Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width | Paper Citation Record

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This paper cites SIAM, 2022.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width SIAM, 2022

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This paper cites cambridge university press, 2009.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width cambridge university press, 2009

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This paper cites Universal approximation bounds for superpositions of a sigmoidal function.IEEE Transactions on Information theory, 39(3):930–945, 1993.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Universal approximation bounds for superpositions of a sigmoidal function.IEEE Transactions on Information theory, 39(3):930–945, 1993

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

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Nearly- tight vc-dimension and pseudodimension bounds for piecewise linear neural networks

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This paper cites Shallow and deep networks are near-optimal approximators of korobov functions.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Shallow and deep networks are near-optimal approximators of korobov functions

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This paper cites Optimal approximation with sparsely connected deep neural networks.SIAM Journal on Mathematics of Data Science, 1(1):8–45, 2019.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Optimal approximation with sparsely connected deep neural networks.SIAM Journal on Mathematics of Data Science, 1(1):8–45, 2019

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Unresolved cited work

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This paper cites Breaking the curse of di- mensionality in sparse polynomial approximation of parametric pdes.Journal de Math´ ematiques Pures et Appliqu´ ees, 103(2):400–428, 2015.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Breaking the curse of di- mensionality in sparse polynomial approximation of parametric pdes.Journal de Math´ ematiques Pures et Appliqu´ ees, 103(2):400–428, 2015

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This paper cites Analytic regularity and poly- nomial approximation of parametric and stochastic elliptic pde’s.Analysis and Ap- plications, 9(01):11–47, 2011.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Analytic regularity and poly- nomial approximation of parametric and stochastic elliptic pde’s.Analysis and Ap- plications, 9(01):11–47, 2011

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This paper cites Approximation by superpositions of a sigmoidal function.Mathe- matics of control, signals and systems, 2(4):303–314, 1989.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Approximation by superpositions of a sigmoidal function.Mathe- matics of control, signals and systems, 2(4):303–314, 1989

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Neural network approximation

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This paper cites Exponential convergence of the deep neural network approximation for analytic functions.Science China Mathematics, 61(10):1733–1740, 2018.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Exponential convergence of the deep neural network approximation for analytic functions.Science China Mathematics, 61(10):1733–1740, 2018

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This paper cites Chapman and Hall/CRC, 2015.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Chapman and Hall/CRC, 2015

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This paper cites Error bounds for approxima- tions with deep relu neural networks in w s, p norms.Analysis and Applications, 18(05):803–859, 2020.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Error bounds for approxima- tions with deep relu neural networks in w s, p norms.Analysis and Applications, 18(05):803–859, 2020

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This paper cites Approximation rates for neural networks with encodable weights in smoothness spaces.Neural Networks, 134:107–130, 2021.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Approximation rates for neural networks with encodable weights in smoothness spaces.Neural Networks, 134:107–130, 2021

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This paper cites Decision theoretic generalizations of the pac model for neural net and other learning applications.Information and computation, 100(1):78–150, 1992.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Decision theoretic generalizations of the pac model for neural net and other learning applications.Information and computation, 100(1):78–150, 1992

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This paper cites Sphere packing numbers for subsets of the boolean n-cube with bounded vapnik-chervonenkis dimension.Journal of Combinatorial Theory, Series A, 69(2):217–232, 1995.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Sphere packing numbers for subsets of the boolean n-cube with bounded vapnik-chervonenkis dimension.Journal of Combinatorial Theory, Series A, 69(2):217–232, 1995

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This paper cites Simultaneous neural network approximation for smooth functions.Neural Networks, 154:152–164, 2022.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Simultaneous neural network approximation for smooth functions.Neural Networks, 154:152–164, 2022

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This paper cites Approximation capabilities of multilayer feedforward networks.Neural networks, 4(2):251–257, 1991.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Approximation capabilities of multilayer feedforward networks.Neural networks, 4(2):251–257, 1991

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This paper cites On estimation of analytic functions.Studia Sci Math Hungarica, 34:191–210, 1998.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width On estimation of analytic functions.Studia Sci Math Hungarica, 34:191–210, 1998

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This paper cites Springer Science & Business Media, 2013.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Springer Science & Business Media, 2013

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Unresolved cited work

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This paper cites Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors.The Annals of Statistics, 51(2):691–716, 2023.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Deep nonparametric regression on approximate manifolds: Nonasymptotic error bounds with polynomial prefactors.The Annals of Statistics, 51(2):691–716, 2023

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This paper cites Approximation bounds for norm con- strained neural networks with applications to regression and gans.Applied and Computational Harmonic Analysis, 65:249–278, 2023.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Approximation bounds for norm con- strained neural networks with applications to regression and gans.Applied and Computational Harmonic Analysis, 65:249–278, 2023

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width On the rate of convergence of fully connected deep neural network regression estimates.The Annals of Statistics, 49(4):2231–2249, 2021

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Multilayer feedforward networks with a nonpolynomial activation function can approximate any function.Neural networks, 6(6):861–867, 1993

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Some super-approximation rates of relu neural net- works for korobov functions.arXiv preprint arXiv:2507.10345, 2025

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Unresolved cited work

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Deep network approxi- mation for smooth functions.SIAM Journal on Mathematical Analysis, 53(5):5465– 5506, 2021

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Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width The ex- pressive power of neural networks: A view from the width.Advances in neural information processing systems, 30, 2017

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Observation 60dc5fc2-39ff-4e12-bd76-292730487ad4 · outbound

This paper cites Representation Benefits of Deep Feedforward Networks.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Representation Benefits of Deep Feedforward Networks

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Observation 2b5ab01b-ee7f-4f18-96e3-200dbf60d6d4 · outbound

This paper cites Springer series in statistics.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Springer series in statistics

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Observation 3909b7e6-352a-4284-a8dd-1e7765a1599b · outbound

This paper cites Cambridge university press, 2019.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Cambridge university press, 2019

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Observation 85c53e66-56fd-4ac5-b853-4a99e847a44a · outbound

This paper cites Deep neural networks with general activations: Super- convergence in sobolev norms.arXiv preprint arXiv:2508.05141, 2025.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Deep neural networks with general activations: Super- convergence in sobolev norms.arXiv preprint arXiv:2508.05141, 2025

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Observation 3f9063ae-25ed-43f8-bde7-0a3b499045b0 · outbound

This paper cites Near-optimal deep neural network approximation for korobov functions with respect to lp and h1 norms.Neural Networks, 180:106702, 2024.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Near-optimal deep neural network approximation for korobov functions with respect to lp and h1 norms.Neural Networks, 180:106702, 2024

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Observation 8231fe03-6fb4-458c-a195-d291bc1e6ed3 · outbound

This paper cites Nearly optimal vc-dimension and pseudo-dimension bounds for deep neural network derivatives.Advances in Neural Information Processing Systems, 36:21721–21756, 2023.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Nearly optimal vc-dimension and pseudo-dimension bounds for deep neural network derivatives.Advances in Neural Information Processing Systems, 36:21721–21756, 2023

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Resolution: unresolved; no resolver link, observed 2026-07-14T10:37:37.440024Z

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Observation 1ded229f-23dc-4eab-9483-fd6363bbd1a5 · outbound

This paper cites On the optimal approximation of sobolev and besov functions using deep relu neural networks.Applied and Computational Harmonic Analysis, page 101797, 2025.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width On the optimal approximation of sobolev and besov functions using deep relu neural networks.Applied and Computational Harmonic Analysis, page 101797, 2025

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Observation 95a5af10-4358-49d6-a072-8eae804afdfe · outbound

This paper cites Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks

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Observation 1eff7212-adc0-494b-9f29-ecff5e18cdbd · outbound

This paper cites Optimal rates of approximation by shallow relu k neural networks and applications to nonparametric regression.Constructive Approximation, 62(2):329–360, 2025.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Optimal rates of approximation by shallow relu k neural networks and applications to nonparametric regression.Constructive Approximation, 62(2):329–360, 2025

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Observation 33d91b89-1643-4130-9eb8-1a04a6a7f018 · outbound

This paper cites Error bounds for approximations with deep relu networks.Neural networks, 94:103–114, 2017.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Error bounds for approximations with deep relu networks.Neural networks, 94:103–114, 2017

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Observation 593a81d2-14bf-4b8b-8af6-96ef24dc1fff · outbound

This paper cites Optimal approximation of continuous functions by very deep relu networks.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Optimal approximation of continuous functions by very deep relu networks

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Observation 281b6637-8c8f-4cbb-bbdd-278a2bb17bc9 · outbound

This paper cites Deep network approximation: Be- yond relu to diverse activation functions.Journal of Machine Learning Research, 25(35):1–39, 2024.

Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width Deep network approximation: Be- yond relu to diverse activation functions.Journal of Machine Learning Research, 25(35):1–39, 2024

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