Paper Citation Record · LEDGER

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

As of 14 August 2026, this Paper Citation Record lists 100 of 103 outbound references and 5 inbound Pith citation observations for arXiv:2411.15958.

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

pith.paper-citation-record.v1
2411.15958 v2

Coverage vector

measured 100 of 103 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T13:54:29.374528Z

measured 105 of 105 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T11:35:29.606079Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-20T07:53:09.867752Z

Reference resolution

100 of 103 outbound references displayed

verified exact1
verified fuzzy33
unresolved65
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 66553399-dd79-4fe9-993e-2efa638760a4 · outbound

This paper cites Optimizer A.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer A

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.853107Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86b0fd86-e510-418f-8837-952f60bb51e6 · outbound

This paper cites (Cited on page 3) Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto, Frank Norbert Proske, Hans Kersting, and Aurelien Lucchi.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (Cited on page 3) Enea Monzio Compagnoni, Luca Biggio, Antonio Orvieto, Frank Norbert Proske, Hans Kersting, and Aurelien Lucchi

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.813943Z

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Observation 8aa043d3-94a4-4588-bdbf-51141d5fb6f1 · outbound

This paper cites Optimizer A.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer A

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.863943Z

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Observation 8a1c1a64-e733-4f96-9d03-66a1f6734ccb · outbound

This paper cites Optimizer B.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer B

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.890835Z

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Observation b431b7b2-0840-4ddd-aadb-1d921f3b062c · outbound

This paper cites Optimizer A.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer A

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.896775Z

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Observation e675553e-9dd2-4b95-9676-83825bf3feef · outbound

This paper cites good model.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise good model

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.884014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6bde3a2b-a900-4793-ae99-03c910835206 · outbound

This paper cites Adaptive methods for nonconvex optimization.Advances in neural information processing systems, 31, 2018.(Cited on page 3) Jingzhao Zhang, Tianxing He, Suvrit Sra, and Ali Jadbabaie.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Adaptive methods for nonconvex optimization.Advances in neural information processing systems, 31, 2018.(Cited on page 3) Jingzhao Zhang, Tianxing He, Suvrit Sra, and Ali Jadbabaie

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.843605Z

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Observation 97875d84-85d1-46f4-ac4c-3cbc64527791 · outbound

This paper cites Stochastic Modified Equations and Dynamics of Dropout Algorithm.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Stochastic Modified Equations and Dynamics of Dropout Algorithm

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.848318Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28871922-2070-418c-ae40-bfd104f2f84b · outbound

This paper cites Optimizer A.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer A

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.857926Z

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Observation a32c27fd-ed69-461d-8161-4b5b7e81a870 · outbound

This paper cites Optimizer A.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer A

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.869887Z

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Unavailable: canonical work link unavailable.

Observation a35227f9-d918-4c87-bc9d-6191649a5324 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.875064Z

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Unavailable: canonical work link unavailable.

Observation 10be5c59-1899-4eeb-977f-d41df230c372 · outbound

This paper cites Optimizer B.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Optimizer B

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.879773Z

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Unavailable: canonical work link unavailable.

Observation 57f45a27-e6aa-4d65-9297-15af92f33b91 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.903986Z

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Observation 78358bad-d6de-40d2-9385-c2153e33044c · outbound

This paper cites Moreover, the solutionXt is said to be unique if any other solutionX ⋆ t is such that P {Xt = X ⋆ t , for all 0 ≤ t ≤ T } = 1.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Moreover, the solutionXt is said to be unique if any other solutionX ⋆ t is such that P {Xt = X ⋆ t , for all 0 ≤ t ≤ T } = 1

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.908912Z

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Unavailable: canonical work link unavailable.

Observation 16357301-7164-4c76-bf13-677e115bd053 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.913141Z

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Unavailable: canonical work link unavailable.

Observation df957d87-b59a-4d2f-aae3-f610c459baf5 · outbound

This paper cites Then, there exists a unique solutionXt to the corresponding SDE, andXt ∈ M2([0, T], Rd).

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Then, there exists a unique solutionXt to the corresponding SDE, andXt ∈ M2([0, T], Rd)

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.918176Z

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Observation 5e795561-f441-4ac7-be6f-0daff1dce3c1 · outbound

This paper cites (x, y) 7→ gx(y) is in C8(Rn × Rn) such that all partial derivatives of g up to order8 are integrable with respect toy and s.t.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (x, y) 7→ gx(y) is in C8(Rn × Rn) such that all partial derivatives of g up to order8 are integrable with respect toy and s.t

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.923203Z

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Unavailable: canonical work link unavailable.

Observation a499e5b0-de2a-45d5-ba50-929537f0739f · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.927361Z

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Observation 5f43a09c-6f8b-4997-bf53-ec45ea300b37 · outbound

This paper cites 20 to be inG, which, as we show below, covers Gaussian and Student’s t, thus being more general than the literature.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 20 to be inG, which, as we show below, covers Gaussian and Student’s t, thus being more general than the literature

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.931731Z

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Unavailable: canonical work link unavailable.

Observation 5615696e-8f46-4164-8634-fa6f3812564a · outbound

This paper cites [2022], we assume that √ Σ(x) is: In G together with its derivatives, Lipschitz, bounded, and satisfy Affine Growth.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise [2022], we assume that √ Σ(x) is: In G together with its derivatives, Lipschitz, bounded, and satisfy Affine Growth

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.936676Z

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Observation a7ae4112-5616-49d1-a122-ce5fb64496ba · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.941471Z

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Unavailable: canonical work link unavailable.

Observation a365ccb1-eb0d-4181-972b-10076dce09ae · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.946385Z

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Observation 3c9bc45f-11a8-4e1f-a26c-3ea5f78f33d6 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.951814Z

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Observation 578aefb1-a82f-4178-b67b-728d080474ee · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.956763Z

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Observation a31c9650-dd69-4b81-bfcb-d51ff8d0e7b5 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.996176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c45e78d2-7165-497a-9425-938fdecbb480 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.979692Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4fe257f9-631a-44dc-9967-e02042e35909 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.962479Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d0cb55f4-2aea-49d6-ab81-3b95f7710542 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.944927Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ebf3ff56-6693-4a0c-aeba-e087a7d0f8cb · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.929705Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1f797437-ef0e-4ca1-9cfc-5ecbf7a3b672 · outbound

This paper cites Therefore, we have that for someK1(x) ∈ G, E∆i − E ¯∆i ≤ K1(x)η2, ∀i = 1,.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Therefore, we have that for someK1(x) ∈ G, E∆i − E ¯∆i ≤ K1(x)η2, ∀i = 1,

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.913442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4fde4374-557f-4617-b594-7c143fd25213 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.898489Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5149363d-05b4-4d4d-b145-396784d7e48d · outbound

This paper cites Therefore, we have that for someK2(x) ∈ G, E∆i∆j − E ¯∆i ¯∆j ≤ K2(x)η2, ∀i, j= 1,.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Therefore, we have that for someK2(x) ∈ G, E∆i∆j − E ¯∆i ¯∆j ≤ K2(x)η2, ∀i, j= 1,

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.880336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cba84279-89d2-43c3-8865-bb9abd1c2d1f · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.862251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0f32214f-703b-45b4-a722-17a81f64838b · outbound

This paper cites Therefore, we have that for someK3(x) ∈ G, E sY j=1 ∆ij − E sY j=1 ¯∆ij ≤ K3(x)η2.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Therefore, we have that for someK3(x) ∈ G, E sY j=1 ∆ij − E sY j=1 ¯∆ij ≤ K3(x)η2

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.844782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0991873f-579a-4403-ade1-19eeb57e5ade · outbound

This paper cites (40) Remark C.18.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (40) Remark C.18

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.828235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c1137f48-4225-4486-b954-5ba1f805a6b8 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.803604Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 04f2044e-a284-4776-8e01-9a6a3c519698 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.786919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation aa9cacee-1016-48be-b3e3-93bc39da5910 · outbound

This paper cites (53) Proof of Lemma C.21.Exploiting the regularity of theErf function, we approximate the SDE in Eq.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (53) Proof of Lemma C.21.Exploiting the regularity of theErf function, we approximate the SDE in Eq

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.767553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 632c7157-6121-43ad-8323-0d639253736d · outbound

This paper cites Therefore, if Σ− 1 2 ∇f (Xt)√ 2 > 3 2, (a) Erf Σ− 1 2 ∇f (Xt)√ 2 ∼ sign Σ− 1 2 ∇f (Xt)√ 2 = sign (∇f (Xt)); (b) Erf Σ− 1 2 ∇f (Xt)√ 2 2 ∼ sign Σ− 1 2 ∇f (Xt)√ 2 2 = (1,.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Therefore, if Σ− 1 2 ∇f (Xt)√ 2 > 3 2, (a) Erf Σ− 1 2 ∇f (Xt)√ 2 ∼ sign Σ− 1 2 ∇f (Xt)√ 2 = sign (∇f (Xt)); (b) Erf Σ− 1 2 ∇f (Xt)√ 2 2 ∼ sign Σ− 1 2 ∇f (Xt)√ 2 2 = (1,

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.752743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3d4590e1-312d-49b4-8049-ab3a6e979a9d · outbound

This paper cites If 1 < x <3 2, we have that mx + q1 < Erf(x) < mx+ q2.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise If 1 < x <3 2, we have that mx + q1 < Erf(x) < mx+ q2

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.731877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c8e6bec8-2f7a-464d-a3ea-aecf4cf31cbb · outbound

This paper cites Therefore, if Σ− 1 2 ∇f (Xt)√ 2 < 1, (a) Erf Σ− 1 2 ∇f (Xt)√ 2 ∼ q 2 π Σ− 1 2 ∇f (Xt); (b) Erf Σ− 1 2 ∇f (Xt)√ 2 2 ∼ 2 π Σ− 1 2 ∇f (Xt) 2.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Therefore, if Σ− 1 2 ∇f (Xt)√ 2 < 1, (a) Erf Σ− 1 2 ∇f (Xt)√ 2 ∼ q 2 π Σ− 1 2 ∇f (Xt); (b) Erf Σ− 1 2 ∇f (Xt)√ 2 2 ∼ 2 π Σ− 1 2 ∇f (Xt) 2

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.716440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a4ed3a4c-ecb6-423d-b410-8a54f2e5215a · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.670098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2d88b7c6-2151-4c74-b9b5-e80cc5498b5d · outbound

This paper cites Proof of Lemma C.22.We prove each point by leveraging the shape of the law ofXt derived in Lemma C.21:.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Proof of Lemma C.22.We prove each point by leveraging the shape of the law ofXt derived in Lemma C.21:

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.649935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bbdf19ac-ab69-4dd6-b50f-2c389824cc13 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.632905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a1679666-d09c-49c5-bfa6-5ebbd65dec45 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.609871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ed41536a-775d-4ad4-ae0d-d2dfa045afba · outbound

This paper cites Therefore, we have d(f (Xt) − f (X∗)) ≤ −2µ r 2 π 1 σmax + η π µ σ2max ! (f (Xt) − f (X∗))dt (84) + η 2 T r(∇2f (Xt))dt + O(Noise).

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Therefore, we have d(f (Xt) − f (X∗)) ≤ −2µ r 2 π 1 σmax + η π µ σ2max ! (f (Xt) − f (X∗))dt (84) + η 2 T r(∇2f (Xt))dt + O(Noise)

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.581467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0b7c29dd-b1ab-453d-adcd-b2454fdfc772 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.689538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 38761bc5-602c-4324-aec9-96315563d90a · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.552955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b8735f64-6392-46f9-8469-b9bc0a7f535d · outbound

This paper cites Proof of Lemma C.22.We prove each point by leveraging the shape of the law ofXt derived in Lemma C.21: 36.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Proof of Lemma C.22.We prove each point by leveraging the shape of the law ofXt derived in Lemma C.21: 36

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.535099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37aa2903-8198-49f9-a07b-7c7c3a6d9d5a · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 55

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.519779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2d0da2d6-7189-4f28-98ca-248a07f1c029 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 56

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.502045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 559b8cf8-7e3d-43da-be8f-211e3c7b7449 · outbound

This paper cites (98) Therefore, for ∆ := q 2 π 1 σmax, E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗)))e−2µ∆t + ηLd 4µ∆ 1 − e−2µ∆t.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (98) Therefore, for ∆ := q 2 π 1 σmax, E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗)))e−2µ∆t + ηLd 4µ∆ 1 − e−2µ∆t

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.477262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7c07f620-268b-4db2-b31f-44515b2653e2 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 58

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.454588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a26a64d7-59ae-4f2d-a66c-2e04509e4680 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.435642Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f7c1d9cb-fafd-467b-af17-830ab86d8992 · outbound

This paper cites Proof of Lemma C.22.We prove each point by leveraging the shape of the law ofXt derived in Lemma C.21:.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Proof of Lemma C.22.We prove each point by leveraging the shape of the law ofXt derived in Lemma C.21:

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.418816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 47c95f7d-56e0-4b54-a45c-e87ab374d77b · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 61

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.401795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d5c8459f-c69e-444f-b726-dd6c3f7c285c · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 62

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.379762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1af0516e-209d-4377-94ac-30472986fcc2 · outbound

This paper cites (108) Lemma C.25.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise (108) Lemma C.25

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.357546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d6218a49-878a-4275-bbec-bd21d3df321c · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 64

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.331008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 47e208fe-51ad-4471-83cf-644ea7af4ff2 · outbound

This paper cites Proof of Lemma C.26.The proof is banal: The expected value derivation leverages the martingale property of the Brownian motion while that of the variance uses the Ito Isomerty.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Proof of Lemma C.26.The proof is banal: The expected value derivation leverages the martingale property of the Brownian motion while that of the variance uses the Ito Isomerty

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.309949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 947d9878-4bcd-48b4-bfa9-473545408e5f · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.268207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a05594bd-8ebf-4799-9092-a1a0b930f757 · outbound

This paper cites Assumption from [Wojtowytsch, 2024].

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Assumption from [Wojtowytsch, 2024]

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.253492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 180aee2f-8b62-4b57-a5c5-67a675865e3a · outbound

This paper cites 1) Bound (Ph.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 1) Bound (Ph

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.238055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bb371f4f-3a88-4c03-95a6-d67008dece9d · outbound

This paper cites Assumption from [Wu et al., 2022].[Wu et al., 2022] proposes a novel structure ofΣ as being aligned with the Fisher Information Matrix and proportional to the loss function.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Assumption from [Wu et al., 2022].[Wu et al., 2022] proposes a novel structure ofΣ as being aligned with the Fisher Information Matrix and proportional to the loss function

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.223344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 09203848-f04f-431e-bf29-127bfc8b3738 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 72

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.287879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c31286e1-6707-4056-a2ac-8f426f4853a3 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 73

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.206136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 30861635-4d8f-4dde-af8b-02cee36200db · outbound

This paper cites 41 Assumption from [Paquette et al., 2024].In this section, we adopt the notation of [Paquette et al., 2024].

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 41 Assumption from [Paquette et al., 2024].In this section, we adopt the notation of [Paquette et al., 2024]

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.174639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0f8d380a-fb62-4b46-bc36-101267d0916a · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 75

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.156161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation decf5fb6-6d7b-4fba-92c4-28726ac928f4 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 76

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.139607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6d6eb4f6-192c-4341-927e-f2ce2733d87d · outbound

This paper cites See Figure 8 for an empirical validation.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise See Figure 8 for an empirical validation

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.121737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5324ea99-5229-4892-821d-f194f76a1a64 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 78

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.107988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d124e6c8-4472-4573-8c94-00249113ed98 · outbound

This paper cites Then, we have that ifΦk := ∇f (xk)√vk+ϵId − ∇fγk (xk)√vk+ϵId 1.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Then, we have that ifΦk := ∇f (xk)√vk+ϵId − ∇fγk (xk)√vk+ϵId 1

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.091793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bcae1941-7ce8-4186-bd52-c0dad497fb60 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 80

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.067624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e941fbcb-ba90-4d02-9a78-429bb0158b70 · outbound

This paper cites Remark C.35.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Remark C.35

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:30.045728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7da49411-6cbf-4220-bfe4-38eea8ffad0b · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 82

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.026001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b58c8916-ff78-4044-baa7-88e629a890e2 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 83

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:30.006258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2451a0bb-4c7a-4ceb-b77f-1d36d909c5f9 · outbound

This paper cites Then, we have.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Then, we have

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.984157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e63420b7-5abc-424b-9f67-fa14c3cfad74 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 85

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.967584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5a90faf6-d050-46ee-a48b-c6698a98a75b · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 86

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.948492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e3931fb1-70a8-4f86-a724-bd43d5ff754d · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 87

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.930170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 30c27201-b811-4ec0-98b2-d59d73fc21dc · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 88

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.916107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 474e0334-3c0e-4a14-897a-d8ce487b00e1 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 89

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.899370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 59a79150-4415-41f2-bbb9-c0adf59acf4e · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.864020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6e055769-b0f9-41bb-be69-7b2de1210665 · outbound

This paper cites However, we observe that if the scale of the noise is too small w.r.t.η, i.e.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise However, we observe that if the scale of the noise is too small w.r.t.η, i.e

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.847515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e06ca494-4231-4544-a69c-2cd124f387b8 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 93

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.824381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0460ce69-54cd-4694-9bd8-40b8da9fd0a7 · outbound

This paper cites scheduler.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise scheduler

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.811134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9a73c55f-c44d-4e99-bb25-485494b13169 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 95

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.797085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ab5a5708-5d88-45ac-abfc-ce6a967874f3 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 96

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.782598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a69a585c-f3f1-424c-933e-f6d9c46fb703 · outbound

This paper cites E.1 Deriving scaling rules Jastrzebski et al.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise E.1 Deriving scaling rules Jastrzebski et al

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.767109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1d57a660-c2c4-413e-9d38-983ea16734b6 · outbound

This paper cites 238 we have: E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗))e−2µt + η 2 Lτ σ2 2µB 1 − e−2µt ; (242).

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 238 we have: E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗))e−2µt + η 2 Lτ σ2 2µB 1 − e−2µt ; (242)

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.751069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bc8f7780-b7f5-4b05-8da7-7e2910debc0c · outbound

This paper cites 240 we have: E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗))e−2µt + η 2 Lτ σ2 2µB κ δ 1 − e−2µt ; (243) 57.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 240 we have: E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗))e−2µt + η 2 Lτ σ2 2µB κ δ 1 − e−2µt ; (243) 57

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.736735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f9bccd5d-a692-4535-ac2a-9d9ee845a429 · outbound

This paper cites 241 we have: E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗))e−2µκt + η 2 Lτ σ2 2µB κ δ 1 − e−2µκt.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 241 we have: E[f (Xt) − f (X∗)] ≤ (f (X0) − f (X∗))e−2µκt + η 2 Lτ σ2 2µB κ δ 1 − e−2µκt

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.721068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ae0ded5b-bad3-4efb-9bdf-d9ddaa2b1bbf · outbound

This paper cites 241 is a better model for SGD(˜η, ˜B) as it represents the dynamics more accurately.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 241 is a better model for SGD(˜η, ˜B) as it represents the dynamics more accurately

Reference 101

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.702481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 72499f5c-f97d-4ebe-a1e9-f1c4aaf89e99 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 102

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:54:29.681634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 32ad52d9-7e97-4108-8357-3e50d9df26f5 · outbound

This paper cites Remark E.3.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Remark E.3

Reference 103

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.665291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7dc754e8-0211-476a-8def-2bb4c6725b3a · outbound

This paper cites as 1 − √ δ(1 − β).

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise as 1 − √ δ(1 − β)

Reference 105

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:54:29.627771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9359c657-9ee5-41ea-83a3-2840b596e300 · outbound

This paper cites an unresolved cited work.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Unresolved cited work

Reference 106

Resolution: verified exact; raw_fallback, observed 2026-08-12T13:54:29.518926Z

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Observation 7907ba93-e9cc-4fe0-98be-a06a3a403871 · outbound

This paper cites 233) with Euler-Maruyama (Algorithm 1) with∆t = η.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise 233) with Euler-Maruyama (Algorithm 1) with∆t = η

Reference 169

Resolution: malformed identifier; raw_fallback, observed 2026-08-12T13:54:29.644082Z

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Observation e44d38be-0401-4187-ad20-26de2a8c7329 · outbound

This paper cites Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models

Reference 2014

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.824588Z

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Observation ee91fb49-195d-4eed-bab3-e8d8cfb30c70 · outbound

This paper cites Stochastic modified equations and dynamics of stochastic gradient algorithms i: Mathematical foundations.The Journal of Machine Learning Research, 20 (1):1474–1520, 2019.

Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise Stochastic modified equations and dynamics of stochastic gradient algorithms i: Mathematical foundations.The Journal of Machine Learning Research, 20 (1):1474–1520, 2019

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-12T13:54:28.829892Z

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Pith citing papers

Observation 160b0a5a-5451-4262-976f-343d284dff67 · inbound

Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness cites this paper.

Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-08T11:35:29.606079Z

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Observation c7fddd65-5c33-4514-87fa-c38da97a0d79 · inbound

Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games cites this paper.

Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T14:23:25.132951Z

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Observation d1564a50-d727-4851-9909-eca23071de4f · inbound

Seesaw: Accelerating Training by Balancing Learning Rate and Batch Size Scheduling cites this paper.

Seesaw: Accelerating Training by Balancing Learning Rate and Batch Size Scheduling Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Reference 32

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Observation 8160b06f-153e-45f5-a024-3234806467ac · inbound

Understanding Dynamics of Adam in Zero-Sum Games: An ODE Approach cites this paper.

Understanding Dynamics of Adam in Zero-Sum Games: An ODE Approach Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Reference 203

Resolution: verified exact; arxiv_id, observed 2026-05-20T07:53:09.871042Z

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Observation a9b3dc32-35e4-45d1-92a3-7c6d630247d0 · inbound

A Defense of the Quadratic Model cites this paper.

A Defense of the Quadratic Model Adaptive Methods through the Lens of SDEs: Theoretical Insights on the Role of Noise

Reference 27

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