Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
The duality structure gradient descent algorithm: analysis and applications to neural networks
As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:1708.00523.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:57:10.254531Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T21:22:37.171223Z
Reference resolution
0 of 0 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation caa699b5-c5c8-458f-a413-cb2797f8e9ef · inbound
Training Deep Learning Models with Norm-Constrained LMOs cites this paper.
Training Deep Learning Models with Norm-Constrained LMOs The duality structure gradient descent algorithm: analysis and applications to neural networks
Reference 176
- Resolution
- verified exact
- arxiv_id, observed 2026-05-21T21:22:37.174182Z
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 be60b65c-7167-4ce2-b1b8-9f11a56f0e7e · inbound
Convergence Bound and Critical Batch Size of Muon Optimizer cites this paper.
Convergence Bound and Critical Batch Size of Muon Optimizer The duality structure gradient descent algorithm: analysis and applications to neural networks
Reference 2016
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T20:57:10.254531Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 92e11f09-9bd4-46a0-8f42-cde8f32e151d · inbound
Training Transformers with Enforced Lipschitz Constants cites this paper.
Training Transformers with Enforced Lipschitz Constants The duality structure gradient descent algorithm: analysis and applications to neural networks
Reference 2024
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:30:29.675581Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 15e2769b-b58c-4de0-a156-62135aed8f4f · inbound
A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo cites this paper.
A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad, Shampoo and Muo The duality structure gradient descent algorithm: analysis and applications to neural networks
Reference 19
- Resolution
- verified exact
- arxiv_id, observed 2026-05-10T07:26:59.836500Z
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 7f0d3422-b192-46fb-8d8d-e6784f27a2cc · inbound
SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales cites this paper.
SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales The duality structure gradient descent algorithm: analysis and applications to neural networks
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T06:45:13.215435Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.