Paper Citation Record · LEDGER

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach

As of 11 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 2 inbound Pith citation observations for arXiv:2503.07976.

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

pith.paper-citation-record.v1
2503.07976 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-23T01:15:43.167721Z

measured 30 of 30 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T17:08:54.066574Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-06-30T17:14:57.111282Z

Reference resolution

28 of 28 outbound references displayed

verified exact2
verified fuzzy26
unresolved0
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External citation measurements

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Outbound references

Observation 3a5d351a-75ae-4124-b437-b2600651a754 · outbound

This paper cites Shallow an d deep networks are near- optimal approximators of Korobov functions.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Shallow an d deep networks are near- optimal approximators of Korobov functions

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.577820Z

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 d7f9b996-342c-47ef-aa8f-70c734fa7ea1 · outbound

This paper cites Sparse grid s.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Sparse grid s

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.639404Z

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Observation cfcc616a-b865-4af3-b8cf-38e53040f13d · outbound

This paper cites Temlyakov, and Tino Ullrich.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Temlyakov, and Tino Ullrich

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.592718Z

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Observation b8b753a2-5823-42e9-8864-23e3585e1e27 · outbound

This paper cites Learning Korobov fun ctions by correntropy and convo- lutional neural networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Learning Korobov fun ctions by correntropy and convo- lutional neural networks

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.619218Z

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Observation 8432f449-35fd-4b8f-8a13-3afec31c2b9c · outbound

This paper cites Deep Learning.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Deep Learning

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.583240Z

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Observation 90e2664b-d31e-42a4-89ae-9d1bd8cb4905 · outbound

This paper cites Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learning.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Deep Convolutional Neural Networks with Zero-Padding: Feature Extraction and Learning

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-23T01:17:20.101290Z

Source-reported events for the cited work

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Observation 6f9297ad-bc26-46a1-a844-5f1a48091260 · outbound

This paper cites Approximation propert ies of deep ReLU CNNs.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Approximation propert ies of deep ReLU CNNs

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.574827Z

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Observation 7e7e5faf-5677-478d-ab43-1b22dfba196e · outbound

This paper cites MgNet: A uniﬁed framework of mul tigrid and convolutional neural network.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach MgNet: A uniﬁed framework of mul tigrid and convolutional neural network

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.571668Z

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Observation 6c36dbc6-c544-4834-9032-b758dc3f490e · outbound

This paper cites De ep residual learning for image recognition.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach De ep residual learning for image recognition

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.601300Z

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Observation d05e63fb-c11c-4e20-98e3-2563e8d81f20 · outbound

This paper cites Densely connected convolutional networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Densely connected convolutional networks

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.589251Z

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Observation 93af4222-de51-4187-93d4-3b8c353650b2 · outbound

This paper cites Physics-informed machine learning.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Physics-informed machine learning

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.586311Z

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Observation ab6e1eb0-d1bf-484a-9721-86effd4ef927 · outbound

This paper cites Statistical theory for image classification using deep convolutional neural networks with cross-entropy loss under the hierarchical max-pooling model.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Statistical theory for image classification using deep convolutional neural networks with cross-entropy loss under the hierarchical max-pooling model

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-23T01:17:20.096416Z

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Observation 1dda8215-713f-4961-9708-ee8907003598 · outbound

This paper cites Imagenet classiﬁcation with deep convolutional neural networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Imagenet classiﬁcation with deep convolutional neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.580774Z

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Observation d643c716-f126-44c8-8641-39b0132cfa0f · outbound

This paper cites Deep learning.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Deep learning

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.595581Z

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Observation 6b5205b3-f0fc-4e42-8298-8a3e949ef99f · outbound

This paper cites Medical image classiﬁcation with convolutional neural network.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Medical image classiﬁcation with convolutional neural network

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.633004Z

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

Observation 010fb7f7-0f42-46b2-af55-6084bedc073a · outbound

This paper cites Approximat ing functions with multi-features by deep convolutional neural networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Approximat ing functions with multi-features by deep convolutional neural networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.627444Z

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 d7a4a4a3-4004-46ec-b281-1cc6b67ae955 · outbound

This paper cites Approximation of function s from Korobov spaces by deep convolutional neural networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Approximation of function s from Korobov spaces by deep convolutional neural networks

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.568922Z

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 b59ec836-e836-4653-9abc-ad81f5a1e2df · outbound

This paper cites New error bounds for de ep ReLU networks using sparse grids.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach New error bounds for de ep ReLU networks using sparse grids

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.613380Z

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Observation 9819b2f9-e3f8-46a0-b5d4-0887d283afff · outbound

This paper cites Tractability of Multivariate Problems: V olume I: Lin- ear Information.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Tractability of Multivariate Problems: V olume I: Lin- ear Information

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.642775Z

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Observation a6ca8566-f6a9-483d-82ec-cb37ff6706de · outbound

This paper cites Expo nential ReLU DNN expression of holomorphic maps in high dimension.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Expo nential ReLU DNN expression of holomorphic maps in high dimension

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.636361Z

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

Observation 14cb2386-ff47-4fe8-bd42-0e9d258c7659 · outbound

This paper cites Equivalence of approximation by convolutional neural networks and fully-connected networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Equivalence of approximation by convolutional neural networks and fully-connected networks

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.630273Z

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

Observation 8185031e-6bfe-4faa-b2d6-7abf1376187e · outbound

This paper cites U- net: Convolutional networks for biomedical image segmentation.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach U- net: Convolutional networks for biomedical image segmentation

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.624615Z

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

Observation c7cf633c-dea5-4499-ae42-b090e590050c · outbound

This paper cites Optimal approximation rates for dee p ReLU neural networks on Sobolev and Besov spaces.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Optimal approximation rates for dee p ReLU neural networks on Sobolev and Besov spaces

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.621876Z

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Observation a902859f-43c2-4438-ac10-6872d0a1946b · outbound

This paper cites V ery deep convolutional net works for large-scale image recogni- tion.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach V ery deep convolutional net works for large-scale image recogni- tion

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.616405Z

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Observation f717be1b-9091-4f41-b02d-aec71cdfb44a · outbound

This paper cites Error bounds for approximations with deep ReLU networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Error bounds for approximations with deep ReLU networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.610346Z

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Observation cb2e7a06-a934-4e6a-89d7-f34a15f540f8 · outbound

This paper cites Object detection with deep learning: A review.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Object detection with deep learning: A review

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.607397Z

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Observation 9f243415-7a5a-4b64-ab1c-77d4cb46d66c · outbound

This paper cites Theory of deep convolutional neural ne tworks: Downsampling.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Theory of deep convolutional neural ne tworks: Downsampling

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.604496Z

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Observation 56842612-dcb6-4e27-880a-ea7c6a16cf24 · outbound

This paper cites Universality of deep convolutional ne ural networks.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach Universality of deep convolutional ne ural networks

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T01:17:20.598401Z

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Pith citing papers

Observation 38e6f1b0-4821-4e92-9626-dce4661f9cdd · inbound

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations cites this paper.

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach

Reference 117

Resolution: verified exact; local_arxiv, observed 2026-05-22T07:31:13.977537Z

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Observation 47a34497-63ae-49fb-8adf-343e391dff7d · inbound

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations cites this paper.

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-06-30T17:14:57.112697Z

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