Paper Citation Record · LEDGER

Gradient descent aligns the layers of deep linear networks

As of 6 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 11 inbound Pith citation observations for arXiv:1810.02032.

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

pith.paper-citation-record.v1
1810.02032 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 11 of 11 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-01T00:37:16.364388Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

22
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 9fbe3cd9-3aca-4a2f-bd38-aad8767b1ed4 · inbound

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models cites this paper.

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models Gradient descent aligns the layers of deep linear networks

Reference 160

Resolution: metadata mismatch; local_arxiv, observed 2026-05-14T23:00:21.450892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c1c9018d-85d8-4613-b9ef-a9b1cac8049a · inbound

Prediction horizon shapes representations in predictive learning cites this paper.

Prediction horizon shapes representations in predictive learning Gradient descent aligns the layers of deep linear networks

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-05-17T23:30:29.285468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 64d2a43b-906c-4817-870c-e6afb88a40a6 · inbound

The Effect of Mini-Batch Noise on the Implicit Bias of Adam cites this paper.

The Effect of Mini-Batch Noise on the Implicit Bias of Adam Gradient descent aligns the layers of deep linear networks

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-05-16T08:07:34.293910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 5c7d5a50-b564-460d-9995-6094367d7ea9 · inbound

Implicit Bias in Deep Linear Discriminant Analysis cites this paper.

Implicit Bias in Deep Linear Discriminant Analysis Gradient descent aligns the layers of deep linear networks

Reference 10

Resolution: metadata mismatch; local_arxiv, observed 2026-05-15T16:50:10.520373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 08ea6666-a977-4098-b3b0-ae34e07774dd · inbound

A Theory of Saddle Escape in Deep Nonlinear Networks cites this paper.

A Theory of Saddle Escape in Deep Nonlinear Networks Gradient descent aligns the layers of deep linear networks

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-11T16:51:05.759084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 4982cdbd-8c6c-454c-9722-b0abd0166899 · inbound

A Theory of Saddle Escape in Deep Nonlinear Networks cites this paper.

A Theory of Saddle Escape in Deep Nonlinear Networks Gradient descent aligns the layers of deep linear networks

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-11T02:25:54.529769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b536fac9-d327-4687-b69f-0e632e4ce183 · inbound

A Theory of Saddle Escape in Deep Nonlinear Networks cites this paper.

A Theory of Saddle Escape in Deep Nonlinear Networks Gradient descent aligns the layers of deep linear networks

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-07-01T00:45:12.078658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 7cd8703b-570e-43db-9de6-244da623ccf6 · inbound

On the global convergence of gradient descent for wide shallow models with bounded nonlinearities cites this paper.

On the global convergence of gradient descent for wide shallow models with bounded nonlinearities Gradient descent aligns the layers of deep linear networks

Reference 47

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:51:31.351983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation d0003375-3f8c-426a-b74b-19ee20a8b0ff · inbound

A Theory on Flow Matching with Neural Networks cites this paper.

A Theory on Flow Matching with Neural Networks Gradient descent aligns the layers of deep linear networks

Reference 186

Resolution: metadata mismatch; local_arxiv, observed 2026-07-03T00:47:30.982898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 548f2c45-f15c-4253-b8d8-7abf240ca5c8 · inbound

Conservation Laws from Data Symmetry in Neural Networks cites this paper.

Conservation Laws from Data Symmetry in Neural Networks Gradient descent aligns the layers of deep linear networks

Reference 7

Resolution: metadata mismatch; local_arxiv, observed 2026-07-03T04:27:36.920204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation f12b4763-c9a2-4f83-875a-f89169785ca5 · inbound

Conservation Laws for Modern Neural Architectures cites this paper.

Conservation Laws for Modern Neural Architectures Gradient descent aligns the layers of deep linear networks

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-07-03T19:58:54.968938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.