Paper Citation Record · LEDGER

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification

As of 8 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2505.22359.

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

pith.paper-citation-record.v1
2505.22359 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:21:02.975560Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

verified exact2
verified fuzzy12
unresolved12
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6a060ba9-e87e-4398-b673-6e041506c62a · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T13:20:59.681906Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ace33abc-287c-41d9-9964-75df1ac6b2c4 · outbound

This paper cites Bousquet.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Bousquet

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:07.248092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 513210e6-83e0-478f-b413-3f1182de607e · outbound

This paper cites Risk and parameter convergence of logistic regression.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Risk and parameter convergence of logistic regression

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T13:20:59.906369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54a426b5-e24e-4134-97c2-0aa8666e1f0e · outbound

This paper cites Ji and M.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Ji and M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:07.045433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b253a81d-3197-418c-b642-4ccc211a75f1 · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:06.885478Z

Source-reported events for the cited work

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Observation f86177ed-2736-423d-bb7f-41b05d71751d · outbound

This paper cites Lei, \"U.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Lei, \"U

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:06.697941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 169fde50-7fc8-48c3-883c-046086905ae5 · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:06.462774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4b9d97d0-f868-49cc-81ca-74767e7fee8b · outbound

This paper cites Gradient Descent Maximizes the Margin of Homogeneous Neural Networks.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Gradient Descent Maximizes the Margin of Homogeneous Neural Networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T13:21:00.645859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8dec3008-4107-4685-8fea-d1ae5d0862a1 · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:06.182437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7191cb59-a821-4c7a-8a77-fa9061451fe3 · outbound

This paper cites Magen and O.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Magen and O

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:05.940475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 93fe03ec-db92-40a6-8912-ebd9c0b5f8a9 · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T13:21:01.071996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d763b41c-1b3d-435d-bf53-42b1f8207ca1 · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:05.748412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ebffe408-8e66-4af3-8f04-1ab7a79b928e · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:05.486050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b7217c9e-7484-49e9-8929-ca43f9c96764 · outbound

This paper cites Rakhlin, K.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Rakhlin, K

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T13:21:01.501375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f343ca6-d5ff-4e83-b98e-e98ad10b3928 · outbound

This paper cites The Implicit Bias of Gradient Descent on Separable Multiclass Data.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification The Implicit Bias of Gradient Descent on Separable Multiclass Data

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:21:03.205409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 27b1b0dc-f2bd-4591-91b2-55b2f3e2b55e · outbound

This paper cites Reeve and A.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Reeve and A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:05.255544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 08ac05ec-45d9-4056-a380-4fd28d8f2670 · outbound

This paper cites Schliserman and T.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Schliserman and T

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:05.086532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e7b3b7cb-ff60-4b39-85a3-fd99dc917acd · outbound

This paper cites Complexity of Vector-valued Prediction: From Linear Models to Stochastic Convex Optimization.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Complexity of Vector-valued Prediction: From Linear Models to Stochastic Convex Optimization

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:21:03.073174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation edacaa4b-bdbc-479d-920a-a4b48f09d037 · outbound

This paper cites Schliserman and T.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Schliserman and T

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:04.927070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d8065bce-54d2-4df8-81d3-170e1adf3556 · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:04.788399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fb4176fe-fa29-4ad7-81ad-b59683710ed5 · outbound

This paper cites Soudry, E.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Soudry, E

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:04.609990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e21e736f-46d7-4e4f-8ebe-edb3da6c9b38 · outbound

This paper cites Srebro, K.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Srebro, K

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:04.496989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 22701761-051e-4a60-9c2e-368f3b919724 · outbound

This paper cites Telgarsky.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Telgarsky

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:04.316789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ce737523-d105-4ae4-aba3-ed9088408ee9 · outbound

This paper cites Wang and C.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Wang and C

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:04.015914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ef0ab836-afd1-4412-a696-5808d96afd3a · outbound

This paper cites an unresolved cited work.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:21:03.726114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8e910f7e-ae4c-46bc-8673-3543303aaf73 · outbound

This paper cites Zhang and M.-L.

Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification Zhang and M.-L

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:21:03.408630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.