Paper Citation Record · LEDGER

Improved Analysis for Sign-based Methods with Momentum Updates

As of 18 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 4 inbound Pith citation observations for arXiv:2507.12091.

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

pith.paper-citation-record.v1
2507.12091 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:13:46.971808Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T17:35:15.202361Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T10:09:44.623885Z

Reference resolution

33 of 33 outbound references displayed

verified exact1
verified fuzzy19
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 818f7331-825b-4571-84e4-78dcacfc2a23 · outbound

This paper cites Arjevani, Y.

Improved Analysis for Sign-based Methods with Momentum Updates Arjevani, Y

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:53.713959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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

This paper cites The Geometry of Sign Gradient Descent.

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 29212f05-e57a-45b7-99de-70a7d4d2d1d4 · outbound

This paper cites Bernstein, Y.-X.

Improved Analysis for Sign-based Methods with Momentum Updates Bernstein, Y.-X

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:53.490216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7ecaf4f6-8d29-43bc-846e-da8d43fc47c9 · outbound

This paper cites Bernstein, J.

Improved Analysis for Sign-based Methods with Momentum Updates Bernstein, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:53.352183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 717c3240-8dce-4bd2-9559-e9cfd4cd3a7a · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:53.153580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a9f03b78-69c0-412f-a230-55b97968f537 · outbound

This paper cites SignSVRG: fixing SignSGD via variance reduction.

Improved Analysis for Sign-based Methods with Momentum Updates SignSVRG: fixing SignSGD via variance reduction

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T17:13:43.470108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03c020a5-15ae-478b-bbdc-7be65909d77e · outbound

This paper cites Crawshaw, M.

Improved Analysis for Sign-based Methods with Momentum Updates Crawshaw, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:52.953750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6215163a-8b89-470d-8988-0b7c7c016e12 · outbound

This paper cites Cutkosky and F.

Improved Analysis for Sign-based Methods with Momentum Updates Cutkosky and F

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:52.779918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ff1d748b-5611-407d-a5cb-702f9381d715 · outbound

This paper cites Duchi, E.

Improved Analysis for Sign-based Methods with Momentum Updates Duchi, E

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:52.548376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 10f1dd4e-09a3-4760-9631-1357eb830b6b · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:52.278344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ebff796a-94b8-41a5-b866-a9bae6fb8abe · outbound

This paper cites Ghadimi and G.

Improved Analysis for Sign-based Methods with Momentum Updates Ghadimi and G

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:52.007068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d3f896aa-ee93-4a53-86e2-95c841bd8c19 · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:51.815926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6ac87be3-03ae-4375-b63d-0c26d869e67b · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:51.645570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b4aea1ac-a726-46f2-83d5-4ebacfd2b449 · outbound

This paper cites Jiang, S.

Improved Analysis for Sign-based Methods with Momentum Updates Jiang, S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:51.381436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6c20472c-8c0f-4fdf-93ef-71f74f3ce58f · outbound

This paper cites Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees.

Improved Analysis for Sign-based Methods with Momentum Updates Stochastic-Sign SGD for Federated Learning with Theoretical Guarantees

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T17:13:44.717529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36e81f35-e1f2-4c66-9b5e-d889603b56f2 · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:51.146009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 880e4529-edb5-4b38-8300-7fbfe7dbd601 · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:50.967643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 728f094c-9088-4570-b514-0e7f603abf81 · outbound

This paper cites Krizhevsky.

Improved Analysis for Sign-based Methods with Momentum Updates Krizhevsky

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:50.741439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e2d703af-e26c-49ad-b50f-a99a666d31df · outbound

This paper cites Kunstner, J.

Improved Analysis for Sign-based Methods with Momentum Updates Kunstner, J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:50.566868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fcfafa74-08d2-4ef8-9896-47a94cb2a1d0 · outbound

This paper cites Li, K.-Y.

Improved Analysis for Sign-based Methods with Momentum Updates Li, K.-Y

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:50.362740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 62401f79-0d71-4530-9a85-350417e91095 · outbound

This paper cites Liu, P.-Y.

Improved Analysis for Sign-based Methods with Momentum Updates Liu, P.-Y

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:50.191769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 158a8a08-2bcc-454e-af8b-c3d05b678f45 · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:49.976649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation de9c48cc-a82f-4411-bb9d-4c81ac7a0b1a · outbound

This paper cites Loshchilov and F.

Improved Analysis for Sign-based Methods with Momentum Updates Loshchilov and F

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:49.827700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 017c9004-3b6a-4cd0-8f46-6705c8ccf911 · outbound

This paper cites Loshchilov and F.

Improved Analysis for Sign-based Methods with Momentum Updates Loshchilov and F

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:49.586975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation acd3bdf4-716d-40e4-a524-d5d11097d4e4 · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:49.325607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2e12e822-1649-4456-adfd-b56870c98d86 · outbound

This paper cites Paszke, S.

Improved Analysis for Sign-based Methods with Momentum Updates Paszke, S

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:49.041525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d7304a42-4076-49c4-8c91-6030f935a0ee · outbound

This paper cites Convergence of Sign-based Random Reshuffling Algorithms for Nonconvex Optimization.

Improved Analysis for Sign-based Methods with Momentum Updates Convergence of Sign-based Random Reshuffling Algorithms for Nonconvex Optimization

Reference 27

Resolution: verified exact; raw_fallback, observed 2026-08-12T02:23:44.492630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 758c44b6-819a-430a-8f08-8d0bfca90b15 · outbound

This paper cites Safaryan and P.

Improved Analysis for Sign-based Methods with Momentum Updates Safaryan and P

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:48.778164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a84b689a-37a9-4d92-99f5-3186312cf25f · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:48.503947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5afe9be0-c68f-4135-9ec6-3b11ee9285f4 · outbound

This paper cites Sutskever, J.

Improved Analysis for Sign-based Methods with Momentum Updates Sutskever, J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:48.243669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c0ef8c0f-8579-4206-90c8-5c7a60d1630d · outbound

This paper cites an unresolved cited work.

Improved Analysis for Sign-based Methods with Momentum Updates Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:13:48.036252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4247f569-7450-401e-bacd-136f42b91ca7 · outbound

This paper cites Zhang, S.

Improved Analysis for Sign-based Methods with Momentum Updates Zhang, S

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:47.824577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6e0d4577-7e7c-4f9d-b66d-f673ed5c3fbf · outbound

This paper cites Zhang, M.

Improved Analysis for Sign-based Methods with Momentum Updates Zhang, M

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:13:47.628553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 32e4bc3f-59fb-493e-bfae-5bfee884adcd · inbound

Convergence Analysis of the Lion Optimizer in Centralized and Distributed Settings cites this paper.

Convergence Analysis of the Lion Optimizer in Centralized and Distributed Settings Improved Analysis for Sign-based Methods with Momentum Updates

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T17:35:15.202361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 85bb3fb9-1bfa-4a6b-9f93-b087048f2673 · inbound

StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models cites this paper.

StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models Improved Analysis for Sign-based Methods with Momentum Updates

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-10T12:15:22.180688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 393b9bef-8070-4a5e-ad09-1a5c30e25602 · 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 Improved Analysis for Sign-based Methods with Momentum Updates

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:21:07.699770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6abdeda7-f619-4722-bf55-8924975c6b25 · inbound

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

Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? Improved Analysis for Sign-based Methods with Momentum Updates

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-04T10:09:44.625298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.