Paper Citation Record · LEDGER

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

As of 16 August 2026, this Paper Citation Record lists 99 of 99 outbound references and 10 inbound Pith citation observations for arXiv:2505.00351.

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pith.paper-citation-record.v1
2505.00351 v2

Coverage vector

measured 99 of 99 reference resolution

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measured 10 of 10 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:14:01.456811Z

measured 1 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

99 of 99 outbound references displayed

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Outbound references

Observation 6a2169db-8dce-487a-a802-2ae316b0f41b · outbound

This paper cites Support vector machines.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Support vector machines

Reference 1

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This paper cites Breaking the curse of dimensionality with convex ne ural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Breaking the curse of dimensionality with convex ne ural networks

Reference 2

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This paper cites On the equivalence between kernel quadrature r ules and random feature ex- pansions.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks On the equivalence between kernel quadrature r ules and random feature ex- pansions

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This paper cites Universal approximation bounds for superpo sitions of a sigmoidal function.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Universal approximation bounds for superpo sitions of a sigmoidal function

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This paper cites Approximation and estimation bounds for artiﬁ cial neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation and estimation bounds for artiﬁ cial neural networks

Reference 5

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation and learning by greedy algorithms

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This paper cites Nearly-tight vc- dimension and pseudodimension bounds for piecewise linear neural ne tworks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Nearly-tight vc- dimension and pseudodimension bounds for piecewise linear neural ne tworks

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This paper cites Bartlett and Shahar Mendelson.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Bartlett and Shahar Mendelson

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Two models of double descent for weak features

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This paper cites Springer Science & Business Media, 2012.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Springer Science & Business Media, 2012

Reference 10

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This paper cites Optimal asymptotic bounds for spherical designs.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Optimal asymptotic bounds for spherical designs

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This paper cites C oncentration inequalities.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks C oncentration inequalities

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Projection bodies

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This paper cites Weak type estimates for Cesaro sums of Jacobi polynomial series , volume 487.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Weak type estimates for Cesaro sums of Jacobi polynomial series , volume 487

Reference 14

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This paper cites Bridgin g traditional and machine learning-based algorithms for solving pdes: the random feature me thod.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Bridgin g traditional and machine learning-based algorithms for solving pdes: the random feature me thod

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks The random fea ture method for solving interface problems

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Unresolved cited work

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This paper cites Learning theory: an approximation theory viewpoint , volume 24.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Learning theory: an approximation theory viewpoint , volume 24

Reference 18

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation by superpositions of a sigmoida l function

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation theory and harmonic analysis on spheres and b alls

Reference 20

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This paper cites Local randomized neural network s with hybridized discontin- uous petrov–galerkin methods for stokes–darcy ﬂows.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Local randomized neural network s with hybridized discontin- uous petrov–galerkin methods for stokes–darcy ﬂows

Reference 21

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Neural ne twork approximation

Reference 22

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Nonlinear approximation

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Constructive approximation, volume 303

Reference 24

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This paper cites Some remarks on greed y algorithms.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Some remarks on greed y algorithms

Reference 25

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Local extreme learning machines and domain decomposition for solving linear and nonlinear partial diﬀerential equations

Reference 26

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Physics informed extreme le arning machine (pielm)–a rapid method for the numerical solution of partial diﬀerential equa tions

Reference 27

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks A priori estimates of the populat ion risk for two-layer neural networks

Reference 28

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks The barron space and the ﬂow-in duced function spaces for neural network models

Reference 29

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Representation formulas and pointwise properties for barron functions

Reference 30

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Generalisation error in learning with random features and the hidden manifold model

Reference 31

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This paper cites Deep neural networks with random gaussian weights: A universal classiﬁcation strategy? IEEE Transactions on Signal Process- ing, 64(13):3444–3457, 2016.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Deep neural networks with random gaussian weights: A universal classiﬁcation strategy? IEEE Transactions on Signal Process- ing, 64(13):3444–3457, 2016

Reference 32

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This paper cites Delving de ep into rectiﬁers: Surpassing human-level performance on imagenet classiﬁcation.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Delving de ep into rectiﬁers: Surpassing human-level performance on imagenet classiﬁcation

Reference 33

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Multilayer feedforward networks are universal approximators

Reference 34

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Universality laws for high-dimensional learn ing with random features

Reference 35

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Universal approximation using incre- mental constructive feedforward networks with random hidden n odes

Reference 36

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Extreme learning machine: theory and applications

Reference 37

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Stochastic choice of basis funct ions in adaptive function ap- proximation and the functional-link net

Reference 38

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Norming sets and spherica l cubature formulas

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.283409Z

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This paper cites A simple lemma on greedy approximation in hilbert spac e and convergence rates for projection pursuit regression and neural network tra ining.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks A simple lemma on greedy approximation in hilbert spac e and convergence rates for projection pursuit regression and neural network tra ining

Reference 40

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This paper cites Approximation by comb inations of relu and squared relu ridge functions with l1 and l0 controls.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation by comb inations of relu and squared relu ridge functions with l1 and l0 controls

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.225839Z

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This paper cites On linear dimensionality of topolog ical vector spaces.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks On linear dimensionality of topolog ical vector spaces

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.188837Z

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This paper cites Some problems in the theory of ridge functions.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Some problems in the theory of ridge functions

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.154226Z

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks K˚ urkov´ a and M

Reference 44

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks K˚ urkov´ a and M

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.093004Z

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Deep learning

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.060811Z

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This paper cites Multilayer feedforward networks with a nonpolynomial activation function can approximate any function.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Multilayer feedforward networks with a nonpolynomial activation function can approximate any function

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:25.020625Z

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Observation b3523eae-c7e7-41d6-aa94-51f1675ebe59 · outbound

This paper cites Approximation of funct ions of ﬁnite variation by superpositions of a sigmoidal function.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation of funct ions of ﬁnite variation by superpositions of a sigmoidal function

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:24.994875Z

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Towar ds a uniﬁed analysis of random fourier features

Reference 49

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This paper cites Lower bounds of the discretiz ation error for piecewise polynomials.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Lower bounds of the discretiz ation error for piecewise polynomials

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Is extreme lea rning machine feasible? a theoretical assessment (part 1)

Reference 51

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Randomized nonlinear component analysis

Reference 52

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This paper cites Dee p neural networks with ﬁxed width can be universal approximators.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Dee p neural networks with ﬁxed width can be universal approximators

Reference 53

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This paper cites Uniform approximatio n rates and metric entropy of shallow neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Uniform approximatio n rates and metric entropy of shallow neural networks

Reference 54

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This paper cites On the near optimality of the stocha stic approximation of smooth functions by neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks On the near optimality of the stocha stic approximation of smooth functions by neural networks

Reference 55

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Random approximants and neural networks

Reference 56

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This paper cites Uniform approximation by neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Uniform approximation by neural networks

Reference 57

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This paper cites Approximation rat es for shallow reluk neural networks on sobolev spaces via the radon transform.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation rat es for shallow reluk neural networks on sobolev spaces via the radon transform

Reference 58

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Do neural networks have better app roximation properties than polynomials or ﬁnite elements for high-dimensional problems? preprint, 2025

Reference 59

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This paper cites Rates of approximation by relu sh allow neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Rates of approximation by relu sh allow neural networks

Reference 60

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Type et cotype dans les espaces munis de structure s locales inconditionnelles

Reference 61

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This paper cites The generalization error of ra ndom features regression: Precise asymptotics and the double descent curve.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks The generalization error of ra ndom features regression: Precise asymptotics and the double descent curve

Reference 62

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This paper cites A new function space from barron cla ss and application to neural network approximation.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks A new function space from barron cla ss and application to neural network approximation

Reference 63

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This paper cites Spherical marcinkiewicz-z ygmund inequalities and positive quadrature.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Spherical marcinkiewicz-z ygmund inequalities and positive quadrature

Reference 64

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Tractability of approximation by general shallow networks

Reference 65

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Eignets for function approximation on m anifolds

Reference 66

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This paper cites Kernel-based analysis of massive data.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Kernel-based analysis of massive data

Reference 67

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation properties of a mu ltilayered feedforward artiﬁcial neural network

Reference 68

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This paper cites Weighted quadrature formulas a nd approximation by zonal function networks on the sphere.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Weighted quadrature formulas a nd approximation by zonal function networks on the sphere

Reference 69

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This paper cites Foundations of Machine Learn- ing.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Foundations of Machine Learn- ing

Reference 70

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This paper cites The random feature mod el for input-output maps between banach spaces.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks The random feature mod el for input-output maps between banach spaces

Reference 71

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This paper cites Learnin g and generalization charac- teristics of the random vector functional-link net.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Learnin g and generalization charac- teristics of the random vector functional-link net

Reference 72

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This paper cites Approximation by ridge functions and neu ral networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation by ridge functions and neu ral networks

Reference 73

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This paper cites Approximation theory of the mlp model in neural net works.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Approximation theory of the mlp model in neural net works

Reference 74

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Remarques sur un r´ esultat non publi´ e de B

Reference 75

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This paper cites Random features for large-sca le kernel machines.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Random features for large-sca le kernel machines

Reference 76

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This paper cites Uniform approximation of functio ns with random bases.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Uniform approximation of functio ns with random bases

Reference 77

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This paper cites Weighted sums of random kitchen sinks: Replacing mini- mization with randomization in learning.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Weighted sums of random kitchen sinks: Replacing mini- mization with randomization in learning

Reference 78

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This paper cites On random weights and unsupervised feature learning.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks On random weights and unsupervised feature learning

Reference 79

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This paper cites Zu einem problem von shephard ¨ uber die projek tionen konvexer k¨ orper.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Zu einem problem von shephard ¨ uber die projek tionen konvexer k¨ orper

Reference 80

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This paper cites Understanding machine learning: From theory to algorithms.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Understanding machine learning: From theory to algorithms

Reference 81

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Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Optimal approximation rates for deep relu ne ural networks on sobolev and besov spaces

Reference 82

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This paper cites Greedy training algorithms for neural networks and applications to pdes.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Greedy training algorithms for neural networks and applications to pdes

Reference 84

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Observation 6aab6b51-5d71-4e4d-9eb3-e2f42a80b11a · outbound

This paper cites High-order approximation ra tes for shallow neural net- works with cosine and ReLUk activation functions.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks High-order approximation ra tes for shallow neural net- works with cosine and ReLUk activation functions

Reference 85

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Observation fb2c3c09-8e1f-4966-8637-466c6d8a8733 · outbound

This paper cites Optimal convergence rates for the orthogonal greedy algorithm.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Optimal convergence rates for the orthogonal greedy algorithm

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.873238Z

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This paper cites Sharp bounds on the approx imation rates, metric entropy, and n-widths of shallow neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Sharp bounds on the approx imation rates, metric entropy, and n-widths of shallow neural networks

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.835267Z

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This paper cites Characterization of the var iation spaces corresponding to shallow neural networks.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Characterization of the var iation spaces corresponding to shallow neural networks

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.795580Z

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Observation 2b6a0765-e825-4698-91b5-c9872b6a5b72 · outbound

This paper cites Singular integrals and diﬀerentiability properties of fun ctions.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Singular integrals and diﬀerentiability properties of fun ctions

Reference 89

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This paper cites Introduction to Fourier analysis on Euclidean spaces , vol- ume 1.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Introduction to Fourier analysis on Euclidean spaces , vol- ume 1

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.750792Z

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Observation 57a7ca6c-16b8-4952-96ef-ce3948af36d7 · outbound

This paper cites Szeg¨ o.Orthogonal polynomials, volume 23 of Amer.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Szeg¨ o.Orthogonal polynomials, volume 23 of Amer

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.725996Z

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Observation 175afac9-2d64-43fd-b2a5-0f81ea3e9455 · outbound

This paper cites Greedy approximation.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Greedy approximation

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.701237Z

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Observation 3022604c-407d-486e-8196-42b7ed935e0c · outbound

This paper cites Wainwright.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Wainwright

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.669149Z

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Observation eb9eca53-1962-48f3-ba06-1614d449425a · outbound

This paper cites An extreme learning machine-bas ed method for computa- tional pdes in higher dimensions.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks An extreme learning machine-bas ed method for computa- tional pdes in higher dimensions

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.644165Z

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Observation c8d1d622-0625-461a-948e-afe80a2ad969 · outbound

This paper cites Iterative methods by space decomposition and sub space correction.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Iterative methods by space decomposition and sub space correction

Reference 95

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Observation f9e539d1-b5bf-49e9-bdf7-bf575261f121 · outbound

This paper cites Finite neuron method and convergence analysis.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Finite neuron method and convergence analysis

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.578817Z

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Observation 8c7607f7-9f2d-4656-ab2f-f3165c01d867 · outbound

This paper cites Randomized Greedy Algorithms for Neural Network Optimization.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Randomized Greedy Algorithms for Neural Network Optimization

Reference 97

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Observation 5ede2d74-dbbb-4f3c-8d0c-1fb0701105fb · outbound

This paper cites Optimal rates of approximat ion by shallow relu k neural networks and applications to nonparametric regression.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Optimal rates of approximat ion by shallow relu k neural networks and applications to nonparametric regression

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.549725Z

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Observation 0d912c59-c073-4b97-b0d1-28d20040f1ee · outbound

This paper cites Sup -norm approximation bounds for networks through probabilistic methods.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Sup -norm approximation bounds for networks through probabilistic methods

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.521724Z

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Observation 48e487e6-761f-4bab-a66b-f79a4a53df9c · outbound

This paper cites Trans ferable neural networks for partial diﬀerential equations.

Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks Trans ferable neural networks for partial diﬀerential equations

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:56:23.479117Z

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Pith citing papers

Observation 9bac93bc-c39a-411b-abb8-949a35bb4f6e · inbound

Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks cites this paper.

Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-15T22:00:20.890588Z

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Observation 634f9e38-9802-44ff-8824-b09a61b69d8d · inbound

Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs cites this paper.

Adaptive Randomized Neural Networks with Locally Activation Function: Theory and Algorithm for Solving PDEs Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:40:59.971219Z

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Observation 68966dfb-20d2-4b5b-b141-551349ffa8d5 · inbound

Exact Convex Reformulations of Linear Neural Networks via Completely Positive Lifting cites this paper.

Exact Convex Reformulations of Linear Neural Networks via Completely Positive Lifting Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-20T13:38:19.309845Z

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Observation d12785ea-5e5b-425e-860b-44dfb252ae19 · 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 Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 150

Resolution: verified exact; arxiv_id, observed 2026-05-22T07:31:14.027898Z

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Observation db603299-b28c-4a12-8c2e-326c47adc6f1 · inbound

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

Reference 54

Resolution: verified exact; arxiv_id, observed 2026-06-30T17:14:57.095714Z

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Observation cb7fde86-4d4a-4fd1-b149-edc860b60e79 · inbound

Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain $L^p$ Ridge Integral Spaces for ReLU$^k$ Networks cites this paper.

Sharp Sobolev Sandwich and Approximation Rates of Radon-Domain $L^p$ Ridge Integral Spaces for ReLU$^k$ Networks Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-07-04T18:40:02.563295Z

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Observation befc5516-450a-4c63-8a59-69cd296033a6 · inbound

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains cites this paper.

Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-01T11:05:41.681859Z

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Observation 667c7e0a-d018-4739-a550-f63b874cfcc8 · inbound

ReLU$^k$ Neural de Rham Complexes cites this paper.

ReLU$^k$ Neural de Rham Complexes Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T04:44:44.166201Z

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Observation c5ea7eb1-6caf-400b-bef6-48cb52c7f067 · inbound

Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View cites this paper.

Do Neural Networks Really Beat the Curse of Dimensionality? A Bit-Complexity View Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T15:14:01.456811Z

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Observation 7bbd1dcd-6000-40cc-a7e6-51bd5e5231d2 · inbound

Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples cites this paper.

Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples Integral Representations of Sobolev Spaces via ReLU$^k$ Activation Function and Optimal Error Estimates for Linearized Networks

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-10T22:36:38.483855Z

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