Paper Citation Record · LEDGER

GrokAlign: Geometric Characterisation and Acceleration of Grokking

As of 18 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 1 inbound Pith citation observation for arXiv:2506.12284.

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

pith.paper-citation-record.v1
2506.12284 v2

Coverage vector

measured 44 of 44 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T01:00:39.989192Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-21T21:13:24.267454Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-21T21:14:22.034596Z

Reference resolution

44 of 44 outbound references displayed

verified exact2
verified fuzzy36
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 61c268fd-ddac-46a3-b142-2fc896a19431 · outbound

This paper cites Lecun, L.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Lecun, L

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T01:00:36.638337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f82bf01-18f0-490a-b8d3-a8a39f584d6b · outbound

This paper cites SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries.

GrokAlign: Geometric Characterisation and Acceleration of Grokking SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:45.099731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6c1bfda6-7729-4ddd-894d-a9969490e372 · outbound

This paper cites Aazhang, and Richard Baraniuk.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Aazhang, and Richard Baraniuk

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:44.806886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f77666c4-5a2b-4562-b1d0-2c159416a354 · outbound

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

GrokAlign: Geometric Characterisation and Acceleration of Grokking Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T01:00:36.935473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d4a8afa-e03b-4965-9aa4-da40e96d8206 · outbound

This paper cites Loss landscape geometry reveals stagewise development of transformers.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Loss landscape geometry reveals stagewise development of transformers

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:44.552782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 313b284b-d6df-4535-8eb1-4739908b4456 · outbound

This paper cites Michaud, and Max Tegmark.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Michaud, and Max Tegmark

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:44.395208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 91292880-dcab-4148-ad56-913abbc18e9b · outbound

This paper cites Deep Networks Always Grok and Here is Why.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Deep Networks Always Grok and Here is Why

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:44.143231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 94a9626e-1f0b-4b26-a0a0-62453201e453 · outbound

This paper cites Robustness may be at odds with accuracy.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Robustness may be at odds with accuracy

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.960791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation eb5571d9-5c39-4cc4-bc45-758cd82ef463 · outbound

This paper cites Theoretically Principled Trade-off between Robustness and Accuracy.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Theoretically Principled Trade-off between Robustness and Accuracy

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.821867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0044ab35-2852-4e9b-9d6e-a9226f3f5644 · outbound

This paper cites Lee, and Wei Hu.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Lee, and Wei Hu

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.651868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a1a5923a-dc69-4a0e-935b-526e5a255775 · outbound

This paper cites Grokking as a First Order Phase Transition in Two Layer Networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Grokking as a First Order Phase Transition in Two Layer Networks

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.512411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d64ce499-b4dc-4d4b-8917-6d6d3f007565 · outbound

This paper cites Gershman, and Cengiz Pehlevan.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Gershman, and Cengiz Pehlevan

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.333008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 20b5bfb7-2e49-4ad5-ac00-e436b91f47ea · outbound

This paper cites Neural tangent kernel: convergence and generalization in neural networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Neural tangent kernel: convergence and generalization in neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.179572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 439c74a6-6ab0-465d-83e9-efd3c8f2385d · outbound

This paper cites Separation of scales and a thermodynamic description of feature learning in some CNNs.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Separation of scales and a thermodynamic description of feature learning in some CNNs

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:43.076588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6432fb5f-bac5-4adb-8563-28059039aa23 · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Progress measures for grokking via mechanistic interpretability

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.993054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d0df5cde-9239-44cc-98c1-c205df3ec890 · outbound

This paper cites Explaining grokking through circuit efficiency.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Explaining grokking through circuit efficiency

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T01:00:37.893406Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b23fbed-7f1a-409f-bdb3-f3527825eb38 · outbound

This paper cites Contractive auto- encoders: explicit invariance during feature extraction.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Contractive auto- encoders: explicit invariance during feature extraction

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.926573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2cb6df73-5df0-4b57-9654-fe66e1ac03c5 · outbound

This paper cites Improving DNN Robustness to Adversarial Attacks Using Jacobian Regularization.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Improving DNN Robustness to Adversarial Attacks Using Jacobian Regularization

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.850646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cf405871-487c-41af-9b42-a358361baee8 · outbound

This paper cites Robust Learning with Jacobian Regularization.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Robust Learning with Jacobian Regularization

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T01:00:38.112185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 961e3384-f150-4ac9-94e6-387f6075448d · outbound

This paper cites On the Connection Between Adversarial Robustness and Saliency Map Interpretability.

GrokAlign: Geometric Characterisation and Acceleration of Grokking On the Connection Between Adversarial Robustness and Saliency Map Interpretability

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.768520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6151c10e-ae9e-43a6-878f-7ee9547def91 · outbound

This paper cites Jacobian adversarially regularized networks for robustness.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Jacobian adversarially regularized networks for robustness

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.677292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2ec44cca-eb61-4937-a655-eb08ba35c973 · outbound

This paper cites Training invariances and the low-rank phenomenon: beyond linear networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Training invariances and the low-rank phenomenon: beyond linear networks

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.596851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5f231a57-4564-47cb-8e38-cd48db196bb7 · outbound

This paper cites The low-rank simplicity bias in deep networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking The low-rank simplicity bias in deep networks

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.503464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3bae733b-1915-4947-bf4d-faf8b39bd422 · outbound

This paper cites Implicit Regularization Towards Rank Minimization in ReLU Networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Implicit Regularization Towards Rank Minimization in ReLU Networks

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.406491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 84f0806f-2391-4880-bbbc-deaf3dd753d0 · outbound

This paper cites Rank minimization, alignment and weight decay in neural networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Rank minimization, alignment and weight decay in neural networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.280354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1467b0fd-60ec-4798-addf-b9c8f1d087f9 · outbound

This paper cites Siegel, Aparna Gupte, and Tomaso A.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Siegel, Aparna Gupte, and Tomaso A

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.207037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cf228774-692d-4cc4-95b2-7cd757d9118b · outbound

This paper cites Fast Jacobian-Vector Product for Deep Networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Fast Jacobian-Vector Product for Deep Networks

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-07T01:00:40.269490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation de0871b4-5b2e-4e0c-b945-13965019ebcd · outbound

This paper cites A Spline Theory of Deep Learning.

GrokAlign: Geometric Characterisation and Acceleration of Grokking A Spline Theory of Deep Learning

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:42.092963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 39b56b07-4ab8-4bd8-9564-8dcad5b53fc4 · outbound

This paper cites Decoupled weight decay regularization.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Decoupled weight decay regularization

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T01:00:38.882637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a0be4cd-594e-470f-aacc-9377d18bc3e2 · outbound

This paper cites Gu and Luca Rigazio.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Gu and Luca Rigazio

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.991765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5196ae04-d5f3-4181-a09e-247832e8436e · outbound

This paper cites A closer look at accuracy vs.

GrokAlign: Geometric Characterisation and Acceleration of Grokking A closer look at accuracy vs

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.896428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 243c6626-68d3-4329-a7fe-6c6bf0bd8918 · outbound

This paper cites Grokfast: Accelerated Grokking by Amplifying Slow Gradients.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Grokfast: Accelerated Grokking by Amplifying Slow Gradients

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T01:00:39.136957Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba6dcd7e-5881-4dbe-9b6f-00e4455bd547 · outbound

This paper cites On Lazy Training in Differentiable Programming.

GrokAlign: Geometric Characterisation and Acceleration of Grokking On Lazy Training in Differentiable Programming

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.789909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a966e09c-ffac-4786-85c5-6ba472d3651a · outbound

This paper cites Lee, Edward Moroshko, Pedro Savarese, Itay Golan, Daniel Soudry, and Nathan Srebro.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Lee, Edward Moroshko, Pedro Savarese, Itay Golan, Daniel Soudry, and Nathan Srebro

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.668125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4a1b7bf3-ea4d-4a9a-b129-75a7e5a14a24 · outbound

This paper cites Lee, Nathan Srebro, and Daniel Soudry.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Lee, Nathan Srebro, and Daniel Soudry

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.564125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 68d2ef77-6cb4-4ae1-9692-15533032f792 · outbound

This paper cites Let me grok for you: Accelerating grokking via embedding transfer from a weaker model.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Let me grok for you: Accelerating grokking via embedding transfer from a weaker model

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.395452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 311ca792-b959-497d-9030-6ba42517b0a4 · outbound

This paper cites Learning multiple layers of features from tiny images.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Learning multiple layers of features from tiny images

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.253784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 39bc73e4-8267-4b19-8343-2344c2dd1b91 · outbound

This paper cites Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:41.100233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 215bb04b-da33-4bf8-b375-93741a3f6be8 · outbound

This paper cites Understanding Grokking Through A Robustness Viewpoint.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Understanding Grokking Through A Robustness Viewpoint

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-07T01:00:40.143032Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7569540f-b536-4e9f-afef-b4a6f9cf14ae · outbound

This paper cites Attention is All you Need.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Attention is All you Need

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:40.971487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d6d8a535-2826-47bd-bece-3c0d22b09606 · outbound

This paper cites Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:40.834039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1e3450e1-eca7-4ddd-9b53-d50d8548a0d3 · outbound

This paper cites Disentangling feature and lazy training in deep neural networks.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Disentangling feature and lazy training in deep neural networks

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:40.691885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c7787172-5fc7-4859-a95e-db65f454e073 · outbound

This paper cites Under the assumptions, the output of the neural network at xp is Aωxp xp.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Under the assumptions, the output of the neural network at xp is Aωxp xp

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:40.575702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 69e23375-60a2-4d81-a0e5-a0a5ab99de57 · outbound

This paper cites Under the assumptions, the output of the deep network at xp is Aωxp xp.

GrokAlign: Geometric Characterisation and Acceleration of Grokking Under the assumptions, the output of the deep network at xp is Aωxp xp

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T01:00:40.435375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 654b7e58-2fcf-4e26-bdbd-ae857e5dd4b0 · inbound

Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking cites this paper.

Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking GrokAlign: Geometric Characterisation and Acceleration of Grokking

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:14:22.037868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.