Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-30T18:30:51.719396Z
Paper Citation Record · LEDGER
LionMuon: Alternating Spectral and Sign Descent for Efficient Training
As of 13 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2605.19811.
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 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T02:09:01.644376Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
29 of 29 outbound references displayed
- verified exact20
- verified fuzzy3
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch5
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 43f8849c-a28f-4161-ba35-c6fa89136fc9 · outbound
This paper cites Kimi K2: Open Agentic Intelligence.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Kimi K2: Open Agentic Intelligence
Reference 1
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-06-30T18:35:00.444559Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2180b086-e9b5-4333-85e6-a98182ccc752 · outbound
This paper cites Benchmarking Neural Network Training Algorithms.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Benchmarking Neural Network Training Algorithms
Reference 2
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.437126Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 38953ceb-7807-42c4-99ae-e5e63941dab1 · outbound
This paper cites Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.434687Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 01da7740-22e8-44c7-b6fb-be9ab4d9a880 · outbound
This paper cites Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.439609Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9230e505-d52a-4291-a4c4-cd2e6caf4c2d · outbound
This paper cites Muon is Scalable for LLM Training.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Muon is Scalable for LLM Training
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.448741Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4654a899-ad8e-4f87-a8f8-b421db0921c2 · outbound
This paper cites Old Optimizer, New Norm: An Anthology.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Old Optimizer, New Norm: An Anthology
Reference 6
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-06-30T18:35:00.429828Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f4dc4099-d745-4f81-a326-b1157c5b1049 · outbound
This paper cites signSGD with Majority Vote is Communication Efficient And Fault Tolerant.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training signSGD with Majority Vote is Communication Efficient And Fault Tolerant
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.440962Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation dc04b226-d658-48f2-94b7-b5215330ee41 · outbound
This paper cites Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Sign Operator for Coping with Heavy-Tailed Noise in Non-Convex Optimization: High Probability Bounds Under $(L_0, L_1)$-Smoothness
Reference 8
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.446615Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cc35cef8-7662-49cc-aa13-c2ca6497693a · outbound
This paper cites Sign-Based Optimizers Are Effective Under Heavy-Tailed Noise.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Sign-Based Optimizers Are Effective Under Heavy-Tailed Noise
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.449615Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 10eb4b9b-f25b-40c9-807e-4dbdf40f11f8 · outbound
This paper cites HTMuon: Improving Muon via Heavy-Tailed Spectral Correction.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training HTMuon: Improving Muon via Heavy-Tailed Spectral Correction
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.452419Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7fcab13c-7c1e-4cef-8d38-e5315bec7f7f · outbound
This paper cites arXiv preprint arXiv:2510.16981 , year=.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training arXiv preprint arXiv:2510.16981 , year=
Reference 11
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.447155Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 56daeb54-9cbf-435b-bc7e-8e8718bdd918 · outbound
This paper cites LiMuon: Light and Fast Muon Optimizer for Large Models.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training LiMuon: Light and Fast Muon Optimizer for Large Models
Reference 12
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-06-30T18:35:00.418531Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5c92b568-e979-44ef-a70b-c4f6472356ca · outbound
This paper cites Noah Amsel, David Persson, Christopher Musco, and Robert M.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Noah Amsel, David Persson, Christopher Musco, and Robert M
Reference 13
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.410785Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 371fd9dd-09fc-4ac1-a3b7-6f2bbbc5d0ab · outbound
This paper cites Grishina, M.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Grishina, M
Reference 14
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-06-30T18:35:00.413285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d115e252-230c-4869-a521-f31401024a2b · outbound
This paper cites Improving Generalization Performance by Switching from Adam to SGD.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Improving Generalization Performance by Switching from Adam to SGD
Reference 15
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.408293Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 855aef53-b5f3-4334-9432-097c22239749 · outbound
This paper cites Adaptive Gradient Methods with Dynamic Bound of Learning Rate.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Adaptive Gradient Methods with Dynamic Bound of Learning Rate
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.425057Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 808b4a2a-c5db-43dd-bab0-47b2db711773 · outbound
This paper cites From Gradient Clipping to Normalization for Heavy Tailed SGD.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training From Gradient Clipping to Normalization for Heavy Tailed SGD
Reference 17
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.432272Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2086ae6f-f4aa-4372-a7af-db28820b9abc · outbound
This paper cites A Note on the Convergence of Muon.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training A Note on the Convergence of Muon
Reference 18
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-06-30T18:35:00.399798Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d8228e00-6052-4b25-9a4b-b76ab2652436 · outbound
This paper cites On the Convergence Analysis of Muon.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training On the Convergence Analysis of Muon
Reference 19
- Resolution
- verified exact
- local_arxiv, observed 2026-06-30T18:35:00.408539Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7ba37536-4c8f-4953-9aee-cfbebf0a49e0 · outbound
This paper cites Asgo: Adaptive structured gradient optimization.arXiv preprint arXiv:2503.20762.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Asgo: Adaptive structured gradient optimization.arXiv preprint arXiv:2503.20762
Reference 20
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.428031Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f92ae67d-bbff-4202-a1bb-8b3252cbb418 · outbound
This paper cites Improved convergence rates of muon optimizer for nonconvex optimiza- tion.arXiv preprint arXiv:2601.19400.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Improved convergence rates of muon optimizer for nonconvex optimiza- tion.arXiv preprint arXiv:2601.19400
Reference 21
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.430715Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e0e4f020-9abe-48f7-80dd-88660370a9b3 · outbound
This paper cites Muon converges under heavy-tailed noise: Nonconvex h\"{o}lder-smooth empirical risk minimiza- tion.arXiv preprint arXiv:2603.15059.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Muon converges under heavy-tailed noise: Nonconvex h\"{o}lder-smooth empirical risk minimiza- tion.arXiv preprint arXiv:2603.15059
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.433297Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8fd65943-b119-450d-a15c-bc72839058d5 · outbound
This paper cites Benchmarking Optimizers for Large Language Model Pretraining.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Benchmarking Optimizers for Large Language Model Pretraining
Reference 23
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.435900Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 707c5bf8-400d-4608-bed4-2a3993ebb481 · outbound
This paper cites First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training First Order Methods with Markovian Noise: from Acceleration to Variational Inequalities
Reference 24
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.438609Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1a6f84b7-e31b-4820-a253-c5ea54f3663d · outbound
This paper cites From gradient clipping to normalization for heavy tailed sgd.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training From gradient clipping to normalization for heavy tailed sgd
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:30.403490Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f41e9d81-4aa2-425f-bd31-d403ed48e99c · outbound
This paper cites t−1X j=0 βj 2 (1−β 2)St−j +β 2Rt−j ⋆ # ≤β t 2 · ∥E0∥⋆ + t−1X j=0 βj+1 2 E[∥Rt−j∥⋆] +E.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training t−1X j=0 βj 2 (1−β 2)St−j +β 2Rt−j ⋆ # ≤β t 2 · ∥E0∥⋆ + t−1X j=0 βj+1 2 E[∥Rt−j∥⋆] +E
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:30.405279Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b0d4910e-c284-498c-bc58-a4eca569b001 · outbound
This paper cites Taking the maximum over these two cases forP∈(1,∞), we getA2 = max{ηM , α·η L}.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Taking the maximum over these two cases forP∈(1,∞), we getA2 = max{ηM , α·η L}
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:30.407420Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 095768b5-29ac-47c3-9cfd-df498c8f224d · outbound
This paper cites an unresolved cited work.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-07-08T04:14:30.409082Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 56d8ac24-bea0-4efd-9a18-262c8b826f4b · outbound
This paper cites feel right.
LionMuon: Alternating Spectral and Sign Descent for Efficient Training feel right
Reference 29
- Resolution
- verified exact
- arxiv_id, observed 2026-06-30T18:35:00.415624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
Observation 4b711375-aa9f-458a-a5c5-e73ab0145520 · inbound
Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback cites this paper.
Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback LionMuon: Alternating Spectral and Sign Descent for Efficient Training
Reference 2023
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T02:09:01.644376Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.