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Paper Citation Record · LEDGER

Sharp uniform approximation for spectral Barron functions by deep neural networks

As of 16 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.

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measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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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Sharp uniform approximation for spectral Barron functions by deep neural networks Unresolved cited work

Reference 9

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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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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

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

Reference 19

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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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Observation c2a204f3-5454-4622-815c-e014b195c951 · outbound

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

Reference 37

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+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

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T19:17:36.748966Z digest=sha256:87436554b29c1cc6d45743d44c2d9b6fdcdc07ce5546d2996c7edcf1de5fe0ee

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T19:17:36.753681Z digest=sha256:ac8468a50405473a119db292ce6e1299132d95618b244e15ddc59debcb2f4462

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
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T19:17:36.760610Z digest=sha256:2075ad40d82bbd3aa7b625e0395e30573ac326bd25e86f4714a1d0ae74a746f7

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

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T19:17:36.766032Z digest=sha256:f6a79998151a3c058da83f5edf4355bff43beb445ca6d82ac72fbd583c4514ac

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 2026-08-16T06:30:59.297886+00:00.

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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
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T19:17:36.777043Z digest=sha256:1e7a2a43235b8ea4fec3f449f79ae892b62803fbb2188eda54312c60db22fe31

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 2026-08-16T06:30:59.297886+00:00.

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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
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