Paper Citation Record · LEDGER

Grokking Beyond the Euclidean Norm of Model Parameters

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2506.05718.

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

pith.paper-citation-record.v1
2506.05718 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:21:24.036574Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T00:44:38.335028Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T21:18:58.709358Z

Reference resolution

31 of 31 outbound references displayed

verified exact0
verified fuzzy13
unresolved15
parse uncertain0
malformed identifier1
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3103a508-dbdb-4db0-a7bd-7c9c9aef1749 · outbound

This paper cites We also have ∥zy∥2 ≤ L since L = supy′∈B(x,r) supz∈∂h(y′) ∥z∥2.

Grokking Beyond the Euclidean Norm of Model Parameters We also have ∥zy∥2 ≤ L since L = supy′∈B(x,r) supz∈∂h(y′) ∥z∥2

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:28.018490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0e0bc94f-9178-4551-a50a-9b9e11bde47d · outbound

This paper cites Then, for any η >0, mint1≤t≤t2 f (x(t)) − f ∗ ≤ (η+Cαβ )β 2 if and only if t2 ≥ t1 + R2 αβη.

Grokking Beyond the Euclidean Norm of Model Parameters Then, for any η >0, mint1≤t≤t2 f (x(t)) − f ∗ ≤ (η+Cαβ )β 2 if and only if t2 ≥ t1 + R2 αβη

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:28.281388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 153ad6b5-7b97-4327-bf5c-171ccc403644 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:26.860202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e4fe17ae-bf06-4851-b425-f55a2ea9bc7f · outbound

This paper cites Unveiling the Dynamics of Information Interplay in Supervised Learning.

Grokking Beyond the Euclidean Norm of Model Parameters Unveiling the Dynamics of Information Interplay in Supervised Learning

Reference 6

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T10:21:24.310078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9b00abb7-2d86-408e-9aa1-55ec7455b83d · outbound

This paper cites Explaining grokking through circuit efficiency.

Grokking Beyond the Euclidean Norm of Model Parameters Explaining grokking through circuit efficiency

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T10:21:21.958566Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf5bf52f-3cc3-4bca-b796-dbe505fab23b · outbound

This paper cites Then for all 0 ≤ j ≤ k − 1, |Rj| ≤ ϵα∥∇g(x(j))∥2 2 if α ≤ 2(ϵ − γ)/L2p (ϵ + γ)α∥∇g(x(j))∥2 2 if α ≤ 2ϵ/L2p (37) Proof.

Grokking Beyond the Euclidean Norm of Model Parameters Then for all 0 ≤ j ≤ k − 1, |Rj| ≤ ϵα∥∇g(x(j))∥2 2 if α ≤ 2(ϵ − γ)/L2p (ϵ + γ)α∥∇g(x(j))∥2 2 if α ≤ 2ϵ/L2p (37) Proof

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:28.153707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0a368504-1029-4fda-a8d8-4d47a5dfc45c · outbound

This paper cites So ∥∇f (y)∥2 2 f (y) ≥ β ∥zy∥2 2 h(y) ≥ βχ(h, x, r′).

Grokking Beyond the Euclidean Norm of Model Parameters So ∥∇f (y)∥2 2 f (y) ≥ β ∥zy∥2 2 h(y) ≥ βχ(h, x, r′)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:27.880780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 498ac956-50b8-46a1-b6e8-72c91c9f1d19 · outbound

This paper cites Theorem C.29.

Grokking Beyond the Euclidean Norm of Model Parameters Theorem C.29

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:27.744556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4e036362-f0e9-4a41-80b3-f611e7f9b69c · outbound

This paper cites g(ˆa) − 1 2 ∥ξ∥2 2 = − 1 2 ξ⊤UU⊤ξ = − 1 2 ∥U⊤ξ∥2.

Grokking Beyond the Euclidean Norm of Model Parameters g(ˆa) − 1 2 ∥ξ∥2 2 = − 1 2 ξ⊤UU⊤ξ = − 1 2 ∥U⊤ξ∥2

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:27.621223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7da838f3-7b67-4e47-b9a4-2819edacee8c · outbound

This paper cites In particular, if a∗ has a nonzero component orthogonal to the column space Col(V) of V, then ˆa cannot perfectly generalize.

Grokking Beyond the Euclidean Norm of Model Parameters In particular, if a∗ has a nonzero component orthogonal to the column space Col(V) of V, then ˆa cannot perfectly generalize

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:27.488158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3dc9044d-d0cc-4532-aa37-701739a29a8b · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:27.314232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 925820de-3188-40ba-b3ad-36cc942b6d9f · outbound

This paper cites 37 Grokking Beyond the Euclidean Norm of Model Parameters.

Grokking Beyond the Euclidean Norm of Model Parameters 37 Grokking Beyond the Euclidean Norm of Model Parameters

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:27.172363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 02d55c49-813e-49fd-8fd0-c682cf0d94b2 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:27.008084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 31fd6f2e-7b20-4f97-be7f-6bc57b602da1 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:26.730043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 411c64f6-dd1a-425f-b558-30c86ab76f5d · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:26.549141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f86d3e39-1a9a-4684-811c-db0abfffc172 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:26.297571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6d1087d9-4fd0-4541-ac06-30757f4d1337 · outbound

This paper cites Suppose we start at some A(1).

Grokking Beyond the Euclidean Norm of Model Parameters Suppose we start at some A(1)

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:26.150100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 90f94905-5f46-48d7-a297-332ff8156b29 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:25.962329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 175b2601-89b9-49b3-9d87-60f6379bc876 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:25.796449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 357a8c2d-12d7-4327-beab-aa81b8f57fc5 · outbound

This paper cites , σ(1) r1 the singular values of A(1).

Grokking Beyond the Euclidean Norm of Model Parameters , σ(1) r1 the singular values of A(1)

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:25.644483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5a5e7180-d237-497b-917f-7f27c3bf3e0a · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:25.512627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 81956f5d-0ac3-477e-8f67-4bd5099b8980 · outbound

This paper cites an unresolved cited work.

Grokking Beyond the Euclidean Norm of Model Parameters Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:21:25.354431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5e98e864-dade-4351-88bd-609a26eadeb5 · outbound

This paper cites grokking without understanding.

Grokking Beyond the Euclidean Norm of Model Parameters grokking without understanding

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:25.111468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9631bca6-19d9-4bab-a3ad-e5d1b25dabb2 · outbound

This paper cites grokking without understanding.

Grokking Beyond the Euclidean Norm of Model Parameters grokking without understanding

Reference 31

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T10:21:24.831209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2beae235-c702-4dc8-891b-30037aa78462 · outbound

This paper cites Implicit Regularization in Deep Learning May Not Be Explainable by Norms.

Grokking Beyond the Euclidean Norm of Model Parameters Implicit Regularization in Deep Learning May Not Be Explainable by Norms

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-07T10:21:21.818876Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8d8cb86-4c54-4f7b-bf81-9f00d07ac523 · outbound

This paper cites Predicting Grokking Long Before it Happens: A look into the loss landscape of models which grok.

Grokking Beyond the Euclidean Norm of Model Parameters Predicting Grokking Long Before it Happens: A look into the loss landscape of models which grok

Reference 1995

Resolution: unresolved; no resolver link, observed 2026-08-07T10:21:21.670705Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9a086b1-a6a4-4aeb-ae0a-47690f3046d7 · outbound

This paper cites Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation.

Grokking Beyond the Euclidean Norm of Model Parameters Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation

Reference 1996

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T10:21:24.523815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8841bc3c-fde8-48e9-be26-f53b641ce56c · outbound

This paper cites memorization.

Grokking Beyond the Euclidean Norm of Model Parameters memorization

Reference 2022

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:28.600774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7d709419-1fd9-4519-8a5a-743d13f3c1c7 · outbound

This paper cites incoherent.

Grokking Beyond the Euclidean Norm of Model Parameters incoherent

Reference 2025

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:21:28.457035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2d3f2e16-1cf3-4a30-93ff-d7499f7080c1 · outbound

This paper cites Progress Measures for Grokking on Real-world Tasks.

Grokking Beyond the Euclidean Norm of Model Parameters Progress Measures for Grokking on Real-world Tasks

Reference 5468

Resolution: unresolved; no resolver link, observed 2026-08-07T10:21:21.569536Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68e6b1b3-ef9c-47e0-8735-5024d86f1f3c · outbound

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

Grokking Beyond the Euclidean Norm of Model Parameters Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking

Reference 7200

Resolution: unresolved; no resolver link, observed 2026-08-07T10:21:21.605878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation deb56c7f-9d17-4841-b950-c1bfaba0e966 · inbound

What Does the Weight Norm Control in Grokking? Logit-Scale Mediation under Cross-Entropy cites this paper.

What Does the Weight Norm Control in Grokking? Logit-Scale Mediation under Cross-Entropy Grokking Beyond the Euclidean Norm of Model Parameters

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-03T21:18:58.711256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.