Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data | Paper Citation Record

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This paper cites Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Weighted Sobolev Approximation Rates for Neural Networks on Unbounded Domains

Reference 1

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This paper cites Designing universal causal deep learning models: The geometric (hyper) transformer.Mathematical Finance, 34(2):671–735, 2024.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Designing universal causal deep learning models: The geometric (hyper) transformer.Mathematical Finance, 34(2):671–735, 2024

Reference 2

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This paper cites Slic superpixels compared to state-of-the-art superpixel methods.IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(11):2274–2282, 2012.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Slic superpixels compared to state-of-the-art superpixel methods.IEEE Transactions on Pattern Analysis and Machine Intelligence, 34(11):2274–2282, 2012

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This paper cites Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data

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This paper cites Scale-sensitive dimensions, uniform convergence, and learnability.Journal of the ACM (JACM), 44(4):615–631, 1997.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Scale-sensitive dimensions, uniform convergence, and learnability.Journal of the ACM (JACM), 44(4):615–631, 1997

Reference 5

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This paper cites Scale-sensitive dimensions, uniform convergence, and learnability.J.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Scale-sensitive dimensions, uniform convergence, and learnability.J

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This paper cites On the properties of variational approximations of gibbs posteriors.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data On the properties of variational approximations of gibbs posteriors

Reference 7

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This paper cites Some fine properties of sets of finite perimeter in ahlfors regular metric measure spaces.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Some fine properties of sets of finite perimeter in ahlfors regular metric measure spaces

Reference 8

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This paper cites On a theory of learning with similarity functions.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data On a theory of learning with similarity functions

Reference 9

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

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Universal approximation bounds for superpositions of a sigmoidal function

Reference 10

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This paper cites Spectrally-normalized margin bounds for neural networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Spectrally-normalized margin bounds for neural networks

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This paper cites Nearly-tight vc-dimension and pseudodimension bounds for piecewise linear neural networks.Journal of MachineLearning Research, 20(63):1– 17, 2019.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Nearly-tight vc-dimension and pseudodimension bounds for piecewise linear neural networks.Journal of MachineLearning Research, 20(63):1– 17, 2019

Reference 12

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Observation 5ff09a1f-13c1-42af-99aa-ec6bd0db3274 · outbound

This paper cites Vapnik-chervonenkis dimension of neural nets.The handbook of brain theory and neural networks, pages 1188–1192, 2003.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Vapnik-chervonenkis dimension of neural nets.The handbook of brain theory and neural networks, pages 1188–1192, 2003

Reference 13

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Observation a205771d-b87e-4d4f-a9b3-3d2cee7721d5 · outbound

This paper cites On numerical computation for the distribution of the convolution ofN independent rectified Gaussian variables.J.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data On numerical computation for the distribution of the convolution ofN independent rectified Gaussian variables.J

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This paper cites Learnability and the vapnik-chervonenkis dimension.Journal of the ACM (JACM), 36(4):929–965, 1989.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Learnability and the vapnik-chervonenkis dimension.Journal of the ACM (JACM), 36(4):929–965, 1989

Reference 15

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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.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Optimal approximation with sparsely connected deep neural networks.SIAM Journal on Mathematics of Data Science, 1(1):8–45, 2019

Reference 16

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This paper cites Practical existence theorems for deep learning approximation in high dimensions.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Practical existence theorems for deep learning approximation in high dimensions

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This paper cites Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics

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This paper cites Physics-informed neural networks (pinns) for fluid mechanics: A review.Acta Mechanica Sinica, 37(12):1727–1738, 2021.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Physics-informed neural networks (pinns) for fluid mechanics: A review.Acta Mechanica Sinica, 37(12):1727–1738, 2021

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Observation 436a3680-a451-4c07-aab9-6f4983f8ed6c · outbound

This paper cites Dimension-free log-sobolev inequalities for mixture distributions.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Dimension-free log-sobolev inequalities for mixture distributions

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This paper cites Characterizing overfitting in kernel ridgeless regression through the eigenspectrum.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Characterizing overfitting in kernel ridgeless regression through the eigenspectrum

Reference 21

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This paper cites A comprehensive analysis on the learning curve in kernel ridge regression.Advancesin Neural Information Processing Systems, 37:24659–24723, 2024.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data A comprehensive analysis on the learning curve in kernel ridge regression.Advancesin Neural Information Processing Systems, 37:24659–24723, 2024

Reference 22

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This paper cites A theoretical analysis of the test error of finite-rank kernel ridge regression.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data A theoretical analysis of the test error of finite-rank kernel ridge regression

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This paper cites Efficient approximation of high-dimensional functions with neural networks.IEEE Transactions on Neural Networks and Learning Systems, 33(7):3079– 3093, 2021.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Efficient approximation of high-dimensional functions with neural networks.IEEE Transactions on Neural Networks and Learning Systems, 33(7):3079– 3093, 2021

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This paper cites Optimal stable nonlinear approximation.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Optimal stable nonlinear approximation

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This paper cites An improved uniform convergence bound with fat-shattering dimension.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data An improved uniform convergence bound with fat-shattering dimension

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This paper cites Scientific machine learning through physics–informed neural networks: Where we are and what’s next.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Scientific machine learning through physics–informed neural networks: Where we are and what’s next

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Observation 67310d2b-505a-4eb0-8a7e-336300263a0f · outbound

This paper cites Approximation by superpositions of a sigmoidal function.Mathematics of Control, Signals and Systems, 2(4):303–314, 1989.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Approximation by superpositions of a sigmoidal function.Mathematics of Control, Signals and Systems, 2(4):303–314, 1989

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This paper cites Nonlinear approxima- tion and (deep) relu networks.Constructive Approximation, 55(1):127–172, 2022.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Nonlinear approxima- tion and (deep) relu networks.Constructive Approximation, 55(1):127–172, 2022

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This paper cites Rogue waves and large deviations in deep sea.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Rogue waves and large deviations in deep sea

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Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Unresolved cited work

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This paper cites Wavelet compression and nonlinear n-widths.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Wavelet compression and nonlinear n-widths

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This paper cites Learning multivariate log-concave distributions.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Learning multivariate log-concave distributions

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This paper cites Memorization with neural nets: Going beyond the worst case.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Memorization with neural nets: Going beyond the worst case

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This paper cites Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data

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This paper cites Vc dimension of graph neural networks with pfaffian activation functions.Neural Networks, 182:106924, 2025.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Vc dimension of graph neural networks with pfaffian activation functions.Neural Networks, 182:106924, 2025

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This paper cites On the efficiency of erm in feature learning.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data On the efficiency of erm in feature learning

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This paper cites Springer, 1997.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Springer, 1997

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This paper cites Benefits of additive noise in composing classes with bounded capacity.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Benefits of additive noise in composing classes with bounded capacity

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This paper cites Sum-of-squares proofs of logarithmic sobolev inequalities on finite markov chains.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Sum-of-squares proofs of logarithmic sobolev inequalities on finite markov chains

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This paper cites Efficient graph-based image segmentation.International Journal of Computer Vision, 59(2):167–181, 2004.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Efficient graph-based image segmentation.International Journal of Computer Vision, 59(2):167–181, 2004

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This paper cites Sample compression, learnability, and the vapnik-chervonenkis dimension.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Sample compression, learnability, and the vapnik-chervonenkis dimension

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This paper cites A practical existence theorem for reduced order models based on convolutional autoencoders.Foundations of Data Science, 7(1):72–98, 2025.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data A practical existence theorem for reduced order models based on convolutional autoencoders.Foundations of Data Science, 7(1):72–98, 2025

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This paper cites Benign overfitting without linearity: Neural network classifiers trained by gradient descent for noisy linear data.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Benign overfitting without linearity: Neural network classifiers trained by gradient descent for noisy linear data

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Observation 2ce89b83-8b00-4725-9ab6-2f79e360e3e9 · outbound

This paper cites On the approximate realization of continuous mappings by neural networks.Neural networks, 2(3):183–192, 1989.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data On the approximate realization of continuous mappings by neural networks.Neural networks, 2(3):183–192, 1989

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This paper cites Scaling description of generalization with number of parameters in deep learning.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Scaling description of generalization with number of parameters in deep learning

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This paper cites Random feature neural networks learn black-scholes type pdes without curse of dimensionality.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Random feature neural networks learn black-scholes type pdes without curse of dimensionality

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.263034Z

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Observation 1b758a22-ea81-4ba1-9d80-5960b993bb1a · outbound

This paper cites Risk bounds for reservoir computing.Journal of Machine Learning Research, 21(240):1–61, 2020.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Risk bounds for reservoir computing.Journal of Machine Learning Research, 21(240):1–61, 2020

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Observation 10ea82f1-372c-4249-9da4-1581a0b0a31e · outbound

This paper cites A new proof of szemerédi’s theorem.Geometric & Functional Analysis GAFA, 11(3):465– 588, 2001.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data A new proof of szemerédi’s theorem.Geometric & Functional Analysis GAFA, 11(3):465– 588, 2001

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Observation b1e9f30e-709f-4185-8e0a-2b2b0b0094b6 · outbound

This paper cites Universal function approximation by deep neural nets with bounded width and relu activations.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Universal function approximation by deep neural nets with bounded width and relu activations

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Observation 746e2942-bd0b-43f4-a09a-fdc5ab73d076 · outbound

This paper cites Probability inequalities for sums of bounded random variables.J.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Probability inequalities for sums of bounded random variables.J

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.214546Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 08cfef2c-51c7-41e7-82e3-a3ae0305dd92 · outbound

This paper cites Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity

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Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.102611Z

Source-reported events for the cited work

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Observation 158e3600-77b1-4f40-8ed8-6e88ba9992d1 · outbound

This paper cites Horn and Charles R.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Horn and Charles R

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.202989Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f77593e1-e5f7-4b5a-8c45-ab169f382f95 · outbound

This paper cites Multilayer feedforward networks are universal approximators.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Multilayer feedforward networks are universal approximators

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.109136Z

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Observation 997a6988-a872-421a-a3e4-14a68d44b62c · outbound

This paper cites Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks.Neural networks, 3(5):551–560, 1990.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks.Neural networks, 3(5):551–560, 1990

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.112083Z

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Observation e7552dd5-ba2d-4c61-88fb-b62f8add477c · outbound

This paper cites Instance-dependent generalization bounds via optimal transport.Journal of Machine Learning Research, 24(349):1–51, 2023.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Instance-dependent generalization bounds via optimal transport.Journal of Machine Learning Research, 24(349):1–51, 2023

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.176332Z

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Observation d969f136-a2dd-4206-b512-655e62077d4f · outbound

This paper cites Learning image priors through patch-based diffusion models for solving inverse problems.Advancesin Neural Information Processing Systems, 37:1625–1660, 2024.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Learning image priors through patch-based diffusion models for solving inverse problems.Advancesin Neural Information Processing Systems, 37:1625–1660, 2024

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.163463Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0be3bad-c53f-4622-9812-aa9046628b05 · outbound

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

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Neural tangent kernel: Convergence and generalization in neural networks

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.151002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e83c85af-11ec-4608-9ac0-2b71d11d29e0 · outbound

This paper cites Deep neural networks with relu-sine-exponential activations break curse of dimensionality in approximation on hölder class.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Deep neural networks with relu-sine-exponential activations break curse of dimensionality in approximation on hölder class

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.138190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dc72d492-8e24-496a-85df-af7b031fe64b · outbound

This paper cites Universal approximation with deep narrow networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Universal approximation with deep narrow networks

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.125790Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bcdab113-170f-4eac-a76b-2a2064ca52ff · outbound

This paper cites Provable memorization capacity of transformers.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Provable memorization capacity of transformers

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.113526Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8e27d569-e0ae-4d24-a828-38a98b7f22df · outbound

This paper cites Benignoverfittingintwo-layerreluconvolutional neural networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Benignoverfittingintwo-layerreluconvolutional neural networks

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.102069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 86addfbe-3a60-4943-8ce0-ee385054a6fc · outbound

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

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Neural operator: Learning maps between function spaces with applications to pdes

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.136527Z

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Observation a56e90ec-ced0-42a2-a087-3fcc4d7f77a1 · outbound

This paper cites Small transformers compute universal metric embeddings.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Small transformers compute universal metric embeddings

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.082419Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 176dbf16-26da-40ad-8009-8b4d397fc23b · outbound

This paper cites Is In-Context Universality Enough? MLPs are Also Universal In-Context.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Is In-Context Universality Enough? MLPs are Also Universal In-Context

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.142441Z

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Observation 81bb2d03-3475-46d6-be2c-21695f9105d6 · outbound

This paper cites Universal approximation theorems for differentiable geometric deep learning.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Universal approximation theorems for differentiable geometric deep learning

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.070137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 30540c55-3a27-450b-96cf-d5c45d04c6ab · outbound

This paper cites Sur l’intégration des fonctions discontinues.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Sur l’intégration des fonctions discontinues

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.057526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dddf0e92-6330-421b-978c-c8e37317f49c · outbound

This paper cites Oracle inequalities for high-dimensional prediction.Bernoulli, 25(2):1225–1255, 2019.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Oracle inequalities for high-dimensional prediction.Bernoulli, 25(2):1225–1255, 2019

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.044688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 63e7e358-402e-445f-b4f4-a824904f7b44 · outbound

This paper cites Springer-Verlag, Berlin, 1991.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Springer-Verlag, Berlin, 1991

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.031713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2a1fb042-7d99-498a-a3a6-1714f0057f71 · outbound

This paper cites Lower bounds on the vc-dimension of smoothly parametrized function classes.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Lower bounds on the vc-dimension of smoothly parametrized function classes

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:13:00.016177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7c873cfe-aec8-48eb-9b9e-cbf4a8df8148 · outbound

This paper cites Higher-Order Transformer Derivative Estimates for Explicit Pathwise Learning Guarantees.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Higher-Order Transformer Derivative Estimates for Explicit Pathwise Learning Guarantees

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.161173Z

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Unavailable: canonical work link unavailable.

Observation 0088cf96-b902-4ff6-8e9a-75492ff46040 · outbound

This paper cites Network In Network.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Network In Network

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.164642Z

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Unavailable: canonical work link unavailable.

Observation 6fc56a7f-4828-4f3a-8fa4-559ef720c079 · outbound

This paper cites Relating data compression and learnability, 1986.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Relating data compression and learnability, 1986

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.998305Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6c96bace-4dd9-488c-928e-9e0afc152a84 · outbound

This paper cites Citeseer, 1996.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Citeseer, 1996

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.986249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1b38a275-b6d7-49ec-9627-47cddf6234f7 · outbound

This paper cites Deep network approximation for smooth functions.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Deep network approximation for smooth functions

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.973285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4b30f3b3-ad1a-481b-8dc4-d397bb0cf661 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machineintelligence, 3(3):218–229, 2021.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.Nature machineintelligence, 3(3):218–229, 2021

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.961050Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9ae10ef9-8649-4c51-8e1c-c38b68ee8561 · outbound

This paper cites Superpixel-based image segmentation using convex optimization.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Superpixel-based image segmentation using convex optimization

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.949037Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 573f25b5-449c-48f0-85e9-b486fa14e952 · outbound

This paper cites Memory capacity of two layer neural networks with smooth activations.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Memory capacity of two layer neural networks with smooth activations

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.936535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fba0bc47-90d7-4a48-af6a-fa2f433139cd · outbound

This paper cites Concentration Inequalities and Model Selection.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Concentration Inequalities and Model Selection

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.925859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48950d9c-bfd4-4772-bdf7-d9932b9f7a2d · outbound

This paper cites The generalization error of random features regression: Precise asymptotics and the double descent curve.Communications on Pure and Applied Mathematics, 75(4):667–766, 2022.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data The generalization error of random features regression: Precise asymptotics and the double descent curve.Communications on Pure and Applied Mathematics, 75(4):667–766, 2022

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.188688Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78b784e5-f09c-4db3-8528-86710a652234 · outbound

This paper cites Understanding the dynamics of the frequency bias in neural networks, 2024.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Understanding the dynamics of the frequency bias in neural networks, 2024

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.909295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cca3c2e9-b0a8-487c-aaf3-3d7161527c3c · outbound

This paper cites Sample compression schemes for vc classes.Journal of the ACM (JACM), 63(3):1–10, 2016.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Sample compression schemes for vc classes.Journal of the ACM (JACM), 63(3):1–10, 2016

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.897932Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 522d6279-3232-45db-850f-b6709127a134 · outbound

This paper cites Simplicity bias in 1-hidden layer neural networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Simplicity bias in 1-hidden layer neural networks

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.888012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b63d93bc-16b8-4ecc-a58c-d357512a98f2 · outbound

This paper cites Robust feature learning for multi-index models in high dimensions.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Robust feature learning for multi-index models in high dimensions

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.877108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ce33b782-8c76-4f5f-8bb2-30939a58d50e · outbound

This paper cites Universal approximation property of Banach space-valued random feature models including random neural networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Universal approximation property of Banach space-valued random feature models including random neural networks

Reference 85

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.203986Z

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Observation b6619cc1-933b-4a46-8e0a-d1023c0888c3 · outbound

This paper cites A PAC-bayesian approach to spectrally- normalized margin bounds for neural networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data A PAC-bayesian approach to spectrally- normalized margin bounds for neural networks

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.865692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b4726d83-07a3-448c-9c65-505922e8074b · outbound

This paper cites Fast samplers for inverse problems in iterative refinement models.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Fast samplers for inverse problems in iterative refinement models

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.853931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a5df71a5-201a-4d21-8009-7a05bdc98ae3 · outbound

This paper cites Optimal approximation of piecewise smooth functions using deep relu neural networks.Neural Networks, 108:296–330, 2018.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Optimal approximation of piecewise smooth functions using deep relu neural networks.Neural Networks, 108:296–330, 2018

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.213464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fbea8ccc-c40d-4ad7-9ccd-e4c20acb5a28 · outbound

This paper cites Mathematical theory of deep learning.arXiv preprint, 2024.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Mathematical theory of deep learning.arXiv preprint, 2024

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.836506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 06c9aeba-d301-4036-afda-7f04b227ce05 · outbound

This paper cites Lipschitz widths.ConstructiveApproximation, 57(2):759–805, 2023.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Lipschitz widths.ConstructiveApproximation, 57(2):759–805, 2023

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.825899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4f1983e7-3f2a-4dcd-bb93-6f05752812b8 · outbound

This paper cites n-widths in approximation theory, volume 7 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)].

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data n-widths in approximation theory, volume 7 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.815676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 57d04c48-57fa-495f-b466-108435c80b6f · outbound

This paper cites I-theory on depth vs width: hierarchical function composition.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data I-theory on depth vs width: hierarchical function composition

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.805870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0a7aeb68-2b29-4e77-9bba-96edff00503b · outbound

This paper cites Compositional sparsity of learnable functions.Bulletin of the American Mathematical Society, 61(3):438–456, 2024.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Compositional sparsity of learnable functions.Bulletin of the American Mathematical Society, 61(3):438–456, 2024

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.795377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 51cf89b3-2748-4482-89e1-b22c9807a7d2 · outbound

This paper cites Random features for large-scale kernel machines.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Random features for large-scale kernel machines

Reference 94

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.232612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3278677a-5582-4c3b-b1bf-31c44acc3a80 · outbound

This paper cites Learning a classification model for segmentation.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Learning a classification model for segmentation

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.778453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3ba7776b-be07-48b9-a56e-1d5d51613b9c · outbound

This paper cites Generating Rectifiable Measures through Neural Networks.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Generating Rectifiable Measures through Neural Networks

Reference 96

Resolution: unresolved; no resolver link, observed 2026-08-05T13:12:59.238677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9158be5c-d05b-4781-b4df-74ae4a796f10 · outbound

This paper cites Nonparametric regression via deep neural networks.The Annals of Statistics, 48(4):1875–1897, 2020.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Nonparametric regression via deep neural networks.The Annals of Statistics, 48(4):1875–1897, 2020

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.768606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3644dd05-d54a-4f3b-acde-722ae91dac93 · outbound

This paper cites Nonlocal techniques for the analysis of deep ReLU neural network approximations.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Nonlocal techniques for the analysis of deep ReLU neural network approximations

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Resolution: verified exact; local_arxiv, observed 2026-08-05T13:12:59.343986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6c35d260-12c5-4c72-9dab-c835f7fb3ef3 · outbound

This paper cites A multivariate Riesz basis of ReLU neural networks.Appl.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data A multivariate Riesz basis of ReLU neural networks.Appl

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.757792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 73412c9b-aee9-453d-9656-283be00b3030 · outbound

This paper cites Pac-bayesian generalisation error bounds for gaussian process classification.

Beyond Universal Approximation Theorems: Algorithmic Uniform Approximation by Neural Networks Trained with Noisy Data Pac-bayesian generalisation error bounds for gaussian process classification

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:12:59.744932Z

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