Paper Citation Record · LEDGER

Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

As of 31 July 2026, this Paper Citation Record lists 0 of 0 outbound references and 23 inbound Pith citation observations for arXiv:2103.00065.

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

pith.paper-citation-record.v1
2103.00065 v3

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-07-31T06:34:12.847434+00:00

measured 23 of 23 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-01T06:19:17.851285Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T13:59:52.014628Z

Reference resolution

0 of 0 outbound references displayed

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verified fuzzy0
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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 b5c34744-65d8-4e17-b670-37cf072e8632 · inbound

A Physics-Inspired Optimizer: Velocity Regularized Adam cites this paper.

A Physics-Inspired Optimizer: Velocity Regularized Adam Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-22T14:34:54.236532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation b9109b34-c621-40c6-a836-0ff90d2b81fc · inbound

Flat Channels to Infinity in Neural Loss Landscapes cites this paper.

Flat Channels to Infinity in Neural Loss Landscapes Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 49

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T08:57:13.180565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation f4603a85-6774-493e-932b-69e80de4147e · inbound

Contribution of task-irrelevant stimuli to drift of neural representations cites this paper.

Contribution of task-irrelevant stimuli to drift of neural representations Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 38

Resolution: metadata mismatch; arxiv_id, observed 2026-05-18T05:15:54.252256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 62266676-88cc-494c-aa57-60709ed26025 · inbound

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

Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T13:20:26.343484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation da9489f5-9e3d-40c3-be9d-e73b69c5c6ae · inbound

Generalization at the Edge of Stability cites this paper.

Generalization at the Edge of Stability Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T02:38:17.376010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 97ff5d34-7b0b-4cec-84e3-fc0defb83d1b · inbound

Layer-wise Geometric Approximation Rates for Deep Networks cites this paper.

Layer-wise Geometric Approximation Rates for Deep Networks Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 9

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T13:36:07.856659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 09268dd0-8a5f-44a0-bfbc-63af3c71e4ec · inbound

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

There Will Be a Scientific Theory of Deep Learning Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 114

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:21:09.133215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation fc28b148-6b29-4d01-823e-5207b8ee2902 · inbound

The Spectral Lifecycle of Transformer Training: Transient Compression Waves, Persistent Spectral Gradients, and the Q/K--V Asymmetry cites this paper.

The Spectral Lifecycle of Transformer Training: Transient Compression Waves, Persistent Spectral Gradients, and the Q/K--V Asymmetry Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-05-13T20:58:15.707347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 5415084a-48c8-4b62-bfd0-0c45f3a1af32 · inbound

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer cites this paper.

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T03:05:53.385062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 52ef7d8d-4af6-4aaf-bafe-c716d5a388ce · inbound

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer cites this paper.

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-05-22T10:26:24.090330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 0003ae66-7cfe-4074-b0a2-e86fa509b454 · inbound

Muon is Not That Special: Random or Inverted Spectra Work Just as Well cites this paper.

Muon is Not That Special: Random or Inverted Spectra Work Just as Well Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-13T04:17:13.710639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 6f93dd4d-da9d-4684-896c-683e334c08f9 · inbound

Convergence of difference inclusions via a diameter criterion cites this paper.

Convergence of difference inclusions via a diameter criterion Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 142

Resolution: verified exact; arxiv_id, observed 2026-05-15T02:23:31.712040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 8beb7f2e-f307-4a9c-a031-4898b8d4f14d · inbound

Does Weight Decay Enhance Training Stability? cites this paper.

Does Weight Decay Enhance Training Stability? Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 18

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T19:53:42.974508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 70d76439-9e88-4f86-8abe-521162f662ea · inbound

Factor Augmented High-Dimensional SGD cites this paper.

Factor Augmented High-Dimensional SGD Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-20T03:33:01.672110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation c556039a-76c0-4e68-a8d2-1196cd84b577 · inbound

Why Muon Outperforms Adam: A Curvature Perspective cites this paper.

Why Muon Outperforms Adam: A Curvature Perspective Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 133

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:06:44.929203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 21f6cb1f-6336-4f55-adec-9b2f04f3573d · inbound

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network cites this paper.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:36:52.024353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 3a27da96-2448-452a-b926-44eb2e35705c · inbound

Preserving Plasticity in Continual Learning via Dynamical Isometry cites this paper.

Preserving Plasticity in Continual Learning via Dynamical Isometry Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T00:07:28.533864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 24a244be-c2b4-48de-b867-027fbd1872cb · inbound

The Hidden Power of Scaling Factor in LoRA Optimization cites this paper.

The Hidden Power of Scaling Factor in LoRA Optimization Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 104

Resolution: verified exact; arxiv_id, observed 2026-07-03T14:08:21.893561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 0afe8914-c7f2-4f60-8274-56f4bc685d12 · inbound

Compute Efficiency and Serial Runtime Tradeoffs for Stochastic Momentum Methods cites this paper.

Compute Efficiency and Serial Runtime Tradeoffs for Stochastic Momentum Methods Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T23:59:07.495055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation caf1d49f-8eb8-4e9b-be18-079834fa318c · inbound

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale cites this paper.

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:29:15.278476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 76d6279e-7039-4194-8d26-d0990a0a8214 · inbound

Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective cites this paper.

Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 30

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T06:29:38.158808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 3cdaa2a7-dee8-4957-810a-7b8432c70ef2 · inbound

Evaluation-Strategy Gap in Fault Diagnosis of Deep Learning Programs cites this paper.

Evaluation-Strategy Gap in Fault Diagnosis of Deep Learning Programs Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T13:59:52.016229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.

Observation 09a69c9f-9173-43b3-9a22-4a954a069fa4 · inbound

Radial Suppression Accelerates Algorithmic Generalization: A Geometric Analysis of Delayed Generalization cites this paper.

Radial Suppression Accelerates Algorithmic Generalization: A Geometric Analysis of Delayed Generalization Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-07-01T09:45:39.731226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-07-31T06:34:12.847434+00:00.