Paper Citation Record · LEDGER

What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

As of 23 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2110.06914.

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

pith.paper-citation-record.v1
2110.06914 v4

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 6 of 6 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T23:59:06.748883Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T13:29:51.107084Z

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 c3ddbce7-a85d-496c-8ab8-520f4038a6a5 · inbound

Flat Minima and Generalization: Insights from Stochastic Convex Optimization cites this paper.

Flat Minima and Generalization: Insights from Stochastic Convex Optimization What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-03T23:59:06.748883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73fa5173-53fe-4a43-aaac-e20723a5eb90 · inbound

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

There Will Be a Scientific Theory of Deep Learning What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Reference 116

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:21:09.087209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 103f340c-adb1-4626-bd1b-27cc3e7db9e5 · inbound

Learning reveals invisible structure in low-rank RNNs cites this paper.

Learning reveals invisible structure in low-rank RNNs What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Reference 52

Resolution: verified exact; arxiv_id, observed 2026-05-09T06:15:39.629570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6e989c14-8fc8-43ed-a284-37603b06c757 · inbound

Structure Before Collapse: Transient semantic geometry in next-token prediction cites this paper.

Structure Before Collapse: Transient semantic geometry in next-token prediction What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Reference 63

Resolution: verified exact; arxiv_id, observed 2026-07-04T13:29:51.108675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a91732b5-8a33-4533-8355-532226874663 · inbound

SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates cites this paper.

SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Reference 180

Resolution: verified exact; arxiv_id, observed 2026-07-01T13:05:45.487916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 616721de-02b5-48b8-ac41-9974eefc8543 · inbound

Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse cites this paper.

Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse What Happens after SGD Reaches Zero Loss? --A Mathematical Framework

Reference 245

Resolution: unresolved; no resolver link, observed 2026-07-12T01:11:50.444218Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.