Paper Citation Record · LEDGER

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM

As of 23 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:1908.00700.

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

pith.paper-citation-record.v1
1908.00700 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:43:22.439322Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

19 of 19 outbound references displayed

verified exact0
verified fuzzy10
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5aaf2088-de28-4c79-9948-9c36f6e0f7bb · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:23.274561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0342eb9f-8516-4047-8736-bd022bd3aeb1 · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:23.096998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fbb9d947-bd00-4788-948e-692406ba250a · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:23.175626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e51f7072-900a-4fdb-8d4c-fd152e6bbfb8 · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:23.362998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 963466fd-420e-47b8-b973-f3945f801973 · outbound

This paper cites small learning rate dilemma.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM small learning rate dilemma

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:23.342676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation be65fb01-931d-40d5-b8d5-ddc2834953a3 · outbound

This paper cites Besides the ﬁgures in main text, we have repeated experiments and show results as follows.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Besides the ﬁgures in main text, we have repeated experiments and show results as follows

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:23.322470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3b5256ea-f896-4f98-812d-33218f1af16f · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:23.294666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 418484ea-8f8d-47f0-8fe3-8c66135330e2 · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:23.078499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 95b1d803-5af4-4a5c-bc71-3f68b94c1f48 · outbound

This paper cites With ﬁxed L,σ,G,β 1, we have C1 =O(β2), C2 =O(dβ), C3 =O(dβ2).

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM With ﬁxed L,σ,G,β 1, we have C1 =O(β2), C2 =O(dβ), C3 =O(dβ2)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:23.055754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 54de26b7-62cc-48f7-9b69-3af6a0b8e669 · outbound

This paper cites By Jensen’s inequality, 1 T T∑ t=1 (f(xt)−f∗)≥f(¯xt)−f∗, where ¯xt = 1 T ∑T t=1xt.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM By Jensen’s inequality, 1 T T∑ t=1 (f(xt)−f∗)≥f(¯xt)−f∗, where ¯xt = 1 T ∑T t=1xt

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:23.012174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e944d485-d18f-4297-82e5-1248aa07e38a · outbound

This paper cites f(¯xt)−f∗≤ D2 2µ1 √ T + β2 1d(σ2 +G2) (1−β1)2µ1T √ T (µ2 2−µ2.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM f(¯xt)−f∗≤ D2 2µ1 √ T + β2 1d(σ2 +G2) (1−β1)2µ1T √ T (µ2 2−µ2

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:22.989752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8df3b6d7-c621-4655-b47c-c9e83e8b3689 · outbound

This paper cites 42 Remark 27 The leading item of convergence order of Adam should be O( ˜C√ T ), where ˜C = D2 2µ1 + µ2 2 µ1 (σ2 +G2) + β1d(σ2+G2) 2µ1(1−β1) (µ2 2−µ2.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM 42 Remark 27 The leading item of convergence order of Adam should be O( ˜C√ T ), where ˜C = D2 2µ1 + µ2 2 µ1 (σ2 +G2) + β1d(σ2+G2) 2µ1(1−β1) (µ2 2−µ2

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:22.966435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 608e165c-dacd-48cd-8630-623f0074dc8f · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:22.928083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8210dcf2-c3fc-41bd-93ff-44c07021f4f7 · outbound

This paper cites f(¯xt)−f∗≤ D2 2µ3 √ T + β2 1d(σ2 +G2) (1−β1)2µ3T √ T (µ2 4−µ2.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM f(¯xt)−f∗≤ D2 2µ3 √ T + β2 1d(σ2 +G2) (1−β1)2µ3T √ T (µ2 4−µ2

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:22.868436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 82fd7832-5332-4e68-b8fe-fcfcae8aaa1c · outbound

This paper cites For brevity, f(¯xt)−f∗ =O( 1√ T ).

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM For brevity, f(¯xt)−f∗ =O( 1√ T )

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:22.735074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4fe05962-6b5d-45b7-9f3f-27ec2e0e46c6 · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:22.677674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6b654323-6b9b-4c27-b712-d50fc0d93ac3 · outbound

This paper cites an unresolved cited work.

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:43:22.652059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9b0abe13-6aed-49ba-a102-9d02fd4992c7 · outbound

This paper cites Set η =O( 1 T 2 ), E[f(xT +1)−f∗]≤ (1− 2λµ3 T 2 )TE[f(x1)−f∗] +O( 1 T ).

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM Set η =O( 1 T 2 ), E[f(xT +1)−f∗]≤ (1− 2λµ3 T 2 )TE[f(x1)−f∗] +O( 1 T )

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:22.552564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 61af7f28-a734-4c6f-ba88-84f5487363b8 · outbound

This paper cites 38 Remark 26 The leading item from the above convergence is C1/ √ T , β plays an essential role in the complexity, and a more accurate convergence should be O(βlog (1+eβ )√ T ).

Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM 38 Remark 26 The leading item from the above convergence is C1/ √ T , β plays an essential role in the complexity, and a more accurate convergence should be O(βlog (1+eβ )√ T )

Reference 2013

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:43:23.036490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.