Paper Citation Record · LEDGER

On best approximation by multivariate ridge functions with applications to generalized translation networks

As of 19 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2412.08453.

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

pith.paper-citation-record.v1
2412.08453 v3

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T17:54:36.885677Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

35 of 35 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e4891f7b-cd3e-44b6-beae-f05d858430eb · outbound

This paper cites Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.708945Z

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Observation ec1cc489-49a7-4ea3-9692-b415c7ceb6c8 · outbound

This paper cites A Survey of Complex-Valued Neural Networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks A Survey of Complex-Valued Neural Networks

Reference 2

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Observation 9f71ef20-a1f0-4262-96c8-924a46e32fdd · outbound

This paper cites Ridgelets: estimating with ridge functions.

On best approximation by multivariate ridge functions with applications to generalized translation networks Ridgelets: estimating with ridge functions

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.696684Z

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Observation d4359feb-bc4b-4a43-a03a-2bbe3666b874 · outbound

This paper cites Dai and Y.

On best approximation by multivariate ridge functions with applications to generalized translation networks Dai and Y

Reference 4

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On best approximation by multivariate ridge functions with applications to generalized translation networks Unresolved cited work

Reference 5

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Observation 60af9cb4-26bf-4f27-8a76-593275688834 · outbound

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On best approximation by multivariate ridge functions with applications to generalized translation networks Unresolved cited work

Reference 6

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Observation 4c7ae43a-96ab-4d33-ad4f-608d94c69ad0 · outbound

This paper cites Robust and resource efficient identification of shallow neural networks by fewest samples.

On best approximation by multivariate ridge functions with applications to generalized translation networks Robust and resource efficient identification of shallow neural networks by fewest samples

Reference 7

Resolution: verified exact; doi, observed 2026-08-11T17:54:36.964973Z

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Observation 8f6d4859-8207-488f-aaae-d7209d8720a6 · outbound

This paper cites Universal approximation with complex-valued deep narrow neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Universal approximation with complex-valued deep narrow neural networks

Reference 8

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Observation 6ea9c7af-8185-4482-bc2b-4c5edfe6a069 · outbound

This paper cites Optimal approximation using complex-valued neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Optimal approximation using complex-valued neural networks

Reference 9

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Observation 12acef25-45b7-4838-8187-f817654d5180 · outbound

This paper cites On the best approximation by ridge functions in the uniform norm.

On best approximation by multivariate ridge functions with applications to generalized translation networks On the best approximation by ridge functions in the uniform norm

Reference 10

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Observation 56790dd9-6b43-40a2-9aac-99d02b3f36e3 · outbound

This paper cites Ismailov.

On best approximation by multivariate ridge functions with applications to generalized translation networks Ismailov

Reference 11

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Source-reported events for the cited work

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Observation 40d6192b-d669-4564-af16-4b49bc572567 · outbound

This paper cites A review of some results on ridge function approximation.

On best approximation by multivariate ridge functions with applications to generalized translation networks A review of some results on ridge function approximation

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.613360Z

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Observation c4818fb8-b406-4b8c-a54b-73e606b0c24f · outbound

This paper cites Kaup and B.

On best approximation by multivariate ridge functions with applications to generalized translation networks Kaup and B

Reference 13

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Observation ac57a963-004e-4316-ae82-f7b20a5d7cca · outbound

This paper cites Complex-valued neural networks: A comprehensive survey.

On best approximation by multivariate ridge functions with applications to generalized translation networks Complex-valued neural networks: A comprehensive survey

Reference 14

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Observation 606cff16-cf8b-4619-b769-024b54ce0ca8 · outbound

This paper cites Fundamentality of ridge functions.

On best approximation by multivariate ridge functions with applications to generalized translation networks Fundamentality of ridge functions

Reference 15

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Observation ae05d60e-4445-4408-b7c0-6fbe0bf697a1 · outbound

This paper cites Luenberger.

On best approximation by multivariate ridge functions with applications to generalized translation networks Luenberger

Reference 16

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Observation 7c6c67d6-fb30-4974-b744-7a39e72b2af6 · outbound

This paper cites On Best Approximation by Ridge Functions.

On best approximation by multivariate ridge functions with applications to generalized translation networks On Best Approximation by Ridge Functions

Reference 17

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Observation 0cd6d1b5-f67e-43b1-8152-4997bef5b45e · outbound

This paper cites Best approximation by ridge functions inLp-spaces.

On best approximation by multivariate ridge functions with applications to generalized translation networks Best approximation by ridge functions inLp-spaces

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.567838Z

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Observation e7fce3ac-7807-44ec-a2de-e85b7f81890c · outbound

This paper cites Lower bounds for approximation by MLP neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Lower bounds for approximation by MLP neural networks

Reference 19

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Observation cf95b354-671c-4617-962c-8186c8b1e52b · outbound

This paper cites Onachoiceofsamplingnodesforoptimalapproximationofsmoothfunctions by generalized translation networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Onachoiceofsamplingnodesforoptimalapproximationofsmoothfunctions by generalized translation networks

Reference 20

Resolution: verified exact; doi, observed 2026-08-11T17:54:36.940163Z

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This paper cites Neural networks for optimal approximation of smooth and analytic functions.

On best approximation by multivariate ridge functions with applications to generalized translation networks Neural networks for optimal approximation of smooth and analytic functions

Reference 21

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Observation 8199f0af-ff09-466c-bbb1-9fcd6f00751c · outbound

This paper cites Degree of approximation by neural and translation networks with a single hidden layer.

On best approximation by multivariate ridge functions with applications to generalized translation networks Degree of approximation by neural and translation networks with a single hidden layer

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.530059Z

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Observation 4c998892-8d80-4488-89ca-f11aaf0cb502 · outbound

This paper cites Easy proof of the Jacobian for then-dimensional polar coordinates.

On best approximation by multivariate ridge functions with applications to generalized translation networks Easy proof of the Jacobian for then-dimensional polar coordinates

Reference 23

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Observation bb59d7ba-299b-420c-82f2-038a69c8d9c7 · outbound

This paper cites Optimal approximation of piecewise smooth functions using deep ReLU neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Optimal approximation of piecewise smooth functions using deep ReLU neural networks

Reference 24

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Observation ac0f303c-7b9c-43d5-8437-12f36a98199b · outbound

This paper cites Approximating by ridge functions.

On best approximation by multivariate ridge functions with applications to generalized translation networks Approximating by ridge functions

Reference 25

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On best approximation by multivariate ridge functions with applications to generalized translation networks Unresolved cited work

Reference 26

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Observation 3034762b-d103-4258-aa1b-b7e16409188d · outbound

This paper cites Prudnikov, Y.

On best approximation by multivariate ridge functions with applications to generalized translation networks Prudnikov, Y

Reference 27

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This paper cites Depth-width tradeoffs in approximating natural functions with neural net- works.

On best approximation by multivariate ridge functions with applications to generalized translation networks Depth-width tradeoffs in approximating natural functions with neural net- works

Reference 28

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This paper cites Deep Network Approximation Characterized by Number of Neurons.

On best approximation by multivariate ridge functions with applications to generalized translation networks Deep Network Approximation Characterized by Number of Neurons

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.420677Z

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This paper cites Optimal approximation rate of ReLU networks in terms of width and depth.

On best approximation by multivariate ridge functions with applications to generalized translation networks Optimal approximation rate of ReLU networks in terms of width and depth

Reference 30

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This paper cites Benefits of depth in neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks Benefits of depth in neural networks

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.405512Z

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Observation 809f45e8-372c-4e59-b9ad-bec4cf070cb2 · outbound

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On best approximation by multivariate ridge functions with applications to generalized translation networks Vershynin

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.392254Z

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This paper cites The universal approximation theorem for complex-valued neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks The universal approximation theorem for complex-valued neural networks

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.379797Z

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Observation 2ef89f7d-bba4-4a13-8176-7d15cb0621a4 · outbound

This paper cites The phase diagram of approximation rates for deep neural networks.

On best approximation by multivariate ridge functions with applications to generalized translation networks The phase diagram of approximation rates for deep neural networks

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.366611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 58cbfc6d-91a9-4c83-bcd2-8b6ba9205c95 · outbound

This paper cites Deep network approximation: Achieving arbitrary accuracy with fixed number of neurons.

On best approximation by multivariate ridge functions with applications to generalized translation networks Deep network approximation: Achieving arbitrary accuracy with fixed number of neurons

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T17:54:37.352850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.