Paper Citation Record · LEDGER

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime

As of 21 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2412.08025.

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

pith.paper-citation-record.v1
2412.08025 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:24:51.314185Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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

34 of 34 outbound references displayed

verified exact5
verified fuzzy13
unresolved15
parse uncertain0
malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f38370d-4d88-4c11-a4d3-69e4634f363d · outbound

This paper cites write newline.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.142602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6474ad6a-05c3-4519-82da-9fb7342e4545 · outbound

This paper cites Learning threshold neurons via the "edge of stability".

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Learning threshold neurons via the "edge of stability"

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:24:51.831893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d11fc630-2f00-4f19-9fcb-0129ce158e23 · outbound

This paper cites Understanding the unstable convergence of gradient descent.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Understanding the unstable convergence of gradient descent

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.187862Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 483bd577-c5e5-4df7-b7fa-e8295fdc932a · outbound

This paper cites Sgd with large step sizes learns sparse features.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Sgd with large step sizes learns sparse features

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.168834Z

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Observation e3ff6228-a4af-462f-9152-7d26fa804205 · outbound

This paper cites Understanding gradient descent on the edge of stability in deep learning.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Understanding gradient descent on the edge of stability in deep learning

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.149905Z

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Observation e352d899-9244-43b9-b649-6f996da1098e · outbound

This paper cites On the implicit bias of initialization shape: Beyond infinitesimal mirror descent.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime On the implicit bias of initialization shape: Beyond infinitesimal mirror descent

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.132896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 751385cd-a14f-4897-8101-24889bee5a00 · outbound

This paper cites Beyond the Edge of Stability via Two-step Gradient Updates.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Beyond the Edge of Stability via Two-step Gradient Updates

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.176834Z

Source-reported events for the cited work

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Observation 1002f453-7854-449a-8dca-7dfd44cc2c7e · outbound

This paper cites From Stability to Chaos: Analyzing Gradient Descent Dynamics in Quadratic Regression.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime From Stability to Chaos: Analyzing Gradient Descent Dynamics in Quadratic Regression

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:24:51.765477Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 33225560-e65c-4f56-83ff-1775a5231b0e · outbound

This paper cites Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.188915Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79ccf2dd-ffcd-4839-baf2-ae9e5c278dab · outbound

This paper cites Adaptive Gradient Methods at the Edge of Stability.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Adaptive Gradient Methods at the Edge of Stability

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.193730Z

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

This paper cites Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability.

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 ed4f646d-e280-46be-bd75-a89bcce84557 · outbound

This paper cites (S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime (S)GD over Diagonal Linear Networks: Implicit Regularisation, Large Stepsizes and Edge of Stability

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:24:51.662471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b86c9b12-6fa4-433f-aa90-2c219fbbed24 · outbound

This paper cites Implicit regularization in matrix factorization.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Implicit regularization in matrix factorization

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.114607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d8c788d9-94d8-494d-ae8a-17e7998f2bdc · outbound

This paper cites Mirrorless mirror descent: A natural derivation of mirror descent.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Mirrorless mirror descent: A natural derivation of mirror descent

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.087944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fe94f36a-9f00-483e-af3e-3c1376b33a84 · outbound

This paper cites Catastrophic fisher explosion: Early phase fisher matrix impacts generalization.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Catastrophic fisher explosion: Early phase fisher matrix impacts generalization

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.065624Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1142ad88-cd98-486b-bef6-16ef4ff7b3a1 · outbound

This paper cites The large learning rate phase of deep learning: the catapult mechanism.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime The large learning rate phase of deep learning: the catapult mechanism

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.219961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8064f1ad-9919-4082-9ff2-43454289109d · outbound

This paper cites Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Analyzing Sharpness along GD Trajectory: Progressive Sharpening and Edge of Stability

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:24:51.619061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ed2273d5-564c-4d62-b9cc-e921175c3c5e · outbound

This paper cites Benign Oscillation of Stochastic Gradient Descent with Large Learning Rates.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Benign Oscillation of Stochastic Gradient Descent with Large Learning Rates

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:24:51.579781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f5136e04-f5ce-42ff-ab9b-3afe1d2fcd84 · outbound

This paper cites Beyond the Quadratic Approximation: the Multiscale Structure of Neural Network Loss Landscapes.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Beyond the Quadratic Approximation: the Multiscale Structure of Neural Network Loss Landscapes

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.234132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea30ca56-aea6-4dda-a65c-28b5fed5ac11 · outbound

This paper cites Implicit bias of the step size in linear diagonal neural networks.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Implicit bias of the step size in linear diagonal neural networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.240397Z

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Unavailable: canonical work link unavailable.

Observation 07560856-4949-4528-8b77-7d4d4db7db25 · outbound

This paper cites Saddle-to-saddle dynamics in diagonal linear networks.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Saddle-to-saddle dynamics in diagonal linear networks

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:52.027908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation dd650404-14d0-47c2-92cc-d494bf0cd3ad · outbound

This paper cites Implicit bias of sgd for diagonal linear networks: a provable benefit of stochasticity.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Implicit bias of sgd for diagonal linear networks: a provable benefit of stochasticity

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.249702Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6adf75ba-b2cd-43a8-8b83-c61f845413c5 · outbound

This paper cites An introduction to dynamical systems: continuous and discrete, volume 19.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime An introduction to dynamical systems: continuous and discrete, volume 19

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:51.992000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 336dda9c-cddc-4344-8e58-bd68ab2c8fae · outbound

This paper cites Trajectory alignment: Understanding the edge of stability phenomenon via bifurcation theory.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Trajectory alignment: Understanding the edge of stability phenomenon via bifurcation theory

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:51.970724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0297764c-e62a-483d-8caa-64c65e08fcf7 · outbound

This paper cites Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:51.952070Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 55b37765-6ee7-4d09-92bd-51942e17622d · outbound

This paper cites Implicit regularization for optimal sparse recovery.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Implicit regularization for optimal sparse recovery

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.268831Z

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Observation bbe7704b-65de-4e4f-9196-a0db20119e6e · outbound

This paper cites Kernel and rich regimes in overparametrized models.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Kernel and rich regimes in overparametrized models

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.274145Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3982304a-2926-4eb0-85d2-b7ec67e59443 · outbound

This paper cites Implicit bias of gradient descent for logistic regression at the edge of stability.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Implicit bias of gradient descent for logistic regression at the edge of stability

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:51.908842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b2a3e90f-2d60-4e9b-8ebb-ae3732c5dff8 · outbound

This paper cites A Walk with SGD.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime A Walk with SGD

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.286278Z

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Observation ef13f003-8d92-4c70-afc1-bc8c30a79cbd · outbound

This paper cites High-dimensional linear regression via implicit regularization.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime High-dimensional linear regression via implicit regularization

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:24:51.884097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9d1bcfc3-f137-4377-9cda-a0af33294d2c · outbound

This paper cites Understanding Edge-of-Stability Training Dynamics with a Minimalist Example.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Understanding Edge-of-Stability Training Dynamics with a Minimalist Example

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.296334Z

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Unavailable: canonical work link unavailable.

Observation 311ec9f8-2df3-4f01-9186-0f50fdbd5437 · outbound

This paper cites @esa (Ref.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime @esa (Ref

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.303475Z

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Observation 39ed2dbd-1f28-4840-906e-522b404a9746 · outbound

This paper cites an unresolved cited work.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-11T18:24:51.308817Z

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Observation c1846828-8e08-40a6-bdb5-a5423f1d0f70 · outbound

This paper cites reference.

Criteria and Bias of Parameterized Linear Regression under Edge of Stability Regime reference

Reference 34

Resolution: malformed identifier; no resolver link, observed 2026-08-11T18:24:51.314185Z

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Pith citing papers

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