Paper Citation Record · LEDGER

The Loss Does Not See the Basis, but Adam Does

As of 9 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2608.05136.

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

pith.paper-citation-record.v1
2608.05136 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T04:31:56.631197Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

34 of 34 outbound references displayed

verified exact8
verified fuzzy7
unresolved16
parse uncertain0
malformed identifier2
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c6859a70-617d-4f6d-b759-b1933a90d1ad · outbound

This paper cites an unresolved cited work.

The Loss Does Not See the Basis, but Adam Does Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T04:31:57.319013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cfb9414a-4ac1-4836-b783-b77f59befee6 · outbound

This paper cites an unresolved cited work.

The Loss Does Not See the Basis, but Adam Does Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:55.249556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa958af5-6941-459e-a190-4cbf2bb4b8f7 · outbound

This paper cites E EXTENDED RELATED WORK Transformation invariance in optimizer design.The engineering literature has grappled with similar design choices at a lower level; for instance, Ling et al.

The Loss Does Not See the Basis, but Adam Does E EXTENDED RELATED WORK Transformation invariance in optimizer design.The engineering literature has grappled with similar design choices at a lower level; for instance, Ling et al

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.286280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b8ee1547-db3b-4fc7-85aa-3a8f6bbcb4e4 · outbound

This paper cites The Spectral Dynamics and Noise Geometry of Muon.

The Loss Does Not See the Basis, but Adam Does The Spectral Dynamics and Noise Geometry of Muon

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-06T04:31:57.189006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 11c47c21-50c2-4460-904d-f1716008ae0f · outbound

This paper cites Old Optimizer, New Norm: An Anthology.

The Loss Does Not See the Basis, but Adam Does Old Optimizer, New Norm: An Anthology

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:55.667638Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac2b7a14-c483-456b-8bfa-6447441819ff · outbound

This paper cites How do simple rotations affect the implicit bias of Adam?arXiv preprint arXiv:2510.23804,.

The Loss Does Not See the Basis, but Adam Does How do simple rotations affect the implicit bias of Adam?arXiv preprint arXiv:2510.23804,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:55.922864Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5254efe4-395a-4bc2-87dd-7c1ef5dc5dac · outbound

This paper cites To Use or not to Use Muon: How Simplicity Bias in Optimizers Matters.

The Loss Does Not See the Basis, but Adam Does To Use or not to Use Muon: How Simplicity Bias in Optimizers Matters

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.175857Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3661442f-be6b-4209-b14c-bc0bee791efc · outbound

This paper cites Manuel Graña, Miguel A.

The Loss Does Not See the Basis, but Adam Does Manuel Graña, Miguel A

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.302366Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43963ec1-6286-408d-8339-21e04b2ddc6a · outbound

This paper cites Distributes the corrected Indian Pines (A VIRIS) and Pavia University (ROSIS) cubes.

The Loss Does Not See the Basis, but Adam Does Distributes the corrected Indian Pines (A VIRIS) and Pavia University (ROSIS) cubes

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.342958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1a1c2bb8-51ec-470c-9d23-21e2ddb7736e · outbound

This paper cites The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks.

The Loss Does Not See the Basis, but Adam Does The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.568711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7d7bae3-8469-42d2-abe9-be85a74a0037 · outbound

This paper cites The unreasonable effectiveness of recurrent neural networks.

The Loss Does Not See the Basis, but Adam Does The unreasonable effectiveness of recurrent neural networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.334934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d51048e5-c27e-4bed-83da-9a2d93c42275 · outbound

This paper cites Improving Generalization Performance by Switching from Adam to SGD.

The Loss Does Not See the Basis, but Adam Does Improving Generalization Performance by Switching from Adam to SGD

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.581841Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0491bac-2379-432b-96ab-1e0af9ffce9e · outbound

This paper cites Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers.

The Loss Does Not See the Basis, but Adam Does Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.584738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d694a4f1-4def-43f0-b4f7-425a2e8b3410 · outbound

This paper cites Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks.

The Loss Does Not See the Basis, but Adam Does Dead-Direction Conditioners: Gauge-Equivariant Preconditioning for Deep Networks

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.595521Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af576cce-b13a-4430-92b4-36b70af9f8d0 · outbound

This paper cites Symmetry breaking in transformers for efficient and interpretable training.arXiv preprint arXiv:2601.22257,.

The Loss Does Not See the Basis, but Adam Does Symmetry breaking in transformers for efficient and interpretable training.arXiv preprint arXiv:2601.22257,

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.598164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e20993a5-f3f0-4f3e-9156-f2cd64bebe53 · outbound

This paper cites FlowAdam: Implicit Regularization via Geometry-Aware Soft Momentum Injection.

The Loss Does Not See the Basis, but Adam Does FlowAdam: Implicit Regularization via Geometry-Aware Soft Momentum Injection

Reference 23

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T04:31:56.768027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fb20c61e-15f1-4c34-92cb-2ce4e1bef9b2 · outbound

This paper cites How the Optimizer Shapes Learned Solutions in Equivariant Neural Networks.

The Loss Does Not See the Basis, but Adam Does How the Optimizer Shapes Learned Solutions in Equivariant Neural Networks

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-06T04:31:56.756734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 57a6d262-7b3e-41e1-8d59-c203a8842aa4 · outbound

This paper cites PolarAdamW: Disentangling Spectral Control and Schur Gauge-Equivariance in Matrix Optimisation.

The Loss Does Not See the Basis, but Adam Does PolarAdamW: Disentangling Spectral Control and Schur Gauge-Equivariance in Matrix Optimisation

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T04:31:56.746013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ff517448-6f35-4cae-af4e-d67445f3e20e · outbound

This paper cites aggressiveness.

The Loss Does Not See the Basis, but Adam Does aggressiveness

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.327326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7ca6ddf0-5085-4152-a06b-7138b80c9951 · outbound

This paper cites • Target and measurements.

The Loss Does Not See the Basis, but Adam Does • Target and measurements

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.311042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 301653ac-434f-40df-859b-344ec8ac11b8 · outbound

This paper cites Two configurations failed to meet that threshold within the allotted steps: FlowAdam-p=0 got to 7×10 −6, and global-norm clipping at p=1 reached 6×10 −7.

The Loss Does Not See the Basis, but Adam Does Two configurations failed to meet that threshold within the allotted steps: FlowAdam-p=0 got to 7×10 −6, and global-norm clipping at p=1 reached 6×10 −7

Reference 30

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T04:31:57.295046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1be24d6b-de0c-408a-850d-b9d497b9ac94 · outbound

This paper cites sc- Adam.

The Loss Does Not See the Basis, but Adam Does sc- Adam

Reference 31

Resolution: verified exact; raw_fallback, observed 2026-08-06T04:31:56.732321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9f9f4c67-e073-4a4d-8cd2-c792bfacf38d · outbound

This paper cites an unresolved cited work.

The Loss Does Not See the Basis, but Adam Does Unresolved cited work

Reference 33

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T04:31:57.278160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4721214f-cb6f-4f05-ae79-c99ba2feb144 · outbound

This paper cites Recent theoretical work attributes a spectral max-margin bias to Muon (Fan et al., 2025; Gronich & Vardi, 2026), and Kang et al.

The Loss Does Not See the Basis, but Adam Does Recent theoretical work attributes a spectral max-margin bias to Muon (Fan et al., 2025; Gronich & Vardi, 2026), and Kang et al

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.270178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8f0cfc9b-424c-4081-9065-9bf63b76051a · outbound

This paper cites • Training.Full-batch optimization over 1500 steps, executed deterministically on CPU (torch.use_deterministic_algorithms).

The Loss Does Not See the Basis, but Adam Does • Training.Full-batch optimization over 1500 steps, executed deterministically on CPU (torch.use_deterministic_algorithms)

Reference 256

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T04:31:57.303211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3a1ec306-87b8-44ae-a140-967729c3e209 · outbound

This paper cites an unresolved cited work.

The Loss Does Not See the Basis, but Adam Does Unresolved cited work

Reference 2015

Resolution: unresolved; raw_fallback, observed 2026-08-06T04:31:57.350586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 327df7a5-dcfe-40d3-bd74-a99e4ea25516 · outbound

This paper cites Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective.

The Loss Does Not See the Basis, but Adam Does Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspective

Reference 2018

Resolution: verified exact; local_arxiv, observed 2026-08-06T04:31:56.856929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cc5d430a-5bb9-4ed2-8a21-9c1797f29dc6 · outbound

This paper cites Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets.

The Loss Does Not See the Basis, but Adam Does Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.589907Z

Source-reported events for the cited work

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Observation 8c7b04f7-de59-49b8-a6f8-32a6474b1c09 · outbound

This paper cites Benchmarking Neural Network Training Algorithms.

The Loss Does Not See the Basis, but Adam Does Benchmarking Neural Network Training Algorithms

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:55.794590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c2e6397-e4dd-4d7a-bbe2-501b81d7c14d · outbound

This paper cites Muon is Scalable for LLM Training.

The Loss Does Not See the Basis, but Adam Does Muon is Scalable for LLM Training

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.587257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8aa1f57-728f-48fd-bf74-0addbb93c2b2 · outbound

This paper cites Understanding and inverse design of implicit bias in stochastic learning: a geometric perspective.

The Loss Does Not See the Basis, but Adam Does Understanding and inverse design of implicit bias in stochastic learning: a geometric perspective

Reference 2023

Resolution: verified exact; local_arxiv, observed 2026-08-06T04:31:57.262062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cd23d19e-54dd-4c47-abb0-cea868c0efa1 · outbound

This paper cites Uniform spectral growth and convergence of Muon in LoRA-style matrix factorization.arXiv preprint arXiv:2602.06385,.

The Loss Does Not See the Basis, but Adam Does Uniform spectral growth and convergence of Muon in LoRA-style matrix factorization.arXiv preprint arXiv:2602.06385,

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-06T04:31:56.576769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca6d6615-0be5-4388-bdf7-8d50353eb3bd · outbound

This paper cites Muonp: Muon with fractional spectral powers.arXiv preprint arXiv:2606.13867,.

The Loss Does Not See the Basis, but Adam Does Muonp: Muon with fractional spectral powers.arXiv preprint arXiv:2606.13867,

Reference 2025

Resolution: verified exact; raw_fallback, observed 2026-08-06T04:31:57.106517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8ab89a40-55e7-455e-a594-eebc9b5f2996 · outbound

This paper cites Marion F.

The Loss Does Not See the Basis, but Adam Does Marion F

Reference 2026

Resolution: verified exact; raw_fallback, observed 2026-08-06T04:31:57.249710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

No inbound Pith citation observations are available.