Paper Citation Record · LEDGER

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer

As of 17 August 2026, this Paper Citation Record lists 7 of 7 outbound references and 4 inbound Pith citation observations for arXiv:2511.06675.

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

pith.paper-citation-record.v1
2511.06675 v2

Coverage vector

measured 7 of 7 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T23:19:41.502541Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:42:54.661140Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-04T07:29:38.380912Z

Reference resolution

7 of 7 outbound references displayed

verified exact0
verified fuzzy0
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e23bfc27-32b8-4d1e-90a5-84a4948eab48 · outbound

This paper cites On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization.

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:40.872865Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c3dfeff4-8cca-4f71-8f68-d374f87a8e0e · outbound

This paper cites Convergence guarantees for RMSProp and ADAM in non-convex optimization and an empirical comparison to Nesterov acceleration.

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer Convergence guarantees for RMSProp and ADAM in non-convex optimization and an empirical comparison to Nesterov acceleration

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:41.029244Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8c6f5ff-bdb3-4257-a3a0-e0016c6a2478 · outbound

This paper cites Directional convergence and alignment in deep learning.

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer Directional convergence and alignment in deep learning

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:41.129479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d82f620-ec19-46ed-ae62-1570c52da588 · outbound

This paper cites arXiv:2505.09572(2025).

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer arXiv:2505.09572(2025)

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:41.249349Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c421d9a7-09c0-4835-a460-366c19885c99 · outbound

This paper cites On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes.

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer On the Convergence of Stochastic Gradient Descent with Adaptive Stepsizes

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:41.386966Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa4fd1c3-58c5-4b6c-86d9-bd91d4f68012 · outbound

This paper cites Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimization.

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer Convergence Analysis of a Momentum Algorithm with Adaptive Step Size for Non Convex Optimization

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:40.815012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94f210f4-1bd2-40f9-8a99-36a26fd8fbfe · outbound

This paper cites On the Convergence of Adam and Beyond.

Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer On the Convergence of Adam and Beyond

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-03T23:19:41.502541Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation f9212024-c1ca-476a-b6be-2912061a98a6 · inbound

Adaptive Preconditioners Trigger Loss Spikes in Adam cites this paper.

Adaptive Preconditioners Trigger Loss Spikes in Adam Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T10:42:54.661140Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ecb5249-ce4a-480d-89db-26a21acc6627 · inbound

Central limit theorem for the averaged Adam optimizer cites this paper.

Central limit theorem for the averaged Adam optimizer Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-07-04T07:29:38.382249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 00d371bc-0cd0-4dca-9650-ee252e6e52e2 · inbound

On the Convergence of Adam, Revisited cites this paper.

On the Convergence of Adam, Revisited Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-12T01:55:46.406234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70120d59-9e1b-49a4-9917-0ad660b0db89 · inbound

Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks cites this paper.

Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks Adam symmetry theorem: characterization of the convergence of the stochastic Adam optimizer

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T20:46:05.467029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.