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Paper Citation Record · LEDGER

Understanding Two-Layer Neural Networks with Smooth Activation Functions

As of 14 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 2026-08-13T06:32:02.005865+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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.468852Z digest=sha256:e7c90af989e1f37c7b870539819f6796a5d5ee2194b82d32b25f1475e27266b7

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.472377Z digest=sha256:77efff4505b45766d5acf67d54bc79ccfa2d14df62fa04d117046a74ffaa2625

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.475261Z digest=sha256:eaa5696e98820e17d6ea2601a824d9bdd70bb1626f9d2a91fefd23903b9b4fb0

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.477981Z digest=sha256:0ed5e3236a844e5ce0d644c675acabbf3d68cc8f9e5f731f02e1d65b59e96c63

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.480920Z digest=sha256:8feff8b79e8b166e2a23599517bebadf00b9832e5a3e88c62d9aadf9c5e4dc87

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.483515Z digest=sha256:6ce2848ffbba51a67f6ed47d0bfd37e870e3712baa01c2d7d99c3dfc80ab6e9e

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.486452Z digest=sha256:058de7ccfb506f3005190d218d4969354fb748c80d2fcabc8cdf9bd4105d49ea

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.488794Z digest=sha256:3bada005b48b6ccea93d5fa0186e3529f7ae8f6d0dcd600e99f55b906cc89bb7

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.492286Z digest=sha256:dcb2a64dd6119769efe58cfda534541923b8abf92321e3e278bff81672387f9d

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.495154Z digest=sha256:a20ea46f8565eafe4e1a80360a70c848209756bb5e3c072128c6a57ace65d027

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.498305Z digest=sha256:48e5882aa5f9e1bfd009186a0d7871d291958b54bdcf34453bad512f9a748747

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.500879Z digest=sha256:10ee921e5305166ab94182fa715bb7605990ed4784dbf4b7b6954577d8b5d22c

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.503836Z digest=sha256:5547c2baef24df731718b188df7d8c05d0529e7401fd157b914c72ac28933ed4

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.506707Z digest=sha256:7315e38a66ace5782a85eded4416c3db39f63d28452a1b73677151622e0905b1

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.509084Z digest=sha256:fb65d062adb0d6e75ccb9cf67e1d05e814dfaaf2c5910f20730ab593bd66b941

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.511669Z digest=sha256:6b6f2ea6c7e8f8eea299b1772dd7f4ce9888c0038d550dd52d1805359b201afd

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.514520Z digest=sha256:1f5af8ebd3c5f1e504f701dc835cdec4cd1ea8b0fe3e49fc8d5888fe06193d90

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=sha256:23fe06f9680e02cc9283705a840236ccf93f65749c6814a6aa86d94e3d89dc81

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.520516Z digest=sha256:6b6761fdfd9983e9315f138d9baf8423eacdcae9e92b082ec4d48711d7add01b

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.523275Z digest=sha256:06e4cf860c01f0f998417f433186b5389df28a8f0db60fc01107b4c416779f88

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.527227Z digest=sha256:59855372c00282d09281e97079dc0f321c952ef1abd44b62c365cc65e1324eca

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.529802Z digest=sha256:8c7c5d4c32f5bf2354ccb23476415fac48198d846ae5637e82ea014134cf14d4

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.532151Z digest=sha256:456a8dcfc22bc788039922ac7b60321b8517d5c8ed07e6d37778a305d6be489f

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.535154Z digest=sha256:66d4c600a3fd46bd719e0d503baf287a9bfcf22881989d34fa554c0a2c49d19d

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.538097Z digest=sha256:c412aecbd88ee89a051488df8c4ea44f9fd92ec8a275c30d07b4cb66596995d3

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=sha256:027d18157f63058f28830e75e6fdb360922d229d965013195428a0debc5f21f8

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.544356Z digest=sha256:76a2693b4ff55cd2f6154fc7a1f3218bcba87f3bf328b74572369ac13349d987

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.547441Z digest=sha256:e5625363dc948ecfeb16a193de939bbe47f3957a75c0505f5a2bd27c02b62907

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.550429Z digest=sha256:6b2f76d58ddcddd47f7d1c88699f52bde07aaba7aa22d9e8dfd1c3eb91e30344

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 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-08-06T18:30:32.553553Z digest=sha256:ad3636138d245788f09d0248b6c12dfd0c84a968931a97f39759fcada0d6f65c

Pith citing papers

No inbound Pith citation observations are available.