Paper Citation Record · LEDGER

Optimal Convergence Rates for Neural Operators

As of 11 August 2026, this Paper Citation Record lists 70 of 70 outbound references and 4 inbound Pith citation observations for arXiv:2412.17518.

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

pith.paper-citation-record.v1
2412.17518 v1

Coverage vector

measured 70 of 70 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T05:34:06.761279Z

measured 74 of 74 standing notices

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measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:25:11.934896Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T16:27:08.385273Z

Reference resolution

70 of 70 outbound references displayed

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External citation measurements

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Outbound references

Observation e247fb77-6218-48d6-bd8f-bd9f06d1c975 · outbound

This paper cites Operator H\"older--Zygmund functions.

Optimal Convergence Rates for Neural Operators Operator H\"older--Zygmund functions

Reference 1

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Observation d36e54b3-ca2f-4893-a1ce-7233f2714cb0 · outbound

This paper cites Segnet: A deep convolutional encoder-decoder architecture for image segmentation.

Optimal Convergence Rates for Neural Operators Segnet: A deep convolutional encoder-decoder architecture for image segmentation

Reference 2

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Observation 1cc04d54-0208-401b-9774-61bb694ef46a · outbound

This paper cites Functional linear regression with functional response.

Optimal Convergence Rates for Neural Operators Functional linear regression with functional response

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.817913Z

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Observation 7a00f232-8b42-40ef-8e81-2205092e6db1 · outbound

This paper cites Kovachki, and Andrew M.

Optimal Convergence Rates for Neural Operators Kovachki, and Andrew M

Reference 4

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Observation b171162c-5186-46b2-bbbc-2b9fc296c881 · outbound

This paper cites Deep Equals Shallow for ReLU Networks in Kernel Regimes.

Optimal Convergence Rates for Neural Operators Deep Equals Shallow for ReLU Networks in Kernel Regimes

Reference 5

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Observation 97978ee1-78cc-4bd8-9996-379bdf74e170 · outbound

This paper cites On the inductive bias of neural tangent kernels.

Optimal Convergence Rates for Neural Operators On the inductive bias of neural tangent kernels

Reference 6

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Observation e99dd445-37f3-4540-8f15-89d987ac2e63 · outbound

This paper cites Optimal rates for regularization of statistical inverse learning problems.

Optimal Convergence Rates for Neural Operators Optimal rates for regularization of statistical inverse learning problems

Reference 7

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Observation 73709e92-d219-4026-bc44-f60dbd480a00 · outbound

This paper cites A Mathematical Guide to Operator Learning.

Optimal Convergence Rates for Neural Operators A Mathematical Guide to Operator Learning

Reference 8

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Observation 1969ec8a-5ca3-40c7-be8f-04f18aa04437 · outbound

This paper cites Caponnetto and Ernesto De Vito.

Optimal Convergence Rates for Neural Operators Caponnetto and Ernesto De Vito

Reference 9

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Observation 27ca77e7-ba36-40a3-afdc-d063ee10ebda · outbound

This paper cites Carmeli, E.

Optimal Convergence Rates for Neural Operators Carmeli, E

Reference 10

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Observation 04a08609-c564-4549-ae1d-4bc5ccbcf6a9 · outbound

This paper cites Reproducing kernel hilbert spaces and mercer theorem, 2005.

Optimal Convergence Rates for Neural Operators Reproducing kernel hilbert spaces and mercer theorem, 2005

Reference 11

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Observation f7c0d8fd-bcbc-476a-b6ff-98f99a298067 · outbound

This paper cites Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS.

Optimal Convergence Rates for Neural Operators Deep Neural Tangent Kernel and Laplace Kernel Have the Same RKHS

Reference 12

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Observation 13546bc0-c7b4-4bfc-a4ef-6d04c9d40b2d · outbound

This paper cites A generalized neural tangent kernel analysis for two-layer neural networks.

Optimal Convergence Rates for Neural Operators A generalized neural tangent kernel analysis for two-layer neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.753714Z

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Observation 9ce85bb8-8a26-4255-beed-066bdd5d63f0 · outbound

This paper cites Dashti, Masoumehand Stuart.

Optimal Convergence Rates for Neural Operators Dashti, Masoumehand Stuart

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.737056Z

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Observation 8c675fa2-03db-43bd-b7c7-3e7fd34b37f4 · outbound

This paper cites Spectra of the conjugate kernel and neural tangent kernel for linear-width neural networks.

Optimal Convergence Rates for Neural Operators Spectra of the conjugate kernel and neural tangent kernel for linear-width neural networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.721498Z

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Observation b8552b52-76c2-4a3e-85c1-0faefa622606 · outbound

This paper cites Spectral Neural Operators.

Optimal Convergence Rates for Neural Operators Spectral Neural Operators

Reference 16

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Observation 7e53f777-e872-4f8a-82c2-0c6297dfe79c · outbound

This paper cites Functional regression models with functional response: a new approach and a comparative study.

Optimal Convergence Rates for Neural Operators Functional regression models with functional response: a new approach and a comparative study

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.706211Z

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Observation 01aaa545-a828-4381-9d9b-2aec87080945 · outbound

This paper cites On the similarity between the laplace and neural tangent kernels.

Optimal Convergence Rates for Neural Operators On the similarity between the laplace and neural tangent kernels

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.691746Z

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Observation f4006e33-797d-4b83-bab1-4fcd6f80485c · outbound

This paper cites Gin, Daniel E.

Optimal Convergence Rates for Neural Operators Gin, Daniel E

Reference 19

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Observation 7505f711-8dbd-4014-9d03-960320c0ac5b · outbound

This paper cites Neural Tangent Kernel: A Survey.

Optimal Convergence Rates for Neural Operators Neural Tangent Kernel: A Survey

Reference 20

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Observation ad2564f4-d8aa-49aa-9728-80e1a61f246f · outbound

This paper cites An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning.

Optimal Convergence Rates for Neural Operators An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning

Reference 21

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Observation 3a38e963-f785-4b16-8e52-b0fbbd72a5a8 · outbound

This paper cites Deep Learning.

Optimal Convergence Rates for Neural Operators Deep Learning

Reference 22

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Observation 5ace67be-c36e-4d0f-8c03-941620d0081b · outbound

This paper cites Conditional mean embeddings as regressors.

Optimal Convergence Rates for Neural Operators Conditional mean embeddings as regressors

Reference 23

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Observation db61017f-f8d4-4261-8510-fc04e002a560 · outbound

This paper cites Nelsen, and Margaret Trautner.

Optimal Convergence Rates for Neural Operators Nelsen, and Margaret Trautner

Reference 24

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Observation 97e855e6-36f9-4271-b040-4331e35cd53c · outbound

This paper cites The finite element method: linear static and dynamic finite element analysis.

Optimal Convergence Rates for Neural Operators The finite element method: linear static and dynamic finite element analysis

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.628154Z

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Observation 417e1d5a-02df-4ef9-a8db-fe78d3f1d39b · outbound

This paper cites Neural tangent kernel: Convergence and generalization in neural networks.

Optimal Convergence Rates for Neural Operators Neural tangent kernel: Convergence and generalization in neural networks

Reference 26

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Observation b09f65cc-6f50-4dc6-aef1-7911cf3ff240 · outbound

This paper cites Kernel neural operator for efficient solving PDEs.

Optimal Convergence Rates for Neural Operators Kernel neural operator for efficient solving PDEs

Reference 27

Resolution: verified exact; doi, observed 2026-08-11T05:34:06.874500Z

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Observation 31d384e2-cd09-44e1-a569-ed494efac066 · outbound

This paper cites Auto-Encoding Variational Bayes.

Optimal Convergence Rates for Neural Operators Auto-Encoding Variational Bayes

Reference 28

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Observation cf8ea293-2dad-46e8-9e26-b1bbd70b29a7 · outbound

This paper cites A rigorous theory of conditional mean embeddings.

Optimal Convergence Rates for Neural Operators A rigorous theory of conditional mean embeddings

Reference 29

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Observation 6eabe4af-187a-4054-858b-99df0a14c27f · outbound

This paper cites On universal approximation and error bounds for fourier neural operators.

Optimal Convergence Rates for Neural Operators On universal approximation and error bounds for fourier neural operators

Reference 30

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Observation 4185308f-17b7-4fbf-9373-cf20ee6a63f1 · outbound

This paper cites Neural operator: learning maps between function spaces with applications to pdes.

Optimal Convergence Rates for Neural Operators Neural operator: learning maps between function spaces with applications to pdes

Reference 31

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Observation 0a6a7e8f-7e5d-417d-8d2d-5683817b3109 · outbound

This paper cites Kovachki, Zong-Yi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M.

Optimal Convergence Rates for Neural Operators Kovachki, Zong-Yi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew M

Reference 32

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Observation 363d1056-362e-4e49-acd0-569c860b1912 · outbound

This paper cites Data Complexity Estimates for Operator Learning.

Optimal Convergence Rates for Neural Operators Data Complexity Estimates for Operator Learning

Reference 33

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Observation fb28ca9a-285c-4ca1-a93c-1e075357e03a · outbound

This paper cites Kovachki, Samuel Lanthaler, and Andrew M.

Optimal Convergence Rates for Neural Operators Kovachki, Samuel Lanthaler, and Andrew M

Reference 34

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Observation 0bfd18b1-06e7-40ff-b47d-02b06d84258a · outbound

This paper cites Operator learning with pca-net: upper and lower complexity bounds.

Optimal Convergence Rates for Neural Operators Operator learning with pca-net: upper and lower complexity bounds

Reference 35

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Observation 9b568bf5-1825-4ab7-a6ff-feb3008c1b7c · outbound

This paper cites Wide neural networks of any depth evolve as linear models under gradient descent.

Optimal Convergence Rates for Neural Operators Wide neural networks of any depth evolve as linear models under gradient descent

Reference 36

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This paper cites Optimal rates for regularized conditional mean embedding learning.

Optimal Convergence Rates for Neural Operators Optimal rates for regularized conditional mean embedding learning

Reference 37

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Observation 3230a28f-1e98-4fcf-ac85-ac1abd8f0441 · outbound

This paper cites Towards optimal sobolev norm rates for the vector-valued regularized least-squares algorithm.

Optimal Convergence Rates for Neural Operators Towards optimal sobolev norm rates for the vector-valued regularized least-squares algorithm

Reference 38

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Observation ce42d74c-46d4-4b8c-80cc-f02f612ffb3e · outbound

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Optimal Convergence Rates for Neural Operators Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 39

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Optimal Convergence Rates for Neural Operators Fourier neural operator for parametric partial differential equations

Reference 40

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This paper cites Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms.

Optimal Convergence Rates for Neural Operators Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms

Reference 41

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Observation 9e0fe2dc-908a-45f4-a923-9c75dca18a37 · outbound

This paper cites Optimal rates for spectral algorithms with least-squares regression over hilbert spaces.

Optimal Convergence Rates for Neural Operators Optimal rates for spectral algorithms with least-squares regression over hilbert spaces

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.629319Z

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This paper cites Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning.

Optimal Convergence Rates for Neural Operators Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning

Reference 43

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Observation 077f389a-0f59-4b09-8790-8a75cb72694a · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

Optimal Convergence Rates for Neural Operators Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.639390Z

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Observation 95a78148-51f4-499b-9a39-f75935092bef · outbound

This paper cites Exponential convergence of deep operator networks for elliptic partial differential equations.

Optimal Convergence Rates for Neural Operators Exponential convergence of deep operator networks for elliptic partial differential equations

Reference 45

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Observation 93540973-9327-47ec-9227-84d65f108cb4 · outbound

This paper cites Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithms.

Optimal Convergence Rates for Neural Operators Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithms

Reference 46

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This paper cites Foundations of Machine Learning.

Optimal Convergence Rates for Neural Operators Foundations of Machine Learning

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.476153Z

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Observation 42fec01c-61cc-4caf-b422-268a7f8fe89d · outbound

This paper cites Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem.

Optimal Convergence Rates for Neural Operators Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.658102Z

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Observation 3e3f2c8a-4c26-4c14-82de-17ae8709b9ff · outbound

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Optimal Convergence Rates for Neural Operators Functional regression

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.461487Z

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Observation eafc8dda-294a-42a5-bd4d-3df5617f850e · outbound

This paper cites How many Neurons do we need? A refined Analysis for Shallow Networks trained with Gradient Descent.

Optimal Convergence Rates for Neural Operators How many Neurons do we need? A refined Analysis for Shallow Networks trained with Gradient Descent

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:34:07.001525Z

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Observation 0e7a9191-d9bf-4b6e-aa1f-fba7c21d4afc · outbound

This paper cites Random feature approximation for general spectral methods, 2023.

Optimal Convergence Rates for Neural Operators Random feature approximation for general spectral methods, 2023

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.445844Z

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Observation 021a1337-f6ae-4970-9c46-0d3ec9d1382b · outbound

This paper cites Optimal rates for averaged stochastic gradient descent under neural tangent kernel regime.

Optimal Convergence Rates for Neural Operators Optimal rates for averaged stochastic gradient descent under neural tangent kernel regime

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.677514Z

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Observation 47bd15e7-6211-4246-a839-a97fb66f8b6d · outbound

This paper cites A measure-theoretic approach to kernel conditional mean embeddings.

Optimal Convergence Rates for Neural Operators A measure-theoretic approach to kernel conditional mean embeddings

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.420469Z

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

Observation b8c7dd52-6d63-41a2-98b4-a0db68dd403b · outbound

This paper cites Statistical optimality of stochastic gradient descent on hard learning problems through multiple passes, 2018.

Optimal Convergence Rates for Neural Operators Statistical optimality of stochastic gradient descent on hard learning problems through multiple passes, 2018

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.686997Z

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Observation 322eb4cd-47da-40ae-8adc-4988a3c76668 · outbound

This paper cites Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective.

Optimal Convergence Rates for Neural Operators Toward a Better Understanding of Fourier Neural Operators from a Spectral Perspective

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.691704Z

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Observation 4a41a8c5-b237-4e90-9c00-99efba625119 · outbound

This paper cites Raissi, P.

Optimal Convergence Rates for Neural Operators Raissi, P

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.696789Z

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Observation b7bb5930-3a89-46fe-a1e8-bb5c0ec71005 · outbound

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Optimal Convergence Rates for Neural Operators Modern non-linear function-on-function regression

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.395177Z

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Observation 7f334c10-3004-4122-a00e-c16db8b496d4 · outbound

This paper cites Generalization properties of learning with random features.

Optimal Convergence Rates for Neural Operators Generalization properties of learning with random features

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.379433Z

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Observation 2872f0f2-c117-4cca-907f-bf5d1d8c701e · outbound

This paper cites Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,\gamma_d)$.

Optimal Convergence Rates for Neural Operators Deep Learning in High Dimension: Neural Network Approximation of Analytic Functions in $L^2(\mathbb{R}^d,\gamma_d)$

Reference 59

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:34:06.964266Z

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Observation 727448b4-650f-4188-b3db-4773a92c24d8 · outbound

This paper cites Mathematical Statistics.

Optimal Convergence Rates for Neural Operators Mathematical Statistics

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.715897Z

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Observation f51fd94a-6adb-4b9d-bd84-974ed432cdd2 · outbound

This paper cites Graph neural network operators: A review.

Optimal Convergence Rates for Neural Operators Graph neural network operators: A review

Reference 61

Resolution: verified exact; doi, observed 2026-08-11T05:34:06.821648Z

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Observation 43083424-2b05-474b-b87b-c3b1297c5e73 · outbound

This paper cites Nonlinear functional regression by functional deep neural network with kernel embedding.

Optimal Convergence Rates for Neural Operators Nonlinear functional regression by functional deep neural network with kernel embedding

Reference 62

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:34:06.941253Z

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Observation a4ba7c12-8c06-462c-a598-8b8054a3e52e · outbound

This paper cites Neural-Kernel Conditional Mean Embeddings.

Optimal Convergence Rates for Neural Operators Neural-Kernel Conditional Mean Embeddings

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.729856Z

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Observation 53435c42-92b0-44eb-982a-bc8aa46bd710 · outbound

This paper cites Support vector machines.

Optimal Convergence Rates for Neural Operators Support vector machines

Reference 64

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.734665Z

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Observation 89ffd2e6-fb8a-49cd-b8de-c332b1cdd4a0 · outbound

This paper cites an unresolved cited work.

Optimal Convergence Rates for Neural Operators Unresolved cited work

Reference 65

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:34:07.345164Z

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Observation b96e5f62-f1b0-4104-8314-648cb0e8a42d · outbound

This paper cites Inverse Problem Theory and Methods for Model Parameter Estimation, volume xii.

Optimal Convergence Rates for Neural Operators Inverse Problem Theory and Methods for Model Parameter Estimation, volume xii

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.743661Z

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Observation d568738b-fb34-454f-b2a6-50d2674cb9dd · outbound

This paper cites an unresolved cited work.

Optimal Convergence Rates for Neural Operators Unresolved cited work

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.748219Z

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Observation 091f2c46-d86b-4e69-b8fd-c37d674253e6 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed deeponets.

Optimal Convergence Rates for Neural Operators Learning the solution operator of parametric partial differential equations with physics-informed deeponets

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.752926Z

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Observation c2aa5254-e40d-4281-b302-0459b939cd8b · outbound

This paper cites Convergence analysis of wide shallow neural operators within the framework of Neural Tangent Kernel.

Optimal Convergence Rates for Neural Operators Convergence analysis of wide shallow neural operators within the framework of Neural Tangent Kernel

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-11T05:34:06.756960Z

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Observation 94b07cce-d5fe-4ffc-a231-250b5068fe03 · outbound

This paper cites A type of generalization error induced by initialization in deep neural networks.

Optimal Convergence Rates for Neural Operators A type of generalization error induced by initialization in deep neural networks

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:34:07.320555Z

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Pith citing papers

Observation 063c8bc8-ad06-4e75-bc06-c971a2173460 · inbound

Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives cites this paper.

Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives Optimal Convergence Rates for Neural Operators

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T15:25:11.934896Z

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Observation b523dbd8-eafc-4d2c-9a4c-ea3805806dab · inbound

Random feature approximation for general spectral methods cites this paper.

Random feature approximation for general spectral methods Optimal Convergence Rates for Neural Operators

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T23:54:51.823150Z

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Observation 52d9b87e-b063-49a7-ad86-74a63a356d55 · inbound

Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel cites this paper.

Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel Optimal Convergence Rates for Neural Operators

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-05-15T01:58:28.944733Z

Source-reported events for the cited work

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Observation 45852925-7645-4e84-a282-34d28ae4bcaf · inbound

Ghost in the Kernel: In-Context Learning with Efficient Transformers via Domain Generalization cites this paper.

Ghost in the Kernel: In-Context Learning with Efficient Transformers via Domain Generalization Optimal Convergence Rates for Neural Operators

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-02T16:27:08.386625Z

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