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Paper Citation Record · LEDGER

Singular perturbations and hierarchical learning in two-layer neural networks

As of 8 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 0 inbound Pith citation observations for arXiv:2607.10869.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.10869 v1

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T08:40:30.522134Z

measured 59 of 59 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

59 of 59 outbound references displayed

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  • unresolved59
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8858b799-7a87-4094-a125-53d8d545cfce · outbound

This paper cites Foundations of Computational Mathematics , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Foundations of Computational Mathematics , pages=

Reference 1

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Observation 5b880716-039c-4bc7-b24c-21992126a07d · outbound

This paper cites 2012 , publisher=.

Singular perturbations and hierarchical learning in two-layer neural networks 2012 , publisher=

Reference 2

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Observation cc5fec36-aeb4-4788-8ab0-d20621f63b28 · outbound

This paper cites Conference on Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference on Learning Theory , pages=

Reference 3

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Observation dad49925-7904-4963-adad-aa304b1912fe · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 4

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Observation 9d932f74-aa1e-4223-9f01-f4869d00896e · outbound

This paper cites 2017 , publisher=.

Singular perturbations and hierarchical learning in two-layer neural networks 2017 , publisher=

Reference 5

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Observation 1f594673-303b-4e7d-8ef9-dd7c46f7d635 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 6

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Observation be88231a-7988-4b88-ae07-bf916218090e · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 7

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Observation 33435898-43f5-4524-bfed-9533a19f4d82 · outbound

This paper cites Proceedings of the National Academy of Sciences , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Proceedings of the National Academy of Sciences , volume=

Reference 8

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Observation 2d4f3a4f-6f9d-42e6-92f6-f001bcb57620 · outbound

This paper cites Communications on Pure and Applied Mathematics , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Communications on Pure and Applied Mathematics , volume=

Reference 9

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Observation ec496c80-ebf8-4157-976f-546b27b1b7de · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 10

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Observation b0c7212a-977d-46b5-8712-d600acdeae87 · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 11

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Observation 2813dc10-53b6-4d41-8be8-c6d9c69f1fbf · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 12

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Observation dd0b971a-3e0e-41ee-8d76-6a3d0a297ada · outbound

This paper cites Conference on learning theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference on learning theory , pages=

Reference 13

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Observation 69257465-2a0b-41f6-a45c-ce71cae5f61f · outbound

This paper cites Mathematical Programming , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Mathematical Programming , volume=

Reference 14

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Observation 3b456018-5165-4729-99ed-58c88e69def6 · outbound

This paper cites Journal of Physics A: Mathematical and general , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Physics A: Mathematical and general , volume=

Reference 15

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Observation 2c8ea12a-cc23-4e89-ab5f-5e241515f05e · outbound

This paper cites Physical Review Letters , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Physical Review Letters , volume=

Reference 16

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Observation 1e43cba6-0283-41ee-8a7a-b998e09f8507 · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 17

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Observation 34673fb9-5987-4ab6-9b0a-38b0f0832434 · outbound

This paper cites Journal of Machine Learning Research , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Machine Learning Research , volume=

Reference 18

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Observation 1656baf1-b30c-479e-a3ee-e51d82ac0730 · outbound

This paper cites Conference on Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference on Learning Theory , pages=

Reference 19

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Observation d0ebc6ae-7365-4347-85c4-a706d32904b3 · outbound

This paper cites The Thirty Sixth Annual Conference on Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks The Thirty Sixth Annual Conference on Learning Theory , pages=

Reference 20

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Observation 5b22f58a-22cd-46cc-ae35-9ada9321020b · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 21

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Observation 563c53dc-0815-4dca-a231-b11254c896e9 · outbound

This paper cites Communications on Pure and Applied Mathematics , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Communications on Pure and Applied Mathematics , volume=

Reference 22

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Observation e55b374b-647f-4c12-9481-44dcbae829ba · outbound

This paper cites Journal of Machine Learning Research , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Machine Learning Research , volume=

Reference 23

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Observation c245bf3f-efc2-4ef5-a670-9102a23d85ad · outbound

This paper cites International Conference on Machine Learning , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks International Conference on Machine Learning , pages=

Reference 24

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Observation 477fc642-d4f7-48f1-b350-a12e049e307b · outbound

This paper cites International Conference on Learning Representations , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks International Conference on Learning Representations , volume=

Reference 25

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Observation 90eead14-4ea5-4a3e-b5f4-2116b4188ea0 · outbound

This paper cites International Conference on Learning Representations , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks International Conference on Learning Representations , volume=

Reference 26

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Observation e36a0348-3603-49c7-b23c-00aa4632d280 · outbound

This paper cites Communications on Pure and Applied Mathematics , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Communications on Pure and Applied Mathematics , volume=

Reference 27

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Observation df8efbb2-3846-4868-8048-1bce46d2dbe1 · outbound

This paper cites Conference on Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference on Learning Theory , pages=

Reference 28

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Observation f70fab69-a2ba-4c7f-ba57-80e2dc721e02 · outbound

This paper cites Journal of Statistical Mechanics: Theory and Experiment , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Statistical Mechanics: Theory and Experiment , volume=

Reference 29

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Observation 724154f5-af20-480c-8767-766401a721d2 · outbound

This paper cites Journal of Machine Learning Research , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Machine Learning Research , volume=

Reference 30

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Observation 21dc30f9-95ac-45ed-a6fb-50c6592bf95a · outbound

This paper cites Journal of Machine Learning Research , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Machine Learning Research , volume=

Reference 31

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Observation 89feaad8-ecdb-459d-8973-e4e00d026582 · outbound

This paper cites Joint Learning in the Gaussian Single Index Model.

Singular perturbations and hierarchical learning in two-layer neural networks Joint Learning in the Gaussian Single Index Model

Reference 32

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Observation 9e8b1685-46fd-4889-9b38-e9aeddb4da7b · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 33

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Observation 2dd894e1-c01f-49f8-a285-f1f9f2ffe158 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 34

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Observation 690de0dd-deca-4d7d-81ce-2ce228ecab0f · outbound

This paper cites 2012 , publisher=.

Singular perturbations and hierarchical learning in two-layer neural networks 2012 , publisher=

Reference 35

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no resolver link, observed 2026-07-14T08:40:30.522134Z

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Observation 455241bb-dcb9-45bf-980a-e4fa4313bb62 · outbound

This paper cites 2023 , publisher=.

Singular perturbations and hierarchical learning in two-layer neural networks 2023 , publisher=

Reference 36

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no resolver link, observed 2026-07-14T08:40:30.522134Z

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Observation 47d52b2a-ed87-4300-a9d5-3545a79603eb · outbound

This paper cites Conference On Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference On Learning Theory , pages=

Reference 37

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Observation d2de4701-9e4c-4d10-8548-f03e263ecad4 · outbound

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Singular perturbations and hierarchical learning in two-layer neural networks The Annals of Probability , volume=

Reference 38

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Observation 9d3f637f-cd4c-4c98-a602-1bf2792793d1 · outbound

This paper cites Advances in neural information processing systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in neural information processing systems , volume=

Reference 39

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Observation 44c2c27a-476c-4773-a053-408539e06876 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 40

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Observation d2b097f5-aad3-4f60-accb-9122874e2e04 · outbound

This paper cites International conference on machine learning , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks International conference on machine learning , pages=

Reference 41

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:940ffefd499c33b0c71e8d47d77fac54fc01bce14b1cfeedfaee1d85d707dc7c

Observation d0128455-979b-4e7e-9591-8664699d8546 · outbound

This paper cites International conference on machine learning , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks International conference on machine learning , pages=

Reference 42

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:0665c0bf00e697ca9b48e7cfb7a21b88deb99843f6a59c8d7d98718da32de4d8

Observation f23c0d6f-e234-421c-9a35-a90a4c1655ba · outbound

This paper cites Conference on Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference on Learning Theory , pages=

Reference 43

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:9352f53d3fce30e5643bd0bbe5895a7480d1392ffe13df96c6203dacc2e63134

Observation 11648ba9-5311-415b-93d4-2fef77e0ba02 · outbound

This paper cites , author=.

Singular perturbations and hierarchical learning in two-layer neural networks , author=

Reference 44

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unresolved
no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:69d206b92ca7944baf939a42ed48a6b71b13d05c2e85bdc5694d0cd0356d5ad1

Observation d3655903-a23b-4890-b384-a902796e6079 · outbound

This paper cites Conference on learning theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference on learning theory , pages=

Reference 45

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:2c154c2159edff0e177842858a4f492e7f3d4c2e54cc46bfae5e9522acc57cdc

Observation a7eb0b4a-c0b9-411a-a295-ebf287e64893 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 46

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:48c32f0631b2bfd2d3369c9522b42e46d0ec6919d1746c3d03469ca89356b0b1

Observation f4f8c725-24ad-428e-acac-3d773b75ab3b · outbound

This paper cites The Thirty Sixth Annual Conference on Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks The Thirty Sixth Annual Conference on Learning Theory , pages=

Reference 47

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:b5919e84b31332c77c332b678c877fba28fd8c4b7f22b4807d8af0743fe1e21c

Observation cb3fdb8b-d009-4e40-8906-3fe3a00384c0 · outbound

This paper cites On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime.

Singular perturbations and hierarchical learning in two-layer neural networks On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime

Reference 48

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:ed7bcca91a7d7a4892fc6e6f3255d2b362a4dce51805a7941ef1e521468314b3

Observation c3f90e9a-d6fa-49e3-8182-caaee3e961ed · outbound

This paper cites Proceedings of Machine Learning Research vol , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Proceedings of Machine Learning Research vol , volume=

Reference 49

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:e30acf8299c9578c7b4168056aa05bc29c2ec6fd2dd44b9bc744610860f306ec

Observation dde06c81-de9c-447b-95ac-f2adca7593b2 · outbound

This paper cites Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks.

Singular perturbations and hierarchical learning in two-layer neural networks Uniform-in-Time Weak Propagation-of-Chaos in Shallow Neural Networks

Reference 50

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:ac7880dd0dfb9a858f24a840e0b1d3480486374fbbda66d6be917b14ac029e9d

Observation 2bfdbfe2-491d-44d2-bdb5-2058e4af5b72 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 51

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:fcdaeda23d3e788fb62f7fca28e1180c7b74dfb4e4aa4546044c7c0348033610

Observation 8eb243db-87d9-4abf-829e-56e0c4f9a5ce · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Advances in Neural Information Processing Systems , volume=

Reference 52

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:62bc0fb766dc43768f16a951aeaf85f70fa7c548e37f1ed682a22cf74a6e5a6a

Observation 78d7d6e1-5526-4ae1-832c-e1a4cc4570af · outbound

This paper cites Journal of Machine Learning Research , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Journal of Machine Learning Research , volume=

Reference 53

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:2f781d3b9a5b4335656c1ff5e76a128b5d81d24f96feee324b24fc9805d928b4

Observation 7a24d414-ab52-4427-9919-900dc888a2aa · outbound

This paper cites Proceedings of the International Conference on Learning Represenatations 2014 , year=.

Singular perturbations and hierarchical learning in two-layer neural networks Proceedings of the International Conference on Learning Represenatations 2014 , year=

Reference 54

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:dcba29f6553e0033da21fff3b15831c031e6025a32af7ae86fdf1ee148c431cd

Observation 784de15a-c03b-4197-8571-f18e7530f66d · outbound

This paper cites Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity.

Singular perturbations and hierarchical learning in two-layer neural networks Saddle-to-Saddle Dynamics in Deep Linear Networks: Small Initialization Training, Symmetry, and Sparsity

Reference 55

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:2c302c478828253abf194b227e35b86e9ba0d5aa5c301549509541c4c250864e

Observation 2bc2c870-875a-4715-9cee-39c173b44529 · outbound

This paper cites Systems & Control Letters , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks Systems & Control Letters , volume=

Reference 56

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no resolver link, observed 2026-07-14T08:40:30.522134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:5e76e5e03d5016f930a82594c71aef8e1e957fd6b814d3fa8e298a8daa5daa34

Observation 3037762c-8244-4424-b38f-46c7b44ef002 · outbound

This paper cites an unresolved cited work.

Singular perturbations and hierarchical learning in two-layer neural networks Unresolved cited work

Reference 57

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:4491798b737d22ec2e5c982aadc5f9d083540670ef92072eeaa4711da389dcb3

Observation 13f33fb3-f91b-4128-88d5-9c3411f98bbd · outbound

This paper cites Conference On Learning Theory , pages=.

Singular perturbations and hierarchical learning in two-layer neural networks Conference On Learning Theory , pages=

Reference 58

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:71d627098f07cbaae368b904e28f4d5a1f824ef4507dae1728024fafef0b518b

Observation 396470a4-99d0-47ee-9e23-cc94fb66b740 · outbound

This paper cites SIAM Journal on Optimization , volume=.

Singular perturbations and hierarchical learning in two-layer neural networks SIAM Journal on Optimization , volume=

Reference 59

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:531ddc7adfd75dbeeecaa455ac44f2888a02bfc3e9d28a682d9e47235be81653

Pith citing papers

No inbound Pith citation observations are available.