Paper Citation Record · LEDGER

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks

As of 10 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.23397.

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

pith.paper-citation-record.v1
2607.23397 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-30T23:28:29.166212Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

24 of 24 outbound references displayed

verified exact0
verified fuzzy0
unresolved24
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 20d2af5b-5e77-4d31-a6a9-4e351ba6708f · outbound

This paper cites Allen-Zhu and Y.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Allen-Zhu and Y

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.094965Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9208b43c-0793-426e-8768-eeb159a3fac5 · outbound

This paper cites Amari, N.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Amari, N

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.098900Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce2decbc-14af-406b-909c-fc6e6fb8649f · outbound

This paper cites Amari and N.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Amari and N

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.102113Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3fec1bc2-4f19-458d-af4c-3436a3d68454 · outbound

This paper cites an unresolved cited work.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.105274Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3da90594-dfdf-4fec-8d11-ed5c423bbe17 · outbound

This paper cites Aoyagi and K.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Aoyagi and K

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.108856Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8447de5d-fde9-4a2d-b9fd-08115ecf2b19 · outbound

This paper cites Aoyagi and S.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Aoyagi and S

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.112012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 256a33de-31a2-4c93-bced-6c91ad607f63 · outbound

This paper cites an unresolved cited work.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.115426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d5c572a-fda7-498f-a203-d4ac22f18d23 · outbound

This paper cites Chizat, E.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Chizat, E

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.118401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6f5acad-eda2-46e8-8b11-a1b927161df2 · outbound

This paper cites Singular Learning Theory for Factor Analysis.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Singular Learning Theory for Factor Analysis

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.121548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98f64693-eca6-4ad3-b1d5-308a57d50659 · outbound

This paper cites Ghorbani, S.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Ghorbani, S

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.124794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47caa038-1953-4891-a802-c1cb2c177663 · outbound

This paper cites an unresolved cited work.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.127777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b167b22-37a8-411c-98b9-83b147e8fe58 · outbound

This paper cites Loss Landscape Degeneracy and Stagewise Development in Transformers.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Loss Landscape Degeneracy and Stagewise Development in Transformers

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.130740Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60dcb9fc-25c7-4b61-98c2-148cac1a2206 · outbound

This paper cites Jacot, F.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Jacot, F

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.133926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2197c168-a14b-4c11-a7e9-c05d5f1e81cb · outbound

This paper cites Kurumadani.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Kurumadani

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.136922Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 283d6811-5312-4ff4-9a28-ce004cf22bc5 · outbound

This paper cites Deep Neural Networks as Gaussian Processes.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Deep Neural Networks as Gaussian Processes

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.139978Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 97ab2d2b-0013-41df-a321-3782cd7adc90 · outbound

This paper cites Murata, S.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Murata, S

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.143174Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4be50055-3cbd-4508-b793-fe36c8fcd5ba · outbound

This paper cites Neal.Bayesian learning for neural networks, volume 118.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Neal.Bayesian learning for neural networks, volume 118

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.146005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3eccfa69-6fa4-4432-a44d-f40db4384fdd · outbound

This paper cites Watanabe.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Watanabe

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.148668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aeceb777-abe9-464d-90ad-adb6cfa1f211 · outbound

This paper cites Watanabe.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Watanabe

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.151559Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d0b1160-49c8-4853-bebf-094b686ec40d · outbound

This paper cites Watanabe.Algebraic geometry and statistical learning theory.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Watanabe.Algebraic geometry and statistical learning theory

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.154277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4278622-d035-492b-827a-b0302b02dcef · outbound

This paper cites an unresolved cited work.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.157470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba616a74-2637-4cd1-9cf7-581a241cb721 · outbound

This paper cites Yamazaki and S.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Yamazaki and S

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.160446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9820a4cd-f01f-4f08-9c51-130f373cd056 · outbound

This paper cites Yamazaki and S.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Yamazaki and S

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.163504Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86d529d8-3cce-4eb0-a94f-1355de2bac50 · outbound

This paper cites Yamazaki and S.

A Statistical Difference between Single-Layer Learning and Hierarchical Learning in Wide Neural Networks Yamazaki and S

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-30T23:28:29.166212Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.