Beyond ICA: Identifiability by Symmetry Breaking | Paper Citation Record

Observation baec8086-2ef0-493b-82c7-de72f61cd57f · outbound

This paper cites Properties from mechanisms: An equiv- ariance perspective on identifiable representation learning.

Beyond ICA: Identifiability by Symmetry Breaking Properties from mechanisms: An equiv- ariance perspective on identifiable representation learning

Reference 1

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Observation bc548a77-22a3-4fc6-8719-8da8b6736266 · outbound

This paper cites Allman, Catherine Matias, and John A.

Beyond ICA: Identifiability by Symmetry Breaking Allman, Catherine Matias, and John A

Reference 2

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Observation 408ecee2-4d1c-4f91-ae1f-b9a0d52a9ef5 · outbound

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Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 3

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Observation db43f5bc-b78b-4465-b29e-966345a31696 · outbound

This paper cites Zimmermann, Yash Sharma, Bernhard Schölkopf, Julius von Kügelgen, and Wieland Brendel.

Beyond ICA: Identifiability by Symmetry Breaking Zimmermann, Yash Sharma, Bernhard Schölkopf, Julius von Kügelgen, and Wieland Brendel

Reference 4

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Observation 9ba62667-e993-4774-a482-8b824f12f1c4 · outbound

This paper cites Interaction Asymmetry: A General Principle for Learning Composable Abstractions.

Beyond ICA: Identifiability by Symmetry Breaking Interaction Asymmetry: A General Principle for Learning Composable Abstractions

Reference 5

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Observation d0802129-70df-40df-8c0a-7aa57a725f86 · outbound

This paper cites Function classes for identifiable nonlinear independent component analysis.

Beyond ICA: Identifiability by Symmetry Breaking Function classes for identifiable nonlinear independent component analysis

Reference 6

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Observation cd967344-7680-4943-886f-7178df01008f · outbound

This paper cites Independent component analysis, a new concept?Signal Processing, 36(3): 287–314, 1994.

Beyond ICA: Identifiability by Symmetry Breaking Independent component analysis, a new concept?Signal Processing, 36(3): 287–314, 1994

Reference 7

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Observation 5bec0b45-a2c9-4672-9b03-9feeed313224 · outbound

This paper cites Analyse générale des liaisons stochastiques.

Beyond ICA: Identifiability by Symmetry Breaking Analyse générale des liaisons stochastiques

Reference 8

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Observation 8584a7da-cab8-49bb-8467-369876aad03a · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 9

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Observation b43b4324-1819-4f0e-afcf-76744afe7200 · outbound

This paper cites Eaton.Group Invariance Applications in Statistics, volume 1 ofRegional Conference Series in Probability and Statistics.

Beyond ICA: Identifiability by Symmetry Breaking Eaton.Group Invariance Applications in Statistics, volume 1 ofRegional Conference Series in Probability and Statistics

Reference 10

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Observation 45a90932-767e-43e5-aa2d-6a799bb16f12 · outbound

This paper cites Fisher III.

Beyond ICA: Identifiability by Symmetry Breaking Fisher III

Reference 11

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Observation f38748da-55c9-43aa-acd6-d1952fa76f3a · outbound

This paper cites Giri.Group Invariance in Statistical Inference.

Beyond ICA: Identifiability by Symmetry Breaking Giri.Group Invariance in Statistical Inference

Reference 12

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Observation 8d09e7ec-105b-4453-a3f8-5f41c670b66a · outbound

This paper cites Rubenstein, Arash Mehrjou, Francesco Locatello, and Bernhard Schölkopf.

Beyond ICA: Identifiability by Symmetry Breaking Rubenstein, Arash Mehrjou, Francesco Locatello, and Bernhard Schölkopf

Reference 13

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Observation f0a8b75a-5526-432f-bbbd-e507be694b26 · outbound

This paper cites Independent mechanism analysis, a new concept? InAdvances in Neural Information Processing Systems, 2021.

Beyond ICA: Identifiability by Symmetry Breaking Independent mechanism analysis, a new concept? InAdvances in Neural Information Processing Systems, 2021

Reference 14

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Observation 9b63b55a-b9aa-4cf8-aa36-9df905974600 · outbound

This paper cites Identifiability of models for clusterwise linear regression.Journal of Classification, 17(2):273–296, 2000.

Beyond ICA: Identifiability by Symmetry Breaking Identifiability of models for clusterwise linear regression.Journal of Classification, 17(2):273–296, 2000

Reference 15

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Observation 964e9904-608b-49f0-960d-712e5a1da5f5 · outbound

This paper cites Towards a Definition of Disentangled Representations.

Beyond ICA: Identifiability by Symmetry Breaking Towards a Definition of Disentangled Representations

Reference 16

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Observation 57c31115-b62d-47be-9fe7-e65c58b6fd97 · outbound

This paper cites Generalization of the concept of identification.

Beyond ICA: Identifiability by Symmetry Breaking Generalization of the concept of identification

Reference 17

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Observation 9433e3aa-e7e1-4809-ab91-78ebd88cfbd9 · outbound

This paper cites Unsupervised feature extraction by time-contrastive learning and nonlinear ICA.

Beyond ICA: Identifiability by Symmetry Breaking Unsupervised feature extraction by time-contrastive learning and nonlinear ICA

Reference 18

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Observation 7ab6cc6f-cd36-4d69-ab71-15f5368a0291 · outbound

This paper cites Nonlinear independent component analysis: Existence and uniqueness results.Neural Networks, 12(3):429–439, 1999.

Beyond ICA: Identifiability by Symmetry Breaking Nonlinear independent component analysis: Existence and uniqueness results.Neural Networks, 12(3):429–439, 1999

Reference 19

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Observation 489b47f1-b4b4-40dd-ba80-c59d5f26f09c · outbound

This paper cites Deep neural networks learn non-smooth functions effectively.

Beyond ICA: Identifiability by Symmetry Breaking Deep neural networks learn non-smooth functions effectively

Reference 20

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Observation d9857da2-2bdc-409d-8759-e60f2df05c84 · outbound

This paper cites Kingma, Ricardo P.

Beyond ICA: Identifiability by Symmetry Breaking Kingma, Ricardo P

Reference 21

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Observation 774b74d7-a48d-43e3-bd56-f0011c877bb3 · outbound

This paper cites Identifiability of deep generative models without auxiliary information.

Beyond ICA: Identifiability by Symmetry Breaking Identifiability of deep generative models without auxiliary information

Reference 22

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Observation d8f4d07a-5f65-43b3-bf01-b95b6a3dbf42 · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 23

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Observation 598c3b10-7f50-4823-8cd6-e374a604b08a · outbound

This paper cites Additive decoders for latent variables identification and cartesian-product extrapolation.

Beyond ICA: Identifiability by Symmetry Breaking Additive decoders for latent variables identification and cartesian-product extrapolation

Reference 24

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Observation d1e4c4fb-a5f8-41f7-9f1b-0a86243e1a3d · outbound

This paper cites Linderman, Matthew J.

Beyond ICA: Identifiability by Symmetry Breaking Linderman, Matthew J

Reference 25

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Observation c41debfa-1de4-47cc-bc6c-22115dd438b1 · outbound

This paper cites Challenging common assumptions in the unsupervised learning of disentangled representations.

Beyond ICA: Identifiability by Symmetry Breaking Challenging common assumptions in the unsupervised learning of disentangled representations

Reference 26

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Observation bf44fc0d-1248-4ef5-9898-1d49f863dd3d · outbound

This paper cites Pritchard, and Aviv Regev.

Beyond ICA: Identifiability by Symmetry Breaking Pritchard, and Aviv Regev

Reference 27

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Observation 74324fd4-4666-411b-8328-1d1842a926e3 · outbound

This paper cites Mechanistic Independence: A Principle for Identifiable Disentangled Representations.

Beyond ICA: Identifiability by Symmetry Breaking Mechanistic Independence: A Principle for Identifiable Disentangled Representations

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T03:34:28.898022Z

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Observation 81c69118-9be5-4cb7-b91a-614c4825b004 · outbound

This paper cites Montúfar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio.

Beyond ICA: Identifiability by Symmetry Breaking Montúfar, Razvan Pascanu, Kyunghyun Cho, and Yoshua Bengio

Reference 29

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Observation 5142d3c2-5204-4c43-b8ba-be89ce34c9cd · outbound

This paper cites Juloski, Giancarlo Ferrari-Trecate, and René Vidal.

Beyond ICA: Identifiability by Symmetry Breaking Juloski, Giancarlo Ferrari-Trecate, and René Vidal

Reference 30

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Observation 1fae3618-ef05-4a5f-82f2-b0e6979d12e8 · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 31

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Observation 324d1482-d4a9-4a46-a85d-f7c62e635827 · outbound

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Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 32

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Observation 119287aa-4f76-4615-83df-3898005a2804 · outbound

This paper cites Toward causal representation learning.Proceedings of the IEEE, 109(5):612–634, 2021.

Beyond ICA: Identifiability by Symmetry Breaking Toward causal representation learning.Proceedings of the IEEE, 109(5):612–634, 2021

Reference 33

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Observation 9388049f-58c4-44f9-9282-2d30b3629d13 · outbound

This paper cites Hoyer, Aapo Hyvärinen, and Antti Kerminen.

Beyond ICA: Identifiability by Symmetry Breaking Hoyer, Aapo Hyvärinen, and Antti Kerminen

Reference 34

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Observation 26b08f85-4341-49e8-aba2-cdf1536d8a31 · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 35

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Observation e156ca07-e1a9-4acc-9ce1-4367599f00de · outbound

This paper cites Deformable medical image registration: A survey.IEEE Transactions on Medical Imaging, 32(7):1153–1190, 2013.

Beyond ICA: Identifiability by Symmetry Breaking Deformable medical image registration: A survey.IEEE Transactions on Medical Imaging, 32(7):1153–1190, 2013

Reference 36

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Observation ab5adcc8-db97-48cc-b4ba-82877f8fd844 · outbound

This paper cites Non-rigid registration for two-photon imaging using triangulation and piecewise affine transformation.Neuroscience, 491:86–99, 2022.

Beyond ICA: Identifiability by Symmetry Breaking Non-rigid registration for two-photon imaging using triangulation and piecewise affine transformation.Neuroscience, 491:86–99, 2022

Reference 37

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Observation d114daf4-2dcb-4217-875b-1d5f46acf908 · outbound

This paper cites Identifiability of finite mixtures.Annals of Mathematical Statistics, 34(4): 1265–1269, 1963.

Beyond ICA: Identifiability by Symmetry Breaking Identifiability of finite mixtures.Annals of Mathematical Statistics, 34(4): 1265–1269, 1963

Reference 38

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Observation fe858c5a-14b9-47ba-84ce-cbf433b392ef · outbound

This paper cites Generalized principal component analysis (GPCA).

Beyond ICA: Identifiability by Symmetry Breaking Generalized principal component analysis (GPCA)

Reference 39

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Observation 2cf2aa7c-404f-4e0e-b868-4391e4df8e81 · outbound

This paper cites $\beta$-intact-V AE: Identifying and estimating causal effects under limited overlap.

Beyond ICA: Identifiability by Symmetry Breaking $\beta$-intact-V AE: Identifying and estimating causal effects under limited overlap

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-01T03:34:29.812485Z

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Observation 03598a21-30c0-4335-842a-654382e7d300 · outbound

This paper cites Indeterminacy in generative models: Characterization and strong identifiability.

Beyond ICA: Identifiability by Symmetry Breaking Indeterminacy in generative models: Characterization and strong identifiability

Reference 41

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Observation 4bf3f4e2-cdf5-4448-a47b-7a346d065b5d · outbound

This paper cites Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing.

Beyond ICA: Identifiability by Symmetry Breaking Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing

Reference 42

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Observation 89735c92-bc6d-4731-92f8-d9e2a6bdd061 · outbound

This paper cites Yakowitz and John D.

Beyond ICA: Identifiability by Symmetry Breaking Yakowitz and John D

Reference 43

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Observation 43192fe9-6436-4eb0-a7f9-b4693b1d2a1b · outbound

This paper cites in particular.

Beyond ICA: Identifiability by Symmetry Breaking in particular

Reference 44

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Observation 8a66dac1-70e2-4183-ba8c-96e4819b376a · outbound

This paper cites almost arbitrary support.

Beyond ICA: Identifiability by Symmetry Breaking almost arbitrary support

Reference 46

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Observation 1af6870d-cdd2-4634-91bb-a35242d968b6 · outbound

This paper cites 2) n/a× (multi-env.

Beyond ICA: Identifiability by Symmetry Breaking 2) n/a× (multi-env

Reference 47

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Observation 5d015e89-57c5-4dd6-a774-7bcac470dd0f · outbound

This paper cites hidden duplicate parameter in a different branch.

Beyond ICA: Identifiability by Symmetry Breaking hidden duplicate parameter in a different branch

Reference 48

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Observation 77ffad6a-eb59-45e8-8233-cc9f261826fe · outbound

This paper cites But the reflection T(x) =−x+ (µ 1 +µ 2) swaps the two components; with equal weights, T♯p=p , so (MST) fails.

Beyond ICA: Identifiability by Symmetry Breaking But the reflection T(x) =−x+ (µ 1 +µ 2) swaps the two components; with equal weights, T♯p=p , so (MST) fails

Reference 49

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Observation e6d1ea97-e5c6-424e-9d46-966c978cb9d0 · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 50

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Observation 0a42de78-e6e7-46c6-a38e-ca3ac09becb0 · outbound

This paper cites ,det ΣK are pairwise distinct, any affine symmetry inducesσ= id, again reducing (MST) to (JST).

Beyond ICA: Identifiability by Symmetry Breaking ,det ΣK are pairwise distinct, any affine symmetry inducesσ= id, again reducing (MST) to (JST)

Reference 51

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Observation 2c22fd59-69bf-4353-97ca-6c590c990bd3 · outbound

This paper cites distinct det(Σ) + 2-component generic position.

Beyond ICA: Identifiability by Symmetry Breaking distinct det(Σ) + 2-component generic position

Reference 52

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Observation 29d78a75-fb97-40e5-8478-0f0fdccaa1c5 · outbound

This paper cites 4) forbid component-swapping, and no single reflection fixes both components individually.

Beyond ICA: Identifiability by Symmetry Breaking 4) forbid component-swapping, and no single reflection fixes both components individually

Reference 53

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Observation 8ca1920f-afe8-4a43-93ef-e55c1da0d560 · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 54

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Observation b9fc6d36-21de-4b49-a2b6-098052244009 · outbound

This paper cites 4) forbid component-swapping, and neither α(x) =x+2 nor α(x) =−x+2 is consistent across both components simultaneously.

Beyond ICA: Identifiability by Symmetry Breaking 4) forbid component-swapping, and neither α(x) =x+2 nor α(x) =−x+2 is consistent across both components simultaneously

Reference 55

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Observation b08f6d17-0d1d-4cd8-b516-d7d45d3a190a · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 56

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Observation 19d245d5-3719-4a0e-8ce1-e2f372cff5ca · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 57

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Observation dc2ac08c-31b1-4bd0-a13f-c49f99135fea · outbound

This paper cites weakly-injective tail attached to a co-toggling core.

Beyond ICA: Identifiability by Symmetry Breaking weakly-injective tail attached to a co-toggling core

Reference 58

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Observation 31b501e2-c246-43f6-92c5-b65669a10485 · outbound

This paper cites an unresolved cited work.

Beyond ICA: Identifiability by Symmetry Breaking Unresolved cited work

Reference 2006

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