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Paper Citation Record · LEDGER

Sharp uniform approximation for spectral Barron functions by deep neural networks

As of 17 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 1 inbound Pith citation observation for arXiv:2507.06789.

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

pith.paper-citation-record.v1
2507.06789 v1

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:17:36.782108Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:17:36.123343Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T17:17:36.227485Z

Reference resolution

44 of 44 outbound references displayed

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External citation measurements

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Outbound references

Observation cf75b80b-aec8-461a-845b-c227c40b7465 · outbound

This paper cites an unresolved cited work.

Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 1

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Observation 48d6c307-4b75-4063-9786-99c9b4b72d33 · outbound

This paper cites Artin, The Gamma function , Athena Series: Selected Topics in Mathematics, Holt, Rine - hart and Winston, 1964.

Sharp uniform approximation for spectral Barron functions by deep neural networks Artin, The Gamma function , Athena Series: Selected Topics in Mathematics, Holt, Rine - hart and Winston, 1964

Reference 2

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Observation c6c5438b-5592-41d0-8024-1c7a89ea1273 · outbound

This paper cites Bach, Breaking the curse of dimensionality with convex neutral ne tworks, J.

Sharp uniform approximation for spectral Barron functions by deep neural networks Bach, Breaking the curse of dimensionality with convex neutral ne tworks, J

Reference 3

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Observation e7aa6015-4c4a-49cc-b562-b77daef27d89 · outbound

This paper cites Ball, Cube slicing in Rn, Proc.

Sharp uniform approximation for spectral Barron functions by deep neural networks Ball, Cube slicing in Rn, Proc

Reference 4

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 5

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 7

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Observation 4044d19d-e249-4369-a0e3-345d06b2096f · outbound

This paper cites Bresler and D.

Sharp uniform approximation for spectral Barron functions by deep neural networks Bresler and D

Reference 8

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Observation ad63f07e-11eb-4c99-8438-6cfcca38f58c · outbound

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 9

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Observation d364d902-04dd-4062-8d88-3b7810ada0ea · outbound

This paper cites Caragea, P.

Sharp uniform approximation for spectral Barron functions by deep neural networks Caragea, P

Reference 10

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This paper cites DeVore, B.

Sharp uniform approximation for spectral Barron functions by deep neural networks DeVore, B

Reference 11

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 12

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 13

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Observation be06491b-f31a-469f-bd42-126be223ab27 · outbound

This paper cites Elbr¨ achter, D.

Sharp uniform approximation for spectral Barron functions by deep neural networks Elbr¨ achter, D

Reference 14

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This paper cites Eldan and O.

Sharp uniform approximation for spectral Barron functions by deep neural networks Eldan and O

Reference 15

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This paper cites Haagerup, The best constants in the Khintchine inequality , Studia Math.

Sharp uniform approximation for spectral Barron functions by deep neural networks Haagerup, The best constants in the Khintchine inequality , Studia Math

Reference 16

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Observation fff94a92-4827-45c4-826c-5a7172196506 · outbound

This paper cites H¨ ormander, Linear partial differential operators , Grundlehren der mathematischen Wis- senschaften, vol.

Sharp uniform approximation for spectral Barron functions by deep neural networks H¨ ormander, Linear partial differential operators , Grundlehren der mathematischen Wis- senschaften, vol

Reference 17

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 18

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 19

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Observation f0e42f12-7023-42ba-b974-e6ab81677007 · outbound

This paper cites Spectral Barron space for deep neural network approximation.

Sharp uniform approximation for spectral Barron functions by deep neural networks Spectral Barron space for deep neural network approximation

Reference 20

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

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Sharp uniform approximation for spectral Barron functions by deep neural networks Makovoz, Random approximants and neural networks , J

Reference 24

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Sharp uniform approximation for spectral Barron functions by deep neural networks Meng and P

Reference 25

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

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Sharp uniform approximation for spectral Barron functions by deep neural networks Montanelli and Q

Reference 27

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Sharp uniform approximation for spectral Barron functions by deep neural networks Montanelli, H

Reference 28

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Sharp uniform approximation for spectral Barron functions by deep neural networks Pilipovi´ c, N

Reference 29

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Sharp uniform approximation for spectral Barron functions by deep neural networks Pinkus, Approximation theory of the MLP model in neural networks , Acta Numer

Reference 30

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This paper cites Rebeschini, Lecture notes in algorithmic foundations of learning: Cove ring numbers bounds for Rademacher complexity.

Sharp uniform approximation for spectral Barron functions by deep neural networks Rebeschini, Lecture notes in algorithmic foundations of learning: Cove ring numbers bounds for Rademacher complexity

Reference 31

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Sharp uniform approximation for spectral Barron functions by deep neural networks Safran, R

Reference 32

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 33

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Sharp uniform approximation for spectral Barron functions by deep neural networks Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks

Reference 34

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 35

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 36

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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 37

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f55ca2b0-5a85-4a80-8812-2e0d1e03e7bf · outbound

This paper cites an unresolved cited work.

Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:17:36.992809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.744343Z digest=sha256:1982429fbbac3876335f2e33568bd486a1afb2234f123b56286c0a044a4475df

Observation a6b55249-e22c-4715-95b5-cbf993e74303 · outbound

This paper cites Telgarsky, Benefits of depth in neural networks , Proceedings of Machine Learning Re- search 49 (2016), 1517–1539.

Sharp uniform approximation for spectral Barron functions by deep neural networks Telgarsky, Benefits of depth in neural networks , Proceedings of Machine Learning Re- search 49 (2016), 1517–1539

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:17:36.974139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.748966Z digest=sha256:da7e6be36d77792adfbecaf09148b3306d1e778f0c47aaa60ebd8d3ddd853222

Observation ea8023e6-095a-4462-8b92-cbb4048cb6da · outbound

This paper cites Tsuji and T.

Sharp uniform approximation for spectral Barron functions by deep neural networks Tsuji and T

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:17:36.955962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.753681Z digest=sha256:48f251c688417a3a6d0ba996c94426ffa305693eeb371dcca410ee56f36339b1

Observation 5743ea47-976e-49b2-b06e-7fd512e5055c · outbound

This paper cites Xu, Finite neuron method and convergence analysis , Commun.

Sharp uniform approximation for spectral Barron functions by deep neural networks Xu, Finite neuron method and convergence analysis , Commun

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:17:36.937672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.760610Z digest=sha256:b9dc22cc9576ea0d02cbf0fcb6d40b2d6bdca2e95dbbccaee47a2ae4900892c7

Observation e84e979d-6496-49d7-9f0a-efbc94057d8d · outbound

This paper cites Yarotsky, Error bounds for approximations with deep ReLU networks , Neural networks 94 (2017), 103–114.

Sharp uniform approximation for spectral Barron functions by deep neural networks Yarotsky, Error bounds for approximations with deep ReLU networks , Neural networks 94 (2017), 103–114

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:17:36.920250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.766032Z digest=sha256:5f3765c8e6546196862e4fe597a6ee45cdcb5ca7ac06b255b6b3bbb2f123e316

Observation 3f0b742b-16d6-4b39-94da-2eacb5b1375d · outbound

This paper cites an unresolved cited work.

Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:17:36.903376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.771795Z digest=sha256:33b4ccb254cb1d3b6692b2e00df6c95282b5a341a7d5772d9410d0f0d7307ea3

Observation 0f1f0435-7fbe-47ae-b1bd-c8275c09336d · outbound

This paper cites Yarotsky and A.

Sharp uniform approximation for spectral Barron functions by deep neural networks Yarotsky and A

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T19:17:36.887321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.777043Z digest=sha256:34cbd32b09c1ef69ca31412d6cd6603ed57c7580e1974fa62d89df963054773f

Observation b8f9dbcd-369a-4abc-a7ea-bfae3b30b849 · outbound

This paper cites an unresolved cited work.

Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-08-06T19:17:36.867207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-06T19:17:36.782108Z digest=sha256:cc663184f927df7f545fc25bd7cdf66b5fd04a169ead44854729d9ca88b5e40b

Pith citing papers

Observation 3a12a570-c30b-41b0-b28b-32df8b2331d0 · inbound

Barron regularity of many particle Schr\"odinger eigenfunctions cites this paper.

Barron regularity of many particle Schr\"odinger eigenfunctions Sharp uniform approximation for spectral Barron functions by deep neural networks

Reference 23

Resolution
verified exact
local_arxiv, observed 2026-08-15T17:17:36.234261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T17:17:36.123343Z digest=sha256:99ea011e311108b7fb15c715f292419eb5634340bd83a72ee28cc41c2742a7a0