Paper Citation Record · LEDGER

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method

As of 21 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.25100.

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pith.paper-citation-record.v1
2607.25100 v1

Coverage vector

measured 24 of 24 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-31T01:28:52.574414Z

measured 24 of 24 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

24 of 24 outbound references displayed

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Outbound references

Observation 872f5845-2ebc-4c1e-ae04-f9abebc8a5bb · outbound

This paper cites Weighted variation spaces and approximation by shallow ReLU networks.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Weighted variation spaces and approximation by shallow ReLU networks

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.217988Z

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Observation 7b39d13f-8685-42de-8830-b3300742333f · outbound

This paper cites Some observations on high-dimensional partial differential equations with Barron data.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Some observations on high-dimensional partial differential equations with Barron data

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.456076Z

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Observation 54143cd1-341d-4100-b70c-ec769592ed0a · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Neural Operator: Learning Maps Between Function Spaces

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.733155Z

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Observation b4649cb9-4dc5-468b-b7cd-e38669275cea · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.035158Z

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Observation aad5e193-a9a1-4d59-9007-673b87f4908d · outbound

This paper cites Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.311702Z

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Observation 5eb4fe4f-4521-4488-a16c-c8a89fcce4cc · outbound

This paper cites Characterization of the Variation Spaces Corresponding to Shallow Neural Networks.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Characterization of the Variation Spaces Corresponding to Shallow Neural Networks

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.744632Z

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Observation ab0b1631-89c7-4914-97ef-70aec3c5653f · outbound

This paper cites Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.956317Z

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Observation f4241aeb-42b5-49b2-b7c6-58c53ab1c766 · outbound

This paper cites Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:52.255571Z

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Observation bfdbe00d-fccb-471e-abf3-1e1d2d311897 · outbound

This paper cites On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:52.356953Z

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Observation 0481235c-f819-4636-a39b-c4ee92791e19 · outbound

This paper cites Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:52.415993Z

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Observation f994d0ef-5542-4436-adf7-27e1dc89e149 · outbound

This paper cites A deep learning framework for multi- operator learning: Architectures and approximation theory.arXiv preprint arXiv:2510.25379,.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method A deep learning framework for multi- operator learning: Architectures and approximation theory.arXiv preprint arXiv:2510.25379,

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:52.493256Z

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Observation da45c706-e881-4da4-afc2-3365e27384d9 · outbound

This paper cites Approximation Rates for Neural Networks with General Activation Functions.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Approximation Rates for Neural Networks with General Activation Functions

Reference 1967

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.623342Z

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Observation 8e0ecda4-51a0-4ccd-9ade-b4989a69da49 · outbound

This paper cites Optimal Learning.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Optimal Learning

Reference 1993

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:49.591907Z

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Observation 5e3781c6-5881-49cd-a574-6c3b05e489e8 · outbound

This paper cites A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case

Reference 1996

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.514439Z

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Observation 7fa3f1a2-dd12-470e-adfc-7b203a9cb2b9 · outbound

This paper cites Group Equivariant Fourier Neural Operators for Partial Differential Equations.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Group Equivariant Fourier Neural Operators for Partial Differential Equations

Reference 1999

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.569807Z

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Observation bd8e9d0b-3ff4-43c0-bc61-33562122ef1f · outbound

This paper cites Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.414359Z

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Observation 78a4209d-db59-4545-8a12-1061626c5442 · outbound

This paper cites A Priori Estimates of the Population Risk for Two-layer Neural Networks.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method A Priori Estimates of the Population Risk for Two-layer Neural Networks

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.346796Z

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Observation d4605f87-b36e-415e-9133-cdfcfc03abac · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Fourier Neural Operator for Parametric Partial Differential Equations

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:51.185547Z

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Observation 33104f7b-ef56-4dc2-9b88-c334c2ddfd27 · outbound

This paper cites Uniform convergence guarantees for the deep ritz method for nonlinear problems.Advances in Continuous and Discrete Models, 2022(1):49,.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Uniform convergence guarantees for the deep ritz method for nonlinear problems.Advances in Continuous and Discrete Models, 2022(1):49,

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.059133Z

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Observation 728abed7-90df-4a3e-81d3-1e02294adef1 · outbound

This paper cites Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:50.918033Z

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Observation d2232cc5-c5c9-4ecc-8351-1df45a1a1a78 · outbound

This paper cites Penalising the biases in norm regularisation enforces sparsity.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Penalising the biases in norm regularisation enforces sparsity

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:49.704555Z

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Observation 7586c435-6170-4f69-9280-dc1cbc91d0e2 · outbound

This paper cites Neural network approximation and estimation of classifiers with classification boundary in a Barron class.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Neural network approximation and estimation of classifiers with classification boundary in a Barron class

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:49.919987Z

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Observation c89e0cce-aaab-425e-b708-512b381679eb · outbound

This paper cites $L^p$ sampling numbers for the Fourier-analytic Barron space.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method $L^p$ sampling numbers for the Fourier-analytic Barron space

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:52.137341Z

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Observation 53bd941d-ca06-4c76-b7ad-755785e41268 · outbound

This paper cites Embedding Inequalities for Barron-type Spaces.

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method Embedding Inequalities for Barron-type Spaces

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-07-31T01:28:52.574414Z

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Pith citing papers

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