Paper Citation Record · LEDGER

Fantastic Pretraining Optimizers and Where to Find Them

As of 5 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 33 inbound Pith citation observations for arXiv:2509.02046.

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

pith.paper-citation-record.v1
2509.02046 v2

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measured 0 of 0 reference resolution

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measured 33 of 33 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 33 of 33 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T23:14:11.425305Z

measured 0 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-07-10T12:15:01.137692Z

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Outbound references

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Pith citing papers

Observation f38538cf-f7e0-436e-b8e9-b6e9313e9272 · inbound

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods cites this paper.

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods Fantastic Pretraining Optimizers and Where to Find Them

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:10:38.720512Z

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Observation 964e456e-177a-4e3b-bc09-f0b9049f41fb · inbound

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates cites this paper.

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates Fantastic Pretraining Optimizers and Where to Find Them

Reference 38

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Observation 3187522e-4ef4-4844-bb9d-9a5227304be8 · inbound

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws cites this paper.

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws Fantastic Pretraining Optimizers and Where to Find Them

Reference 66

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Observation 1cda9634-30c0-49fb-bbc4-4c47b6d58783 · inbound

Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization cites this paper.

Decoupling Variance and Scale-Invariant Updates in Adaptive Gradient Descent for Unified Vector and Matrix Optimization Fantastic Pretraining Optimizers and Where to Find Them

Reference 60

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Observation eae161c7-baa0-42d0-bf11-6d220841f47d · inbound

veScale-FSDP: Flexible and High-Performance FSDP at Scale cites this paper.

veScale-FSDP: Flexible and High-Performance FSDP at Scale Fantastic Pretraining Optimizers and Where to Find Them

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-15T19:06:30.851781Z

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Observation 45c9cbeb-8e58-40d2-a287-70f50c676984 · inbound

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction cites this paper.

HTMuon: Improving Muon via Heavy-Tailed Spectral Correction Fantastic Pretraining Optimizers and Where to Find Them

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:55:26.412629Z

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Observation 0423938f-6997-4215-8d7a-8b4f96ee6e75 · inbound

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization cites this paper.

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization Fantastic Pretraining Optimizers and Where to Find Them

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-15T07:49:50.822903Z

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Observation 1f5344e2-3042-47f1-a1c2-303c255b71b2 · inbound

Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory cites this paper.

Sharp Capacity Scaling of Spectral Optimizers in Learning Associative Memory Fantastic Pretraining Optimizers and Where to Find Them

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-05-14T23:38:16.348622Z

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Observation 82352a83-1657-48a1-ae2c-5a141f6d954d · inbound

Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima cites this paper.

Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima Fantastic Pretraining Optimizers and Where to Find Them

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:57.149494Z

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Observation 976464af-4b08-4e2e-818d-ef83aef632dc · inbound

Learning Rate Transfer in Normalized Transformers cites this paper.

Learning Rate Transfer in Normalized Transformers Fantastic Pretraining Optimizers and Where to Find Them

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T09:51:28.109887Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 667184e4-2aa4-4ca9-945d-e97cf1d7bc88 · inbound

Nora: Normalized Orthogonal Row Alignment for Scalable Matrix Optimizer cites this paper.

Nora: Normalized Orthogonal Row Alignment for Scalable Matrix Optimizer Fantastic Pretraining Optimizers and Where to Find Them

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-11T23:36:18.174334Z

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Observation 62576796-335e-471c-bb0b-376f8ad12a17 · inbound

When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds cites this paper.

When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$-norm Lower Bounds Fantastic Pretraining Optimizers and Where to Find Them

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:21:07.633144Z

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Observation fbb0ff62-ebc5-4ca2-8e0d-a4c89742f877 · inbound

Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less cites this paper.

Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less Fantastic Pretraining Optimizers and Where to Find Them

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:26:08.470520Z

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Observation b5ce6606-3afd-4753-8fbe-36c999d936d4 · inbound

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI cites this paper.

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI Fantastic Pretraining Optimizers and Where to Find Them

Reference 109

Resolution: verified exact; arxiv_id, observed 2026-05-12T01:16:13.971114Z

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Observation c7aaea17-60d5-4bbb-a83d-bfc264e11e66 · inbound

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI cites this paper.

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI Fantastic Pretraining Optimizers and Where to Find Them

Reference 111

Resolution: verified exact; arxiv_id, observed 2026-06-30T23:15:07.177366Z

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Observation 83300933-3b3f-4df1-9f4f-f735584b1a98 · inbound

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI cites this paper.

MLS-Bench: A Holistic and Rigorous Assessment of AI Systems on Building Better AI Fantastic Pretraining Optimizers and Where to Find Them

Reference 110

Resolution: unresolved; no resolver link, observed 2026-07-12T17:14:49.310598Z

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Observation d1edfce4-3e4b-4d1c-8c6e-0eb732e10983 · inbound

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds cites this paper.

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds Fantastic Pretraining Optimizers and Where to Find Them

Reference 64

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:36:26.240024Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation e115f5b4-becb-48f0-acdc-f7a5f41557a1 · inbound

Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds cites this paper.

Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds Fantastic Pretraining Optimizers and Where to Find Them

Reference 51

Resolution: verified exact; arxiv_id, observed 2026-05-13T06:57:27.817835Z

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Observation b457b631-d7cc-4b75-8145-dab4e41cbdb1 · inbound

Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics cites this paper.

Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics Fantastic Pretraining Optimizers and Where to Find Them

Reference 193

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Observation d0f2ed9f-c84e-42de-956b-b61d2f203592 · inbound

Outer-Momentum Restarting in High-Dimensional Two-Phase Optimization cites this paper.

Outer-Momentum Restarting in High-Dimensional Two-Phase Optimization Fantastic Pretraining Optimizers and Where to Find Them

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-06-29T13:33:27.476640Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d2eb29d1-de31-4c07-b3b5-2c583f1487ae · inbound

Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling cites this paper.

Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling Fantastic Pretraining Optimizers and Where to Find Them

Reference 51

Resolution: verified exact; arxiv_id, observed 2026-06-28T22:52:44.833271Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d05cb868-6074-46e3-9e81-f8ae3f2a6616 · inbound

Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering cites this paper.

Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering Fantastic Pretraining Optimizers and Where to Find Them

Reference 62

Resolution: verified exact; arxiv_id, observed 2026-07-02T01:56:27.790713Z

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Observation 94d13898-bea1-4079-be73-c505814531f1 · inbound

Spectral Scaling Laws of Muon cites this paper.

Spectral Scaling Laws of Muon Fantastic Pretraining Optimizers and Where to Find Them

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-02T02:06:26.373672Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c55b2ee8-6336-4457-bbaa-a0082a444df8 · inbound

Why Muon Outperforms Adam: A Curvature Perspective cites this paper.

Why Muon Outperforms Adam: A Curvature Perspective Fantastic Pretraining Optimizers and Where to Find Them

Reference 193

Resolution: verified exact; arxiv_id, observed 2026-07-02T07:06:44.956876Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 315181d6-8688-4f0d-8d49-f5a4015455a4 · inbound

PC Layer: Polynomial Weight Preconditioning for Improving LLM Pre-Training cites this paper.

PC Layer: Polynomial Weight Preconditioning for Improving LLM Pre-Training Fantastic Pretraining Optimizers and Where to Find Them

Reference 99

Resolution: verified exact; arxiv_id, observed 2026-07-02T12:16:57.322210Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0f6ff847-ce4b-42c1-ab40-20cae83a4c92 · inbound

Small Experiments, Cheaper Decisions: A Case Study in Staged Promotion for Micro-Pretraining cites this paper.

Small Experiments, Cheaper Decisions: A Case Study in Staged Promotion for Micro-Pretraining Fantastic Pretraining Optimizers and Where to Find Them

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-03T05:17:40.215468Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 41bc17bf-7394-426d-8a02-71951dd78a56 · inbound

Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? cites this paper.

Open Problem: Is AdamW Effective Under Heavy-Tailed Noise? Fantastic Pretraining Optimizers and Where to Find Them

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-04T10:09:44.613383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7e68ca9e-a1e0-4405-a021-8e296fbd3b85 · inbound

OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers cites this paper.

OmniOpt: Taxonomy, Geometry, and Benchmarking of Modern Optimizers Fantastic Pretraining Optimizers and Where to Find Them

Reference 113

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Observation 6be500e9-9444-4337-8825-62c5431bb87a · inbound

PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer cites this paper.

PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer Fantastic Pretraining Optimizers and Where to Find Them

Reference 54

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ISO: An RLVR-Native Optimization Stack cites this paper.

ISO: An RLVR-Native Optimization Stack Fantastic Pretraining Optimizers and Where to Find Them

Reference 13

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Observation b463f58c-5e27-4376-9c2e-65ce27c0606e · inbound

OPTScientist: Multi-Agent Discovery of Typed Optimizer Programs for Transformer Pretraining cites this paper.

OPTScientist: Multi-Agent Discovery of Typed Optimizer Programs for Transformer Pretraining Fantastic Pretraining Optimizers and Where to Find Them

Reference 14

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Observation 90465926-40c6-49b7-91bd-65939b77e029 · inbound

Learning What to Remember: Test-Time Training via Context Distillation cites this paper.

Learning What to Remember: Test-Time Training via Context Distillation Fantastic Pretraining Optimizers and Where to Find Them

Reference 49

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Observation a804afeb-c13b-4e0a-bfb5-af328c78be09 · inbound

CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization cites this paper.

CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization Fantastic Pretraining Optimizers and Where to Find Them

Reference 36

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