant to changes of the latent density, even when such changes induce statistical dependencies among factors. Within this framework, we propose several related independence criteria -- ranging from support-based and sparsity-based to higher-order conditions -- and show that each yields identifiability of latent subspaces, even under nonlinear, non-invertible mixing. We further establish a hierarchy among these criteria and provide a graph-theoretic characterization of latent subspaces as connected components. Together, these results clarify the conditions under which disentangled representations can be identified without relying on statistical assumptions.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 41 of its 61 references that are in the map. First posted on arXiv 26 Sep 2025.

Builds on

41 of 61 references.

References · 41

  1. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 941
  2. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 503
  3. 2021Self-Supervised Learning with Data Augmentations Provably Isolates Content from Stylecited by 312
  4. 2018Towards a Definition of Disentangled Representationscited by 296
  5. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 282
  6. 2020Inductive Biases for Deep Learning of Higher-Level Cognitioncited by 275
  7. 2016Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICAcited by 273
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  9. 2020On the Binding Problem in Artificial Neural Networkscited by 233
  10. 2021Contrastive Learning Inverts the Data Generating Processcited by 221
  11. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  12. 2022Interventional Causal Representation Learningcited by 142
29 more
  1. 2022Weakly supervised causal representation learningcited by 140
  2. 2020Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Codingcited by 122
  3. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
  4. 2021Independent mechanism analysis, a new concept?cited by 97
  5. 2019The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICAcited by 86
  6. 2022On the Identifiability of Nonlinear ICA: Sparsity and Beyondcited by 85
  7. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  8. 2023Multi-View Causal Representation Learning with Partial Observabilitycited by 74
  9. 2022Identifiability of deep generative models without auxiliary informationcited by 70
  10. 2022Weakly Supervised Representation Learning with Sparse Perturbationscited by 65
  11. 2023Identifiability Results for Multimodal Contrastive Learningcited by 61
  12. 2023Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolationcited by 58
  13. 2021Identifiable Deep Generative Models via Sparse Decodingcited by 54
  14. 2019FSPool: Learning Set Representations with Featurewise Sort Poolingcited by 53
  15. 2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
  16. 2023Provably Learning Object-Centric Representationscited by 45
  17. 2024Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependenciescited by 41
  18. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  19. 2023Generalizing Nonlinear ICA Beyond Structural Sparsitycited by 34
  20. 2022Partial Disentanglement via Mechanism Sparsitycited by 29
  21. 2022Embrace the Gap: VAEs Perform Independent Mechanism Analysiscited by 28
  22. 2023Object-centric architectures enable efficient causal representation learningcited by 21
  23. 2021Learning disentangled representations via product manifold projectioncited by 20
  24. 2024Interaction Asymmetry: A General Principle for Learning Composable Abstractionscited by 20
  25. 2021Local Disentanglement in Variational Auto-Encoders Using Jacobian L1 Regularizationcited by 17
  26. 2023Towards a Unified Framework of Contrastive Learning for Disentangled Representationscited by 13
  27. 2021Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencodercited by 7
  28. 2023Independent Mechanism Analysis and the Manifold Hypothesiscited by 7
  29. 2023The Responsibility Problem in Neural Networks with Unordered Targetscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Content-Style Identification via Differential Independencecited by 2
  2. 2026Disentanglement Beyond Generative Models with Riemannian ICAcited by 0
  3. 2026Beyond ICA: Identifiability by Symmetry Breakingcited by 0