Paper Citation Record · LEDGER

On the Origin of Implicit Regularization in Stochastic Gradient Descent

As of 21 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 14 inbound Pith citation observations for arXiv:2101.12176.

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

pith.paper-citation-record.v1
2101.12176 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 14 of 14 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:17:24.977858Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T07:56:04.664291Z

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 e82c2006-771c-4225-873b-0e03eddb9ee9 · inbound

ConsistentFeature: A Plug-and-Play Component for Neural Network Regularization cites this paper.

ConsistentFeature: A Plug-and-Play Component for Neural Network Regularization On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-12T04:23:00.414541Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3bc75599-3baf-4d5f-b66d-7cd7fac037ac · inbound

Parameter Symmetry Potentially Unifies Deep Learning Theory cites this paper.

Parameter Symmetry Potentially Unifies Deep Learning Theory On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-08T19:58:26.846533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07613736-b5c4-4731-872c-95b963c63c15 · inbound

Improving Adaptive Moment Optimization via Preconditioner Diagonalization cites this paper.

Improving Adaptive Moment Optimization via Preconditioner Diagonalization On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-08T12:40:42.527482Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b7fe061-c67d-4684-8ae9-bb01e2d42015 · inbound

CGD: Modifying the Loss Landscape by Gradient Regularization cites this paper.

CGD: Modifying the Loss Landscape by Gradient Regularization On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T11:17:24.977858Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e052d641-3d40-4dbb-a5fd-ce1b4374dae9 · inbound

PCaM: A Progressive Focus Attention-Based Information Fusion Method for Improving Vision Transformer Domain Adaptation cites this paper.

PCaM: A Progressive Focus Attention-Based Information Fusion Method for Improving Vision Transformer Domain Adaptation On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:13.191636Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f96776b4-9007-4f4d-9ef0-1cff63f4758b · inbound

Quantum Learning with Tunable Loss Functions cites this paper.

Quantum Learning with Tunable Loss Functions On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-05T14:25:34.749658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f929555-39e3-4068-8a80-a12c73392053 · inbound

Estimating Implicit Regularization in Deep Learning cites this paper.

Estimating Implicit Regularization in Deep Learning On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 35

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T18:26:12.939958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 02b4ada8-10ca-45b1-8e48-6e24ebc16b0d · inbound

Convergence of difference inclusions: a diameter criterion and step-size conditions cites this paper.

Convergence of difference inclusions: a diameter criterion and step-size conditions On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 91

Resolution: verified exact; arxiv_id, observed 2026-05-15T02:23:31.691399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b66cfb7d-6808-4888-a784-2e0447680fd7 · inbound

Thermodynamic Irreversibility of Training Algorithms cites this paper.

Thermodynamic Irreversibility of Training Algorithms On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-22T04:41:04.236302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 28536ab3-918c-4a15-a1a8-534bdb87aebb · inbound

Second-Order Path Kernel Interpolation Formulas in Machine Learning cites this paper.

Second-Order Path Kernel Interpolation Formulas in Machine Learning On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-07-02T16:47:10.301742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 095571c4-1a73-4dd7-84fe-896870c6b559 · inbound

Gradient-Descent Steps to Success over Mean Accuracy: A Paradigm Shift for ML cites this paper.

Gradient-Descent Steps to Success over Mean Accuracy: A Paradigm Shift for ML On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:49:39.659741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 353ac356-baa8-4c09-9e26-422d56466c67 · inbound

Avoiding unsafe sets when training with Langevin Dynamics cites this paper.

Avoiding unsafe sets when training with Langevin Dynamics On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 27

Resolution: metadata mismatch; local_arxiv, observed 2026-07-09T07:56:04.665423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation eb04adba-cfe3-4a2b-8354-2c56c0b7045b · inbound

Avoiding unsafe sets when training with Langevin Dynamics cites this paper.

Avoiding unsafe sets when training with Langevin Dynamics On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T08:08:40.041993Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0de17a18-440c-4cf5-b9d1-38b6ee8c8803 · inbound

First-Order Predictable but Pairwise Fragile: Local Task Adaptation in Trained Transformers cites this paper.

First-Order Predictable but Pairwise Fragile: Local Task Adaptation in Trained Transformers On the Origin of Implicit Regularization in Stochastic Gradient Descent

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T19:55:52.781886Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.