Paper Citation Record · LEDGER

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks

As of 11 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 1 inbound Pith citation observation for arXiv:2412.09752.

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

pith.paper-citation-record.v1
2412.09752 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T16:51:00.536240Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-08T19:06:22.016193Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-08T19:15:30.439186Z

Reference resolution

42 of 42 outbound references displayed

verified exact1
verified fuzzy25
unresolved16
parse uncertain0
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External citation measurements

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Outbound references

Observation c9af28d5-d075-49d3-b170-1177ab00f48f · outbound

This paper cites A NTONION , X.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks A NTONION , X

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.390395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 70f59e82-ec56-45d2-8eed-21e56c14ed48 · outbound

This paper cites B ARENBLATT AND Y.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks B ARENBLATT AND Y

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.375162Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 54f959ce-de22-4389-b278-6b75cde85c77 · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 3

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Observation 641d4fde-41f6-44f0-9952-4eb046aaec31 · outbound

This paper cites B IASI , Self-similar solutions to the compressible euler equations and their instabilities, Communications in Nonlinear Science and Numerical Simulation, 103 (2021), p.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks B IASI , Self-similar solutions to the compressible euler equations and their instabilities, Communications in Nonlinear Science and Numerical Simulation, 103 (2021), p

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.345531Z

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Observation 03172e1b-5fee-4c89-817d-6c3ab381fe95 · outbound

This paper cites B ISCHOF AND M.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks B ISCHOF AND M

Reference 5

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Source-reported events for the cited work

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Observation 984e0d4c-d085-48e0-bae3-8a1f8366b569 · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:51:01.329224Z

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Observation f1c14406-c98d-46dc-ac38-fdefd461f9cd · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:51:01.313402Z

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Observation 940344c3-3da4-4617-a5ea-8c407a127d72 · outbound

This paper cites C HIU , J.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks C HIU , J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.297195Z

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Observation 033bb0d2-b291-4ddb-b326-0d20e4fddb20 · outbound

This paper cites C YBENKO , Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems, 2 (1989), pp.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks C YBENKO , Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems, 2 (1989), pp

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.280507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e000fef0-a1d7-49eb-82fc-fb8024584679 · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:51:01.262544Z

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Observation 1bcaacb6-b2c3-4a70-bd76-d99558e030d1 · outbound

This paper cites An operator preconditioning perspective on training in physics-informed machine learning.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks An operator preconditioning perspective on training in physics-informed machine learning

Reference 11

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Source-reported events for the cited work

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Observation d11ab607-c243-42ac-b1c1-1a7701bc5ac9 · outbound

This paper cites E GGERS AND M.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks E GGERS AND M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.243433Z

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Observation c353f79d-8927-41a8-ae06-26f8ba6b47f5 · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 13

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Observation fe98b127-3a21-492f-9ee9-57a4946c66f5 · outbound

This paper cites F AREA , O.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks F AREA , O

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.213142Z

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Observation 19d7d06b-3afc-43cf-9680-9a9b468eddff · outbound

This paper cites H ABERMAN , Elementary applied partial differential equations: with Fourier series and boundary value problems , Prentice-Hall Englewood Cliffs, NJ, 1987.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks H ABERMAN , Elementary applied partial differential equations: with Fourier series and boundary value problems , Prentice-Hall Englewood Cliffs, NJ, 1987

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.196395Z

Source-reported events for the cited work

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Observation 831a0274-c738-47b0-891c-a655a5fb04de · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:51:01.179588Z

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Observation 8a7ea37e-9cd8-4fb5-ab32-9eb68945fe94 · outbound

This paper cites H ORNIK , Approximation capabilities of multilayer feedforward net- works, Neural networks, 4 (1991), pp.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks H ORNIK , Approximation capabilities of multilayer feedforward net- works, Neural networks, 4 (1991), pp

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.163940Z

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Observation 564ad5a6-0f65-4df7-9331-5cc55f7743ec · outbound

This paper cites J AHANI -NASAB AND M.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks J AHANI -NASAB AND M

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.148132Z

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Observation 7e713e6f-c50e-4925-84c9-60ec816093ba · outbound

This paper cites K RISHNAPRIYAN , A.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks K RISHNAPRIYAN , A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.132459Z

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Observation 9439ac1b-d23d-46fd-ac78-2709357f575f · outbound

This paper cites M ADDU , D.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks M ADDU , D

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.116707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c5b6f9d4-cc92-4603-9fd3-559aacae10a0 · outbound

This paper cites M ARKIDIS , The old and the new: Can physics-informed deep- learning replace traditional linear solvers? , Frontiers in big Data, 4 (2021), p.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks M ARKIDIS , The old and the new: Can physics-informed deep- learning replace traditional linear solvers? , Frontiers in big Data, 4 (2021), p

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.101424Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e39d9b5c-a2d6-4a1d-bd24-15a22d584917 · outbound

This paper cites M CGREIVY AND A.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks M CGREIVY AND A

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.086247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7aeeff4b-5259-4dfd-ba84-1a75c55db6e1 · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:51:01.071366Z

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Observation 43d26ea9-b602-4cad-ab5a-3c7c81cdff4c · outbound

This paper cites N OCEDAL AND S.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks N OCEDAL AND S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.057167Z

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Observation 06c10354-e75d-4eaf-995c-fc628a13048d · outbound

This paper cites O H AND F.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks O H AND F

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.042777Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a7a89d43-226c-4b3f-832c-0c8fbee2663c · outbound

This paper cites P ASZKE , S.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks P ASZKE , S

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.026767Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3671ed4f-665b-4514-b8bc-06d0fa8d8cac · outbound

This paper cites P ENWARDEN , A.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks P ENWARDEN , A

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:01.011214Z

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Observation 3ec86ec7-b7ed-4a6d-958d-be8c12ca1bca · outbound

This paper cites R AHAMAN , A.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks R AHAMAN , A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.995255Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 206f2395-3486-43ce-9811-b1fa6650880d · outbound

This paper cites R AISSI , P.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks R AISSI , P

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.980208Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 72355189-f33e-45b7-a36b-2752d0ffdc04 · outbound

This paper cites Challenges in Training PINNs: A Loss Landscape Perspective.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Challenges in Training PINNs: A Loss Landscape Perspective

Reference 30

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Source-reported events for the cited work

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Observation 2a128bd0-acb0-4a2a-9131-80226b9cd0e5 · outbound

This paper cites R OMAN , The formula of faa di bruno , The American Mathematical Monthly, 87 (1980), pp.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks R OMAN , The formula of faa di bruno , The American Mathematical Monthly, 87 (1980), pp

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.964524Z

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Observation 2fe378d7-4432-4019-88d5-1fa47e9d2389 · outbound

This paper cites S HARMA AND V.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks S HARMA AND V

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.947373Z

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Observation cd0cf97d-1916-45a2-bd0e-79762014a544 · outbound

This paper cites an unresolved cited work.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:51:00.931255Z

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Observation 486cf8e9-bf1c-445d-a2a5-7b411d3c87ae · outbound

This paper cites S IMARD , B.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks S IMARD , B

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.915157Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bdd8f5b3-14ed-4ed7-b985-82827a8b77ea · outbound

This paper cites Sobolev Training for Physics Informed Neural Networks.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Sobolev Training for Physics Informed Neural Networks

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T16:51:00.502906Z

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Observation 70fe2c39-e161-41a8-a94f-19907921dd55 · outbound

This paper cites Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-11T16:51:00.507623Z

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Unavailable: canonical work link unavailable.

Observation 64c964ba-7a24-4ca0-a70c-ae86eb656765 · outbound

This paper cites An Expert's Guide to Training Physics-informed Neural Networks.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks An Expert's Guide to Training Physics-informed Neural Networks

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-11T16:51:00.512622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06bcdd48-e19e-4890-bd27-2f7d2cf17a23 · outbound

This paper cites Understanding and mitigating gradient pathologies in physics-informed neural networks.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Understanding and mitigating gradient pathologies in physics-informed neural networks

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-11T16:51:00.517590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36a1c248-3703-4d7b-a665-5bc1bbeda857 · outbound

This paper cites W ANG , X.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks W ANG , X

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.890273Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 952b95f1-31f2-4fa4-9191-d481067e8388 · outbound

This paper cites W ANG , C.-Y.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks W ANG , C.-Y

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:51:00.867285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6b1c0949-18d7-478c-bf49-970bfdb84bbe · outbound

This paper cites Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-11T16:51:00.531290Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a411e0b5-0553-449e-86a7-fcbc5cfde9cd · outbound

This paper cites Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss.

A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Loss

Reference 42

Resolution: verified exact; local_arxiv, observed 2026-08-11T16:51:00.582720Z

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 85f7a439-c97f-4b7f-ab61-873713f3c71c · inbound

SplineNet: An Isogeometric Deep Learning Method for Complex Shells cites this paper.

SplineNet: An Isogeometric Deep Learning Method for Complex Shells A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networks

Reference 12

Resolution: metadata mismatch; local_arxiv, observed 2026-07-08T19:15:30.440419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.