Paper Citation Record · LEDGER

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics

As of 15 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2605.20441.

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

pith.paper-citation-record.v1
2605.20441 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-21T07:30:07.287938Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-11T00:46:52.525784Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-11T00:47:42.502859Z

Reference resolution

38 of 38 outbound references displayed

verified exact26
verified fuzzy2
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch9

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 63cb4991-8b79-49e8-9397-a0facd43c8ae · outbound

This paper cites Sarwan Ali.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Sarwan Ali

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.966504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e5b41ef9-6680-409a-92d4-915726608a92 · outbound

This paper cites Critical Windows of Complexity Control: When Transformers Decide to Reason or Memorize.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Critical Windows of Complexity Control: When Transformers Decide to Reason or Memorize

Reference 3

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.924356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a17c2ce4-080e-45b3-9991-f71bc57ba780 · outbound

This paper cites title =.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics title =

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.947731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 27b08966-77e7-45f8-af57-69210c16f909 · outbound

This paper cites URLhttps://arxiv.org/abs/2312.03012.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics URLhttps://arxiv.org/abs/2312.03012

Reference 5

Resolution: verified exact; doi, observed 2026-05-21T07:34:02.498536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 36dead87-a14a-4154-85fb-19e520b6c8ca · outbound

This paper cites Francesco D’Angelo, Maksym Andriushchenko, Aditya Varre, and Nicolas Flammarion.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Francesco D’Angelo, Maksym Andriushchenko, Aditya Varre, and Nicolas Flammarion

Reference 6

Resolution: verified exact; doi, observed 2026-05-21T07:34:02.496594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0733276e-875e-428c-8f84-2442b994d38b · outbound

This paper cites Why Do We Need Weight Decay in Modern Deep Learning?.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Why Do We Need Weight Decay in Modern Deep Learning?

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.934011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation eb077f23-aaf5-4586-ba2e-49c31f385306 · outbound

This paper cites an unresolved cited work.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-05-21T07:34:48.571326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 99b448d0-bb6a-4de8-9beb-de8a7e182b88 · outbound

This paper cites SGD and Weight Decay Secretly Minimize the Rank of Your Neural Network.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics SGD and Weight Decay Secretly Minimize the Rank of Your Neural Network

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.899180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 23efa9f5-74f6-4ad7-984c-58d2853e01ce · outbound

This paper cites ILDR: Geometric Early Detection of Grokking.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics ILDR: Geometric Early Detection of Grokking

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-05-21T07:34:02.896321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation dfe1797b-f439-4bd1-9248-077b8b865cf7 · outbound

This paper cites The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior

Reference 12

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.912613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e337bf70-0384-44ee-8372-bd81ddf9d01c · outbound

This paper cites Max Hennick and Guillaume Corlouer.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Max Hennick and Guillaume Corlouer

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.890172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1cc87a52-2c15-41f5-b70c-c39c8eab41ab · outbound

This paper cites Bill Z Jia, Yitong Qi, J David Wong-Campos, Sean G Megason, and Adam E Cohen.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Bill Z Jia, Yitong Qi, J David Wong-Campos, Sean G Megason, and Adam E Cohen

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.909265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 15211429-16f3-4e8c-8bec-d330d49ab307 · outbound

This paper cites What Can Grokking Teach Us About Learning Under Nonstationarity?.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics What Can Grokking Teach Us About Learning Under Nonstationarity?

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.918767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e5b384ef-6887-4d9b-abcb-0f073b499076 · outbound

This paper cites Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.936796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 19a787c8-4885-46cc-8d3d-6c45644c04ee · outbound

This paper cites Charles H.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Charles H

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.939509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fc8cd75e-9a3b-4464-89bd-d8cb1583e7b1 · outbound

This paper cites URLhttps://arxiv.org/abs/2002.06716.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics URLhttps://arxiv.org/abs/2002.06716

Reference 19

Resolution: verified exact; doi, observed 2026-05-21T07:34:02.514157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b73ac9ea-f3c4-487d-9ee0-91580821594d · outbound

This paper cites The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics The Geometry of Grokking: Norm Minimization on the Zero-Loss Manifold

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-06-02T02:03:35.760630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a4eaf7eb-2596-4d5a-9f05-ef42e8214ef8 · outbound

This paper cites An exactly solvable model for emergence and scaling laws in the multitask sparse parity problem.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics An exactly solvable model for emergence and scaling laws in the multitask sparse parity problem

Reference 22

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T07:34:02.921528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation df6ef2ec-3b39-472e-b453-38c2ca8d41a9 · outbound

This paper cites From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.958448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ccb8584c-d0c8-474f-9781-0f912535f761 · outbound

This paper cites Catherine Olsson, Nelson Elhage, Neel Nanda, et al.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Catherine Olsson, Nelson Elhage, Neel Nanda, et al

Reference 24

Resolution: verified exact; doi, observed 2026-05-21T07:34:02.511512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation fc252018-5b57-465d-aef8-f5b41d09123a · outbound

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

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-05-21T07:34:02.958939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e6e66285-1d2b-4dc8-8fb3-2037cd3e8ff7 · outbound

This paper cites an unresolved cited work.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Unresolved cited work

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.956165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 73a6b39d-fba6-46f7-955e-22d0521a0525 · outbound

This paper cites Specialization of softmax attention heads: insights from the high-dimensional single-location model.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Specialization of softmax attention heads: insights from the high-dimensional single-location model

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-06-05T02:16:27.181524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 337fa020-6c5e-4318-a39f-7ff5878b2652 · outbound

This paper cites Saxe, James L.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Saxe, James L

Reference 28

Resolution: metadata mismatch; doi, observed 2026-05-21T07:34:02.504746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d00a0804-dd41-4366-9ed2-d584e820e91a · outbound

This paper cites Are Emergent Abilities of Large Language Models a Mirage?.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Are Emergent Abilities of Large Language Models a Mirage?

Reference 29

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T07:34:02.955873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5b5452ba-7101-4485-8978-320dd2a4ba0f · outbound

This paper cites Yiding Song and Hanming Ye.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Yiding Song and Hanming Ye

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.944612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4c898d6a-5759-4154-8dc7-df9780ee12e9 · outbound

This paper cites Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds

Reference 32

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.927253Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 05834b9f-59cc-4377-a774-a515f0eb6958 · outbound

This paper cites Topological Signatures of Grokking.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Topological Signatures of Grokking

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-05-21T07:34:02.934882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation eeb7d9de-9342-4412-bab7-55b4d78e71d2 · outbound

This paper cites URLhttps://arxiv.org/abs/2509.21519.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics URLhttps://arxiv.org/abs/2509.21519

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.509454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e9068c25-6c64-436d-8038-70d0f542fdd0 · outbound

This paper cites Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficient.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficient

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.937838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 188339c4-54a7-43ba-a730-018e3bd40428 · outbound

This paper cites Grokking as Dimensional Phase Transition in Neural Networks.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Grokking as Dimensional Phase Transition in Neural Networks

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-05-21T07:34:02.950188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d9bc0e3f-99db-4859-a1e5-9b2f3d3061ae · outbound

This paper cites Distributional Spectral Diagnostics for Localizing Grokking Transitions.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Distributional Spectral Diagnostics for Localizing Grokking Transitions

Reference 38

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.931073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 4109816b-5557-4f07-a6cd-9e8e337b3d09 · outbound

This paper cites To Grok Grokking: Provable Grokking in Ridge Regression.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics To Grok Grokking: Provable Grokking in Ridge Regression

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-06-01T02:02:25.462475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1ee690dd-785d-4d53-86c1-1c6b3c105bde · outbound

This paper cites Spectral Edge Dynamics: An Analytical-Empirical Study of Phase Transitions in Neural Network Training.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Spectral Edge Dynamics: An Analytical-Empirical Study of Phase Transitions in Neural Network Training

Reference 40

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.512204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e1300db9-8227-443a-8e04-40534a28f3fe · outbound

This paper cites The Geometric Inductive Bias of Grokking: Bypassing Phase Transitions via Architectural Topology.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics The Geometric Inductive Bias of Grokking: Bypassing Phase Transitions via Architectural Topology

Reference 41

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T07:34:02.928159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e244fedc-d20f-4310-9b41-8d6fad97546a · outbound

This paper cites URLhttps://arxiv.org/abs/2603.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics URLhttps://arxiv.org/abs/2603

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-21T07:34:02.503449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9a0b6a70-9400-4815-9013-180f694aa09a · outbound

This paper cites Across 183 valid layer-epoch rows, the mean absolute raw-PR error is2.10×10−7, the maximum raw-PR error is1.73×10−6, and the maximum affine-normalized PR error is2.56×10−7.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Across 183 valid layer-epoch rows, the mean absolute raw-PR error is2.10×10−7, the maximum raw-PR error is1.73×10−6, and the maximum affine-normalized PR error is2.56×10−7

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T07:34:48.567462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 26caf9a8-4f83-4762-9730-daf77293c808 · outbound

This paper cites Three of five cohorts now fall in the empirical 95% CI; the across-cohort mean shifts toλbound c = 0.0185±0.0074(range[0 .012, 0.028]), with the mean itself inside the empirical CI.

Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics Three of five cohorts now fall in the empirical 95% CI; the across-cohort mean shifts toλbound c = 0.0185±0.0074(range[0 .012, 0.028]), with the mean itself inside the empirical CI

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T07:34:48.569444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation afe5a82c-ec6f-4503-838c-c31ce6aa29b8 · inbound

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics cites this paper.

At-Grok Is Not Converged:A Measurement-Validity Audit for Grokking Representation Metrics Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-07-11T00:47:42.525067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.