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Paper Citation Record · LEDGER

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

As of 9 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 7 inbound Pith citation observations for arXiv:2506.23803.

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

pith.paper-citation-record.v1
2506.23803 v1

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:45:11.134525Z

measured 58 of 58 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 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:59:06.707164Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T19:28:52.526118Z

Reference resolution

51 of 51 outbound references displayed

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External citation measurements

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Outbound references

Observation bbde8893-e07c-46a3-883a-a44f63f220df · outbound

This paper cites GPT-4 Technical Report.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration GPT-4 Technical Report

Reference 1

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Observation 2747ed3a-08fc-4512-ae4d-2e8a7aad62cf · outbound

This paper cites an unresolved cited work.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 2

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Observation b54dc744-853c-4981-9fe8-98cd9f7c104c · outbound

This paper cites Gemini: A Family of Highly Capable Multimodal Models.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Gemini: A Family of Highly Capable Multimodal Models

Reference 3

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Observation f90fb7ca-4340-4bdd-b2b9-def58a6fcc40 · outbound

This paper cites Old Optimizer, New Norm: An Anthology.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Old Optimizer, New Norm: An Anthology

Reference 4

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Observation 1614fd93-2405-4001-a0ed-8625627f4b48 · outbound

This paper cites an unresolved cited work.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 5

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Observation 39078556-a1de-4752-ae88-d80b570e38ff · outbound

This paper cites C., Hinder, O., and Sidford, A.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration C., Hinder, O., and Sidford, A

Reference 6

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Observation cf1f5fbb-eb8f-45d2-82ff-d998bf65a6b0 · outbound

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 7

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Observation 2ee85536-97fe-4f2d-93b6-13f8d96f2b7c · outbound

This paper cites and Orabona, F.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration and Orabona, F

Reference 8

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Observation 20f09051-f0a0-48ac-92b2-6a8b475c8e89 · outbound

This paper cites and Mishchenko, K.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration and Mishchenko, K

Reference 9

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Observation 33cd4f38-8763-46cc-bcc4-fb8a211dc138 · outbound

This paper cites A Simple Convergence Proof of Adam and Adagrad.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration A Simple Convergence Proof of Adam and Adagrad

Reference 10

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 11

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 12

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Observation eec4d80a-66ba-48bc-bab4-5f409b23f940 · outbound

This paper cites The Llama 3 Herd of Models.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration The Llama 3 Herd of Models

Reference 13

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Observation ec972189-ac1b-4d13-bdd4-9845d0056038 · outbound

This paper cites A Unified Approach to Adaptive Regularization in Online and Stochastic Optimization.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration A Unified Approach to Adaptive Regularization in Online and Stochastic Optimization

Reference 14

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 15

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 16

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Observation ae89f7d9-c6e8-4608-8da7-5fa5ce088447 · outbound

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 17

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This paper cites Provable Complexity Improvement of AdaGrad over SGD: Upper and Lower Bounds in Stochastic Non-Convex Optimization.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Provable Complexity Improvement of AdaGrad over SGD: Upper and Lower Bounds in Stochastic Non-Convex Optimization

Reference 18

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 19

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Observation a4af74bf-c0e5-4d91-b24d-b647f2be821c · outbound

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration and Vempala, S

Reference 20

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Observation fb106931-08e3-4e83-b97f-0eff4c1d749d · outbound

This paper cites Y., Bach, F., and Cevher, V.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Y., Bach, F., and Cevher, V

Reference 21

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 22

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Observation 74cfff2d-a93b-4727-a3e0-82acde7b3ebd · outbound

This paper cites Adam: A Method for Stochastic Optimization.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Adam: A Method for Stochastic Optimization

Reference 23

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 25

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration On Linear Convergence in Smooth Convex-Concave Bilinearly-Coupled Saddle-Point Optimization: Lower Bounds and Optimal Algorithms

Reference 26

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Y., Yurtsever, A., and Cevher, V

Reference 29

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration and Orabona, F

Reference 30

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration DeepSeek-V3 Technical Report

Reference 31

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration AdaGrad under Anisotropic Smoothness

Reference 32

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Decoupled Weight Decay Regularization

Reference 33

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Adaptive Bound Optimization for Online Convex Optimization

Reference 34

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Prodigy: An Expeditiously Adaptive Parameter-Free Learner

Reference 35

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SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

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

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Observation d99e145f-a786-429e-ba2c-9e7157c18695 · outbound

This paper cites an unresolved cited work.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 39

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raw_fallback, observed 2026-08-06T21:45:11.862929Z

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.

source=arxiv_source observed=2026-08-06T21:45:10.066974Z digest=sha256:aa6a2c471e43e2ae115138a27a8227313dc92db3879968e199329fb44968c364

Observation 697105f1-47ad-4c49-84b3-236b98b37cd2 · outbound

This paper cites Normalized Gradients for All.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Normalized Gradients for All

Reference 40

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no resolver link, observed 2026-08-06T21:45:10.173055Z

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source=arxiv_source observed=2026-08-06T21:45:10.173055Z digest=sha256:d845d7569d92925108e970c8d5761466506139b865aa8fd8479974f9658399aa

Observation f0cc30fd-9aa9-480a-9191-b15dd7783770 · outbound

This paper cites Parameter-free Stochastic Optimization of Variationally Coherent Functions.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Parameter-free Stochastic Optimization of Variationally Coherent Functions

Reference 41

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no resolver link, observed 2026-08-06T21:45:10.269469Z

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source=arxiv_source observed=2026-08-06T21:45:10.269469Z digest=sha256:dc35c1112540b6dc247d41c771abe0d3eaa1417e5247eb9afdff75b36f3eef45

Observation e4130b31-d998-42f3-953b-d7412c498269 · outbound

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

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Training Deep Learning Models with Norm-Constrained LMOs

Reference 42

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no resolver link, observed 2026-08-06T21:45:10.340159Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:45:10.340159Z digest=sha256:d7a96f0d6c92debcb1621a238622ffe52f3db2cbd5e517cc47519fb6c965788f

Observation e4944d50-7cdd-4d1f-97ba-5951206a5b22 · outbound

This paper cites On the Convergence of Adam and Beyond.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration On the Convergence of Adam and Beyond

Reference 43

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no resolver link, observed 2026-08-06T21:45:10.435409Z

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source=arxiv_source observed=2026-08-06T21:45:10.435409Z digest=sha256:781c75e92a9f45ac1f49047b7d999b26031a22c28714fdae8ec25d521f1a269c

Observation a44a1b75-d60b-4fa6-ac84-2ea22d3d0d44 · outbound

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

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 44

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no resolver link, observed 2026-08-06T21:45:10.527295Z

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source=arxiv_source observed=2026-08-06T21:45:10.527295Z digest=sha256:9539a0bb35a7c389400bf618ae5ff33792c83e2f37be13a894e9706bedfcf7cc

Observation 59755750-6feb-4d7b-b7c4-5de363aa3851 · outbound

This paper cites an unresolved cited work.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 45

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no resolver link, observed 2026-08-06T21:45:10.621040Z

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source=arxiv_source observed=2026-08-06T21:45:10.621040Z digest=sha256:5988bf890eea5020e8aa620d3b66afebcba2f3409f0d67d10b9c55b448578a75

Observation 74e56e68-b94f-4711-896f-dacdb5b11925 · outbound

This paper cites Less Regret via Online Conditioning.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Less Regret via Online Conditioning

Reference 46

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no resolver link, observed 2026-08-06T21:45:10.718058Z

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source=arxiv_source observed=2026-08-06T21:45:10.718058Z digest=sha256:e63b408ece56cfc579a62cec9a0cb3bd17b55a7bc1106f71998ebe208745c457

Observation 793450a1-bfc8-4977-856f-4393c66ed055 · outbound

This paper cites an unresolved cited work.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 47

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raw_fallback, observed 2026-08-06T21:45:11.651645Z

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.

source=arxiv_source observed=2026-08-06T21:45:10.786937Z digest=sha256:6b5d695b8f85b6dc36ca41439e5a6eb16b914c71d875d44160bb011307afaca5

Observation 6f35e6e7-a8fc-4f64-8d64-302a01c57e61 · outbound

This paper cites an unresolved cited work.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Unresolved cited work

Reference 48

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no resolver link, observed 2026-08-06T21:45:10.858954Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:45:10.858954Z digest=sha256:6f472796a567743bb410bdfe10eec5c1a5f0e9bf4afa9b9c3d1052999c347d99

Observation 24ff1deb-6b4e-4f71-ab8a-a6e2e0f36207 · outbound

This paper cites SOAP: Improving and Stabilizing Shampoo using Adam.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration SOAP: Improving and Stabilizing Shampoo using Adam

Reference 49

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no resolver link, observed 2026-08-06T21:45:10.938805Z

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source=arxiv_source observed=2026-08-06T21:45:10.938805Z digest=sha256:52142e14e99ef0cebd38d03328b42be69abeab5a63128b615681f3e4d67bb625

Observation 72a36abf-55eb-450a-9cb7-caf4b560e30f · outbound

This paper cites Structured Preconditioners in Adaptive Optimization: A Unified Analysis.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration Structured Preconditioners in Adaptive Optimization: A Unified Analysis

Reference 50

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no resolver link, observed 2026-08-06T21:45:11.037116Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-08-06T21:45:11.037116Z digest=sha256:1a5d211aa221595603ea1fae95cac5ef894d400bec81d61e348222094b1dac3c

Observation 2329a3ed-3733-4600-9ed9-cf14d3a08a8f · outbound

This paper cites SGD Converges to Global Minimum in Deep Learning via Star-convex Path.

SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration SGD Converges to Global Minimum in Deep Learning via Star-convex Path

Reference 51

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no resolver link, observed 2026-08-06T21:45:11.134525Z

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source=arxiv_source observed=2026-08-06T21:45:11.134525Z digest=sha256:5fb5e0d0853fb5910bc83b3ea74dba4fdd8dcc61010046c1901c903b057bbea0

Pith citing papers

Observation 07235cc9-91c2-4069-b10d-7b69961963f5 · inbound

Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimization cites this paper.

Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimization SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 20

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no resolver link, observed 2026-08-06T17:59:06.707164Z

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source=arxiv_source observed=2026-08-06T17:59:06.707164Z digest=sha256:27fe1dd66c089ff684fb9c1b7af37f68e5a4d1798bcae901e08a2ba86336f142

Observation 9dc0d79f-39bd-4637-bbcc-d4781fe1d75c · inbound

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates cites this paper.

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 18

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no resolver link, observed 2026-08-05T11:25:45.012797Z

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source=pdf_text observed=2026-08-05T11:25:45.012797Z digest=sha256:0bf0258c4060789fb86be1790c1c92abc2e7868d9c5c0d446dae18dda3b79e98

Observation c9a607b4-ad88-4e2e-8d96-abcb47f371e7 · inbound

Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates cites this paper.

Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 34

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no resolver link, observed 2026-08-03T22:20:05.560830Z

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Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-03T22:20:05.560830Z digest=sha256:79503ec46783166274d6fdcf2bd72929bb3a2c7bdb757ef6960c6603b180fd6a

Observation cc5d4f3e-5a3a-454c-b201-933e048942f3 · inbound

Optimal Projection-Free Adaptive SGD for Matrix Optimization cites this paper.

Optimal Projection-Free Adaptive SGD for Matrix Optimization SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 7

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verified exact
arxiv_id, observed 2026-05-13T20:58:15.752358Z

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.

source=pdf_text observed=2026-05-13T20:56:41.466669Z digest=sha256:9cd3944f39d66c818c4411cf8fb66a39e3c33e7064735cc4fda9b394db1250f2

Observation a0b4851a-f922-47be-9520-7981bf052ba0 · inbound

Stochastic Non-Smooth Convex Optimization with Unbounded Gradients cites this paper.

Stochastic Non-Smooth Convex Optimization with Unbounded Gradients SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 17

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verified exact
arxiv_id, observed 2026-05-19T15:17:39.222473Z

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.

source=pdf_text observed=2026-05-19T15:17:01.028675Z digest=sha256:7a0b04f5e0ba995a664bc3437c5748e6c282ffcbcda0dc75a42f475d54885949

Observation 950fcdc0-8f36-49b3-a394-e27f733ff750 · inbound

On subspace-constrained preconditioning for randomized iterative methods cites this paper.

On subspace-constrained preconditioning for randomized iterative methods SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 40

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verified exact
arxiv_id, observed 2026-06-29T06:23:08.769236Z

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.

source=pdf_text observed=2026-06-29T06:21:37.788799Z digest=sha256:85b6627e50f8b71b9afad75d45e04031fd3c3ab7f13bc0a4dee28914f75429f2

Observation a1c52059-f65c-4386-ae26-912d914faaee · inbound

A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning cites this paper.

A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning SGD with Adaptive Preconditioning: Unified Analysis and Momentum Acceleration

Reference 17

Resolution
metadata mismatch
arxiv_id, observed 2026-07-03T19:28:52.527509Z

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.

source=pdf_text observed=2026-06-27T01:47:08.991345Z digest=sha256:7fc4f18622c6de6962d57f65c39a82a41e8f4cedc271f5c76bb329a89631a9b3