Paper Citation Record · LEDGER

Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 15 inbound Pith citation observations for arXiv:2209.15594.

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

pith.paper-citation-record.v1
2209.15594 v2

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 15 of 15 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:02:02.722413Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T01:36:25.956789Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 1f81effb-2561-47aa-8d35-7dfb5cac33f9 · inbound

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime cites this paper.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.198993Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1a7b6cb-426e-498a-a214-fc73dc0b9ce0 · inbound

Explicit Eigenvalue Regularization Improves Sharpness-Aware Minimization cites this paper.

Explicit Eigenvalue Regularization Improves Sharpness-Aware Minimization Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T17:03:52.546794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72ce4171-3c84-466e-aae6-18d88d9c1737 · inbound

Understanding Nonlinear Implicit Bias via Region Counts in Input Space cites this paper.

Understanding Nonlinear Implicit Bias via Region Counts in Input Space Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-15T21:02:02.722413Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d90b3ed-1708-4a31-9ffe-4439889297a8 · inbound

A Simple Baseline for Stable and Plastic Neural Networks cites this paper.

A Simple Baseline for Stable and Plastic Neural Networks Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-06T17:42:25.909229Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7604fb6-215e-4de5-bd4d-98f76b7bd56c · inbound

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws cites this paper.

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T04:14:13.930335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 119d2b94-81d1-4d1a-8015-e2aa696a5d79 · inbound

Large Spikes in Stochastic Gradient Descent: A Large-Deviations View cites this paper.

Large Spikes in Stochastic Gradient Descent: A Large-Deviations View Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 12

Resolution: metadata mismatch; arxiv_id, observed 2026-05-15T13:30:51.070901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4a59c5dd-41c2-4ac3-b191-b20c925b3126 · inbound

Momentum Further Constrains Sharpness at the Edge of Stochastic Stability cites this paper.

Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-10T13:20:26.360965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fd4b51c4-943d-48db-aa5a-087876556671 · inbound

Generalization at the Edge of Stability cites this paper.

Generalization at the Edge of Stability Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-10T02:38:17.378266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7ef65137-366f-4513-a22c-8cad09e9440a · inbound

There Will Be a Scientific Theory of Deep Learning cites this paper.

There Will Be a Scientific Theory of Deep Learning Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 188

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T15:21:09.326744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e0331472-078d-48c9-ab24-2081f85a1847 · inbound

Does Weight Decay Enhance Training Stability? cites this paper.

Does Weight Decay Enhance Training Stability? Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 23

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T19:53:42.986120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 78f984c0-33c7-466d-9ed4-f0f7f048d90c · inbound

AMUSE: Anytime Muon with Stable Gradient Evaluation cites this paper.

AMUSE: Anytime Muon with Stable Gradient Evaluation Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-05-22T07:24:43.302560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8438635a-c40b-4a4f-9b14-2df854aa0bdb · inbound

Non-normal spectral signatures of instability in neural network training dynamics cites this paper.

Non-normal spectral signatures of instability in neural network training dynamics Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-25T05:20:25.103050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation edece159-2f00-4d91-aee3-386638b14828 · inbound

Mapping Whisper Representations to Human ECoG Responses with Interpretable Time-Resolved Neural Encoding cites this paper.

Mapping Whisper Representations to Human ECoG Responses with Interpretable Time-Resolved Neural Encoding Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 33

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T01:36:25.959011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 79358591-213f-4307-9368-4f7e2c9b7964 · inbound

A Defense of the Quadratic Model cites this paper.

A Defense of the Quadratic Model Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T06:58:10.110169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f139322-272b-4ed7-8ee9-0d94c53d1198 · inbound

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations cites this paper.

Mini-batch Noise Lowers Sharpness via Dominant-Subspace Fluctuations Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T03:56:20.955662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.