Paper Citation Record · LEDGER

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification

As of 8 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2507.05533.

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

pith.paper-citation-record.v1
2507.05533 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:36:20.666328Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy5
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7a2ac66f-d9d4-410d-a706-63b8c7f364de · outbound

This paper cites ‖‖CDn W+W0 WXan−CDn W+W0 (W+W 0)Xan ‖‖ 2≤ ~O (√s√mτw∥A∥1 + √ kσw∥A∥1 ) (29).

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification ‖‖CDn W+W0 WXan−CDn W+W0 (W+W 0)Xan ‖‖ 2≤ ~O (√s√mτw∥A∥1 + √ kσw∥A∥1 ) (29)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:36:21.179924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1555f1c3-6a69-41b5-9b38-e4b15efb9b23 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:21.054730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ddca0e72-ee4a-49a8-b15d-879752d69245 · outbound

This paper cites ‖‖Dn V(0)−Dn V+V0 ‖‖ 0≤O ( (τv σv )2/3m ) (31).

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification ‖‖Dn V(0)−Dn V+V0 ‖‖ 0≤O ( (τv σv )2/3m ) (31)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:36:21.144582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 10ef93d0-bcc5-4292-8c04-8f4af8f67acf · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:21.004651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4665cbbd-e2f9-4800-b923-349b7df31b4f · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:21.107445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3cd82a5c-4f13-460b-9830-79974ce6cd34 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:21.084204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a10171dd-b5eb-444e-bd15-5659aa3101bb · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:21.031036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 67363432-6d39-4124-84f1-8d1b1cb52f18 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.977236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 29299cdf-a134-4b0a-a759-edd9d590362f · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.940552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e07c217a-b610-4eba-ba2d-e352b79d4047 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.920894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2002e6c7-e86b-48d1-8777-c63c3109c58e · outbound

This paper cites En∈V,(X,yn)∼D [‖‖CDn W0+W(W∗−W)Xa n−(Fn(X,A)−out 1 n(X,A)) ‖‖ 2 ] ≤~α2∥A∥1 (45) Proof:.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification En∈V,(X,yn)∼D [‖‖CDn W0+W(W∗−W)Xa n−(Fn(X,A)−out 1 n(X,A)) ‖‖ 2 ] ≤~α2∥A∥1 (45) Proof:

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:36:20.895037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a25a4f60-73ee-4f56-90e5-6b20486131a9 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.870976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8b0e056c-26e8-4dcc-b9d0-d3cd193a6a7a · outbound

This paper cites 3.∥W ∗Xan∥2 ≤O(∥W ∗∥F∥Xan∥2)≤O(τ w∥A∥1).

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification 3.∥W ∗Xan∥2 ≤O(∥W ∗∥F∥Xan∥2)≤O(τ w∥A∥1)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:36:20.847581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0605fa19-481d-43e9-a3ae-c6d9f9d4ea02 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.828838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1c27a755-549a-485f-b522-98d97c5b4142 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.811807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6e97aa33-872b-413e-8071-d71ce24a294a · outbound

This paper cites 25 Published in Transactions on Machine Learning Research (June/2025).

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification 25 Published in Transactions on Machine Learning Research (June/2025)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:36:20.794146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 12743e66-fdcc-4874-a25f-a160d29f8279 · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.767600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7ef9749b-c578-438d-821f-157de8afda3f · outbound

This paper cites an unresolved cited work.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:36:20.747072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 90431217-3237-4bda-8600-f6ebd509baf4 · outbound

This paper cites Graph Neural Networks Exponentially Lose Expressive Power for Node Classification.

Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification Graph Neural Networks Exponentially Lose Expressive Power for Node Classification

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-06T19:36:20.539582Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.