Paper Citation Record · LEDGER

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems

As of 10 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 4 inbound Pith citation observations for arXiv:2507.14122.

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

pith.paper-citation-record.v1
2507.14122 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:19:03.602887Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:26:04.963978Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T07:26:30.072417Z

Reference resolution

30 of 30 outbound references displayed

verified exact3
verified fuzzy12
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 01bf6257-dcde-46cf-883d-16fe652ea470 · outbound

This paper cites Towards Weaker Variance Assumptions for Stochastic Optimization.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Towards Weaker Variance Assumptions for Stochastic Optimization

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T16:18:59.106218Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb77d374-791b-42ce-b4f7-c9fb6ddd7a44 · outbound

This paper cites Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T16:18:59.232727Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2053a0c6-fab3-4941-9319-63ba3f726469 · outbound

This paper cites and Moulines, E.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems and Moulines, E

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:11.604059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 79e2159d-5ec5-4219-a8d1-ddc6923566b8 · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:11.201086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c6b8a25e-be03-4619-a7da-9219a2100a01 · outbound

This paper cites E., and Nocedal, J.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems E., and Nocedal, J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:10.892859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c1a8aa81-3bb8-4699-803f-d8a8734f8136 · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T16:18:59.939888Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de23c43e-b2ed-4039-ba5d-c8c7ed40feac · outbound

This paper cites Handbook of Convergence Theorems for (Stochastic) Gradient Methods.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Handbook of Convergence Theorems for (Stochastic) Gradient Methods

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T16:19:00.127615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0aa66c01-6005-47b6-8d8e-24d60d8930da · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:10.552367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6b7e7f17-bb84-48fc-a2c6-000c9ec8931e · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:10.132034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 790d4004-280a-4bf8-a666-bff28352c79b · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:09.865926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 83756c35-27d7-4a08-ab07-1c676cf1c5df · outbound

This paper cites Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillation.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Analysis of an Idealized Stochastic Polyak Method and its Application to Black-Box Model Distillation

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T16:19:00.830624Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b167a0c4-e9c5-4dd3-82d5-53b2aacf2feb · outbound

This paper cites M., Loizou, N., Qian, X., Sailanbayev, A., Shulgin, E., and Richtárik, P.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems M., Loizou, N., Qian, X., Sailanbayev, A., Shulgin, E., and Richtárik, P

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:09.589813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6bde2ef6-1921-45d8-9801-c933f8db3c97 · outbound

This paper cites Tight Analyses for Non-Smooth Stochastic Gradient Descent.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Tight Analyses for Non-Smooth Stochastic Gradient Descent

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:19:04.824541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 887e9d3a-514a-428e-9ab8-22622b0d6fae · outbound

This paper cites Making the Last Iterate of SGD Information Theoretically Optimal.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Making the Last Iterate of SGD Information Theoretically Optimal

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:19:04.417156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 66e39cf7-5e4b-4bed-9bfb-6f50fae86f93 · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T16:19:01.325727Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 340ea8c3-01f0-4d1f-a259-cab43cee3651 · outbound

This paper cites and Richtárik, P.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems and Richtárik, P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:09.340810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bb68977f-d715-4bb6-a58b-f91a09d543d7 · outbound

This paper cites D., Nguyen, T.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems D., Nguyen, T

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:09.070428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f83648f9-0e4f-47db-ab63-33a61160a81b · outbound

This paper cites and Zhou, Z.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems and Zhou, Z

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:08.768618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f8e96da3-f275-42b1-beba-cb66ca2fc5e2 · outbound

This paper cites H., and Lacoste-Julien, S.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems H., and Lacoste-Julien, S

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:08.389637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5669f04c-be95-4ab1-a9b2-f0cac243a35a · outbound

This paper cites How do you prove Gautschi's inequality for the gamma function? https://math.stackexchange.com/q/98348.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems How do you prove Gautschi's inequality for the gamma function? https://math.stackexchange.com/q/98348

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:08.084812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ed9d900c-7eac-4468-8ee0-854fb2abd990 · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:07.736448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8c42ffc0-fd9d-4323-892d-05ad9ed96c00 · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:07.282323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7111ce79-bd6c-4136-9211-3773698c8188 · outbound

This paper cites H., Dijk, M., Richtarik, P., Scheinberg, K., and Takac, M.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems H., Dijk, M., Richtarik, P., Scheinberg, K., and Takac, M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:06.886463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 714fdaf1-6cf3-4872-8571-da97bd232550 · outbound

This paper cites an unresolved cited work.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:19:06.516429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d25ae0e8-25e0-4c92-90fa-5ca5ed9e198b · outbound

This paper cites and D'Orazio, R.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems and D'Orazio, R

Reference 25

Resolution: verified exact; raw_fallback, observed 2026-08-06T16:19:04.005885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d9204642-3910-45fc-99fc-50b054b8b70e · outbound

This paper cites and Monro, S.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems and Monro, S

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:06.190790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 172202a5-3182-470f-909a-18a09f6dd50f · outbound

This paper cites M., and Defazio, A.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems M., and Defazio, A

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:05.704064Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9c2a6ae2-51b2-4d54-b425-a97ae9ffd879 · outbound

This paper cites Less Regret via Online Conditioning.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Less Regret via Online Conditioning

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T16:19:03.284655Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1bf05ad2-1691-4b51-b7b1-38f66ea13ec3 · outbound

This paper cites and Bach, F.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems and Bach, F

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:19:05.271742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 21fb4db9-beaf-4fe6-be07-a0986dc2ac29 · outbound

This paper cites Exact convergence rate of the last iterate in subgradient methods.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems Exact convergence rate of the last iterate in subgradient methods

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T16:19:03.602887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 411a359e-f944-490c-a478-8bcb901662be · inbound

Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime cites this paper.

Fast Last-Iterate Convergence of SGD in the Smooth Interpolation Regime Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T17:26:04.963978Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 391611ee-09ef-45c3-9222-b6a2be1738eb · inbound

Gradient Descent's Last Iterate is Often (slightly) Suboptimal cites this paper.

Gradient Descent's Last Iterate is Often (slightly) Suboptimal Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T12:30:23.751347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b13b5bac-fd1a-4d9c-a5ac-c0ff36a14156 · inbound

Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance cites this paper.

Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:46:07.505460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2fa1d111-f531-400d-a7d1-a8d59fcb2d1e · inbound

Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance cites this paper.

Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:26:30.075468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.