Paper Citation Record · LEDGER

The Geometry of Sign Gradient Descent

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 11 inbound Pith citation observations for arXiv:2002.08056.

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

pith.paper-citation-record.v1
2002.08056 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 11 of 11 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:20:53.717677Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T10:09:44.617472Z

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 f31b3914-cdee-4130-8209-3bdcfbd97135 · inbound

Training Deep Learning Models with Norm-Constrained LMOs cites this paper.

Training Deep Learning Models with Norm-Constrained LMOs The Geometry of Sign Gradient Descent

Reference 156

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:22:37.000960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 707beac3-ca49-4756-8f35-369b2ef9cdaa · inbound

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) cites this paper.

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs) The Geometry of Sign Gradient Descent

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-15T20:20:53.717677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a7a798b-7578-496f-9e38-1b29fce794a4 · inbound

Stacey: Promoting Stochastic Steepest Descent via Accelerated $\ell_p$-Smooth Nonconvex Optimization cites this paper.

Stacey: Promoting Stochastic Steepest Descent via Accelerated $\ell_p$-Smooth Nonconvex Optimization The Geometry of Sign Gradient Descent

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T06:04:35.135917Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb2eb7c3-ae2f-4b2c-b0ef-56e7d8547bef · inbound

Improved Analysis for Sign-based Methods with Momentum Updates cites this paper.

Improved Analysis for Sign-based Methods with Momentum Updates The Geometry of Sign Gradient Descent

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T17:13:42.950570Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dba5c5b5-20ea-4d03-88a6-9fb3b1d7c2be · inbound

A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo cites this paper.

A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo The Geometry of Sign Gradient Descent

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-10T07:26:59.831701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6e66c2d5-ab08-4275-844a-826008ed54e0 · inbound

When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds cites this paper.

When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds The Geometry of Sign Gradient Descent

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:21:07.752228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1a26534a-2a18-4038-9238-482c3f75d6d6 · inbound

Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less cites this paper.

Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less The Geometry of Sign Gradient Descent

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:26:08.613799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 957ae3ab-4180-4345-94ff-d30afab10f9d · inbound

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks cites this paper.

Beyond $\ell_2$-norm and $\ell_\infty$-norm: A Curvature-Inspired $\ell_p$-Norm Scheme for Deep Neural Networks The Geometry of Sign Gradient Descent

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T22:16:16.321542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 99521690-d7bd-4000-af7c-09199bda5652 · inbound

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning cites this paper.

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning The Geometry of Sign Gradient Descent

Reference 69

Resolution: verified exact; arxiv_id, observed 2026-07-03T17:08:43.681857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3fdd39a4-53e3-43a9-9da4-a0c674edcf74 · inbound

Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? cites this paper.

Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? The Geometry of Sign Gradient Descent

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-04T10:09:44.619336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 72915bd1-5b5d-4b25-88e5-24a2556d677b · inbound

Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions cites this paper.

Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions The Geometry of Sign Gradient Descent

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T21:42:14.072979Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.