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Paper Citation Record · LEDGER

Understanding Two-Layer Neural Networks with Smooth Activation Functions

As of 9 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2507.14177.

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

pith.paper-citation-record.v1
2507.14177 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:30:32.553553Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

30 of 30 outbound references displayed

  • verified exact0
  • verified fuzzy9
  • unresolved21
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1fb772f2-ba22-43a7-8351-cc5bd9cab5b5 · outbound

This paper cites M., Lopez-de-Teruel, P.

Understanding Two-Layer Neural Networks with Smooth Activation Functions M., Lopez-de-Teruel, P

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.794559Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.468852Z digest=sha256:38ad14fbaab42de3358553823aa9cfd3a94784c43c8069eaadbe55dd6168cbff

Observation d4a84d60-ded8-49f1-85df-995d145f775e · outbound

This paper cites A., & Bonaiuto, J.

Understanding Two-Layer Neural Networks with Smooth Activation Functions A., & Bonaiuto, J

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.786868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.472377Z digest=sha256:cc86fbcc7f6d8c6c5b346d031361f08998979ecf4f4d8022594e45c5fe599147

Observation bceffb44-3e38-4a5c-927d-9fbe44166126 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.778785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.475261Z digest=sha256:735674c65c19d8c56cd74ac2f1542cf8cb8bea2b25207665a76c154e94debce8

Observation 5cdfe736-b711-45ec-a5bb-728422a4290b · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.770862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.477981Z digest=sha256:f86a1889016e0918234360397f992416bc489e6c3efdd22d746053ef54500b42

Observation eef46734-4a39-4d6a-b80d-6c78d9e35f92 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.763401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.480920Z digest=sha256:4bdb726b9290faed1733ab7837b0dee63f577cdb026923824f5e725d9121abca

Observation 18451998-d84d-4327-b544-8c2898bbcf4b · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.756578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.483515Z digest=sha256:9e3a23cbddc57d306600bff5cffe662cbde5382c666ba7604dc0ac65079aced6

Observation d90aa17a-1a37-4051-b003-b20ead2c0373 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.748561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.486452Z digest=sha256:c39f69ecac023f35fdc6f378e71e0c99d1bf643a78867569211a4613414674c1

Observation 13f38173-f5ef-4bec-be4b-3608d625e19b · outbound

This paper cites K., & Wang, R.

Understanding Two-Layer Neural Networks with Smooth Activation Functions K., & Wang, R

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.741211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.488794Z digest=sha256:1e32058087574530336634dd82233d47244e39c234dfb609c7b7b68ec7562c7f

Observation 146f6113-a61a-4f6c-85b8-222245492233 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.732766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.492286Z digest=sha256:94ca99976ff6936b137212fb7d47d9fad942a17f5731eeed67d322e587cfd75f

Observation ef8fd930-9d6d-4291-b367-0561f26dbcda · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.725984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.495154Z digest=sha256:db08d861991eab780f7200ee891487ce8a251b8b65c9f3d972dc5b09aaf0578d

Observation 8c8a4f4b-98a9-4432-8fde-e66d656bd0f7 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.719334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.498305Z digest=sha256:ac6cb13bd9b04cde19125fe5e93f0b4d365109c61345ae7ba61a5f7c6507c837

Observation 6383565c-cdf7-40cb-bb71-51dd5892f921 · outbound

This paper cites J., & Ismailov, V.

Understanding Two-Layer Neural Networks with Smooth Activation Functions J., & Ismailov, V

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.711615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.500879Z digest=sha256:3aba1f77585a2a254e49a7d6092ce601cfd7fa2c36e66ae643100b798638b730

Observation 24a2efcd-e5e5-4b20-8f94-bbf38b059e5a · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.704036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.503836Z digest=sha256:15b794bad519c4bdc06b5cb3cbdb7693dc17999923e680a1ae727cd6d10e90f8

Observation 3a827ebe-ab0e-4584-b46e-9b3ab212584f · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.697148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.506707Z digest=sha256:efa476ec0a5025c46414c72e8266f374f39267dc83adb8aaec7254d9f4b5561d

Observation fb794574-7460-4294-9972-1a15990fa623 · outbound

This paper cites E., & Salakhutdinov, R.

Understanding Two-Layer Neural Networks with Smooth Activation Functions E., & Salakhutdinov, R

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.689551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.509084Z digest=sha256:f809302883f29e25a7f9dbc2d50aa4881cd6720e80cfaf1dc6983e590a6faab8

Observation 7d2611a8-a6b2-4226-8039-d9af5887dce2 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.681626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.511669Z digest=sha256:8232a5c49735ce10d54c6f8fbf64939585e317d7516ff52e7e95b7b87743ccc4

Observation 5b1e54c1-cb07-4f37-be31-ccd7f85c89ca · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.674685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.514520Z digest=sha256:a2b73fc4355b1b1f33519fea238197dce217e9d732641594d43334b53739fccf

Observation 255db283-4ba4-4e91-8d50-43b8d4454519 · outbound

This paper cites On the Principles of ReLU Networks with One Hidden Layer.

Understanding Two-Layer Neural Networks with Smooth Activation Functions On the Principles of ReLU Networks with One Hidden Layer

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-06T18:30:32.517561Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T18:30:32.517561Z digest=sha256:884b337f1d09eca3bb0f45f11723dc4b42ffa5d6e66ec5d4f99fffb11d2751fa

Observation 9415785f-d2a7-40c8-9407-555778fdf6f2 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.667701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.520516Z digest=sha256:a653bf925b54f053fa06c9a40927bca26a3d3cf2ab70cca0470b629d7c711fa0

Observation d528f465-731a-47f2-b43b-413b5b2b7b8d · outbound

This paper cites R., Koester, J.

Understanding Two-Layer Neural Networks with Smooth Activation Functions R., Koester, J

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.660211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.523275Z digest=sha256:7e55f62c65c4985f9b8e1494c4f05048baf579ebf0c72e29604a3676f5efb479

Observation c36982d2-b0fb-478a-aaf0-27bebb938c0f · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.652031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.527227Z digest=sha256:30aefd186962d713703890a6f62173c5181b77d9eafc79814a32a94c6626c192

Observation 225fa931-7b8b-4a16-b0e1-22123da9d3e8 · outbound

This paper cites Y., Pinkus, A., & Schocken, S.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Y., Pinkus, A., & Schocken, S

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.644212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.529802Z digest=sha256:119f913e5337e989a6768563a1def9dafa1130ec0c3eddd35dab6278412c0da9

Observation e7bf4542-25a5-43ef-aca6-ca8b8268df08 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.635710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.532151Z digest=sha256:b06c0b904d299f2cf1c6901cf8d944374300123e8fab9c018c57ad0c3c8a89ac

Observation d815b2c6-9a9a-4ebb-b58a-7840db35717b · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.626938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.535154Z digest=sha256:2f73de5f65f9aee435a36e656fcdb7444cd04434c13e21e734537bca2200e1c0

Observation e2f0f3de-5bbc-40d0-8a67-74ac7a98ebbb · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.618968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.538097Z digest=sha256:8d75ccff5a6e4e138a0b4c9348c61f296a50de35535e71edb4eb3b77cb45f78a

Observation 0a17feb3-5f44-48d0-b8ad-d3908feaa84c · outbound

This paper cites E., Hinton, G.

Understanding Two-Layer Neural Networks with Smooth Activation Functions E., Hinton, G

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-06T18:30:32.541358Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T18:30:32.541358Z digest=sha256:ce13c24a6586d62967a88dfe166e2360c11125d2ed257774735ee9eda5ad1fee

Observation 8b717098-bb5a-4def-ad4c-bb9ce0f1ab5e · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.607600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.544356Z digest=sha256:fe4fd1b86b1bdf7e8dd99582ba0dae32975ff871be961d21572b3649c8129a67

Observation 353b50d9-58c0-4887-92a7-8f550e69a445 · outbound

This paper cites & White, H.

Understanding Two-Layer Neural Networks with Smooth Activation Functions & White, H

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.600113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.547441Z digest=sha256:f3a355be635225ebcde3fb17f7df78cca97ffbc9d05d76b837ee68a6bb4e8f83

Observation 0a74596b-a279-4b69-8a74-7a88bae364c9 · outbound

This paper cites an unresolved cited work.

Understanding Two-Layer Neural Networks with Smooth Activation Functions Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-06T18:30:32.591641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.550429Z digest=sha256:fcc0b2fe2a103fcce69ab2256edcb642ce8b0143b2ddb1e69a7ea5a80fff922d

Observation 93d27dc6-b02a-436c-aba5-8064f319cf87 · outbound

This paper cites B., & Cao, F.

Understanding Two-Layer Neural Networks with Smooth Activation Functions B., & Cao, F

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T18:30:32.582468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.553553Z digest=sha256:08641df76b3646127c14361230f31be55dde3fd1e5247b145fe46e863e317847

Pith citing papers

No inbound Pith citation observations are available.