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Paper Citation Record · LEDGER

Singular perturbations and hierarchical learning in two-layer neural networks

As of 7 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 2026-08-07T06:34:17.273281+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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  • verified fuzzy0
  • 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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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:6cb7eb4f78b9c4beb1e989e283bd82508a06803e6994f707109a8ef8f77293c0

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

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

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

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

This paper cites The Annals of Probability , volume=.

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

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

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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=sha256:05f2a44e28ad25631939da208b944ed2261f177dbd23437c9cd949954d56b926

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

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:7ccad40ec910997278f89469f4ba29ccd89498b53fd14f1431dac107ee11faa1

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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Source-reported events for the cited work

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:d8427d9833ce8d90f9fe5d7e5e944848f80d947c343d577a97ff698ff80c42be

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

Source-reported events for the cited work

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:0f538ea14cc583d406f242da365b12215ea6b856073d4f518b2e5fb69b8b69ed

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=sha256:997a0fc57e793c78a2f62a76fddec61abb472d160f2dd41d247ce54580b662c9

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:e0567217082e6d5e396c8a8897a2221e7db7c68e753a94d4a7035acd4966fe2b

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=sha256:44eae6887305bc8819a6fd2554d565663760047ea2a8d3ca8f10694dbfa32ebe

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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Source-reported events for the cited work

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:c6ebdcd16d71ccc2e697816031dd15e4172c82e9bed8de906eb76d09d10d2a39

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

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:20a656b34389d39ceb4c117a37571d04aa89704a99fec6e0fb4b4334eef70060

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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Source-reported events for the cited work

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:4639f4a27a1950a85d713d8e39ad3b05433345968918ca323ba630559d14d14c

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

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source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:bf9b72672f41e160bd1353becdc7873270ca99354d57ffac4eb192a062dac680

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=sha256:910f7711798646fcb39c1c5725be7ee32f3fe39d8a0197a278f50de1b7fef7e6

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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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-07-14T08:40:30.522134Z digest=sha256:c353ef98384e09b2cdd4eaee8dfe800ea0fab4f92887f0927afb773f98debabf

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:f43760d30ee2723690d4beb47b793242299c21f91c4b77769ba9086559a76cee

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=sha256:8f4bfda7410680c46251200f5bc95b4d83c078f15dcd299dd5825e4daf553849

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:ab2edccb0e34c39e8428a7b67d35673a7e47769a1b4161dd0532a12a9af1e06b

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=sha256:2394da4ff68250f6fba499170fa5d007791241114e30712ee0bcbe43cf37d5cb

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=sha256:3e312cab0dfe45c9472c9847ac5d19d47dd6510cb31ada4c983d8654beb8812e

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=sha256:68f84463dd3b664c11b7a00e9788fd26d6cbb06f7366fa20cb24e58edae02add

Pith citing papers

No inbound Pith citation observations are available.