Paper Citation Record · LEDGER

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

As of 12 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 2 inbound Pith citation observations for arXiv:2412.07728.

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

pith.paper-citation-record.v1
2412.07728 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:41:00.730775Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T01:22:49.144572Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact4
verified fuzzy1
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d5b63b37-d7e9-4890-af21-567afea6a4bf · outbound

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

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.703270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f9f0f36-a549-4ca7-baed-7c1869705b86 · outbound

This paper cites Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.709678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2bca728-6fe0-4931-9579-192bdbb05371 · outbound

This paper cites Deep Ritz revisited.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Deep Ritz revisited

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.715085Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b35d9fa-bd85-4f12-8fe9-f263e50b3b56 · outbound

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

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Optimal bump functions for shallow ReLU networks: Weight decay, depth separation and the curse of dimensionality

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:41:00.821009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fa7e21f5-6244-4c67-8dec-42a9074eb061 · outbound

This paper cites Convergence Rate Analysis for Deep Ritz Method.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Convergence Rate Analysis for Deep Ritz Method

Reference 1989

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:41:01.040381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dd713953-51bb-428c-96d2-f20396da1a34 · outbound

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

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Fourier Neural Operator for Parametric Partial Differential Equations

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.696677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c21dd88-fb2d-4cbd-bccd-53b9fb1221ed · outbound

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

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Some observations on high-dimensional partial differential equations with Barron data

Reference 2020

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:41:00.984480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0d880e8f-8867-49f0-a147-bc82104b16fc · outbound

This paper cites Uniform convergence guarantees for the deep ritz method for nonlinear problems.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Uniform convergence guarantees for the deep ritz method for nonlinear problems

Reference 2021

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:41:01.061524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f72d64a3-b50a-4e92-b202-d619de9f0f83 · outbound

This paper cites On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective On the Banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.671545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd956a2f-75cc-4b51-a0be-68a1ad2f7697 · outbound

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

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.690696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff80adea-cb0f-4b04-91fc-74a115bc14df · outbound

This paper cites Error Analysis of Deep Ritz Methods for Elliptic Equations.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Error Analysis of Deep Ritz Methods for Elliptic Equations

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T18:41:00.684834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f13e1c25-fe5e-4227-9e59-0c78e42ba12d · outbound

This paper cites Embedding Inequalities for Barron-type Spaces.

Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective Embedding Inequalities for Barron-type Spaces

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:41:00.785082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

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

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method cites this paper.

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

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc115aac-ee50-49ef-bdc5-17ae04a7d49c · inbound

The Barron-Lipschitz Energy Gap and Depth Separation Phenomena in Scientific Machine Learning cites this paper.

The Barron-Lipschitz Energy Gap and Depth Separation Phenomena in Scientific Machine Learning Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-01T01:22:49.144572Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.