Paper Citation Record · LEDGER

Mechanistic Insights into Grokking from the Embedding Layer

As of 23 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 3 inbound Pith citation observations for arXiv:2505.15624.

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

pith.paper-citation-record.v1
2505.15624 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:20:33.600845Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 3 of 3 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 2026-07-11T00:47:42.529781Z

Reference resolution

29 of 29 outbound references displayed

verified exact0
verified fuzzy7
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a1567f65-7ae7-4bfb-9799-d8f790b73b5c · outbound

This paper cites Unifying Grokking and Double Descent.

Mechanistic Insights into Grokking from the Embedding Layer Unifying Grokking and Double Descent

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:31.311984Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d143eb0-f0f2-4aec-a7f8-7cb0c7af2b31 · outbound

This paper cites Grokking Modular Polynomials.

Mechanistic Insights into Grokking from the Embedding Layer Grokking Modular Polynomials

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:31.413642Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9945eda6-9954-4e43-90e3-a9ff8dec296c · outbound

This paper cites Deep Grokking: Would Deep Neural Networks Generalize Better?.

Mechanistic Insights into Grokking from the Embedding Layer Deep Grokking: Would Deep Neural Networks Generalize Better?

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:31.512408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c346a6e-f423-4725-bf80-2df3f2041573 · outbound

This paper cites Grokking modular arithmetic.

Mechanistic Insights into Grokking from the Embedding Layer Grokking modular arithmetic

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:31.589869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03ef6097-b76f-4801-a308-79708ae23106 · outbound

This paper cites an unresolved cited work.

Mechanistic Insights into Grokking from the Embedding Layer Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:20:36.091392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 516a2bc2-0ad6-4865-97d4-94074518c8a5 · outbound

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

Mechanistic Insights into Grokking from the Embedding Layer Deep Networks Always Grok and Here is Why

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:31.770732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8055ed54-856d-4d60-b4da-3bfb127837fd · outbound

This paper cites Jeffares, A.

Mechanistic Insights into Grokking from the Embedding Layer Jeffares, A

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:35.927084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c2cb3d8b-281f-492e-9aac-cb0261ace342 · outbound

This paper cites Kobayashi, Y.

Mechanistic Insights into Grokking from the Embedding Layer Kobayashi, Y

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:35.782635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation efec256d-0e15-427f-a806-b591c61bfe1b · outbound

This paper cites Kumar.Grokking as the transition from lazy to rich training dynamics.

Mechanistic Insights into Grokking from the Embedding Layer Kumar.Grokking as the transition from lazy to rich training dynamics

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:35.650629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation dd889ea2-f70c-49c0-805a-a2fce27314aa · outbound

This paper cites Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be.

Mechanistic Insights into Grokking from the Embedding Layer Noise Is Not the Main Factor Behind the Gap Between SGD and Adam on Transformers, but Sign Descent Might Be

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.185977Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6d12055-1c57-463e-97b5-fb5fb706bda7 · outbound

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

Mechanistic Insights into Grokking from the Embedding Layer Grokfast: Accelerated Grokking by Amplifying Slow Gradients

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.279376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b8b276ee-db82-4c96-b527-582ea220c614 · outbound

This paper cites an unresolved cited work.

Mechanistic Insights into Grokking from the Embedding Layer Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:20:35.527786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6f712040-a429-4652-8368-7fb819591959 · outbound

This paper cites an unresolved cited work.

Mechanistic Insights into Grokking from the Embedding Layer Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:20:35.411399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4edad32a-ca95-44e4-aa99-fd44fb87a4c7 · outbound

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

Mechanistic Insights into Grokking from the Embedding Layer Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.525471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe6b5f78-8ed3-44df-a795-4e4e76431139 · outbound

This paper cites Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition.

Mechanistic Insights into Grokking from the Embedding Layer Why Do You Grok? A Theoretical Analysis of Grokking Modular Addition

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.612854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdd0ef98-8ed2-4d81-83c7-a3921b229c0f · outbound

This paper cites Nakkiran, G.

Mechanistic Insights into Grokking from the Embedding Layer Nakkiran, G

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:35.198115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ef27649e-48a9-407b-ad40-f0bea8a86ee0 · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

Mechanistic Insights into Grokking from the Embedding Layer Progress measures for grokking via mechanistic interpretability

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.787652Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86065612-bebb-4c33-b7ee-6d21d2f4474e · outbound

This paper cites Toward Understanding Why Adam Converges Faster Than SGD for Transformers.

Mechanistic Insights into Grokking from the Embedding Layer Toward Understanding Why Adam Converges Faster Than SGD for Transformers

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.846977Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ff63fd5-d0ac-42d9-b025-6f6a941825fc · outbound

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

Mechanistic Insights into Grokking from the Embedding Layer Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.907248Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a6f4584-9cee-4797-9c82-1e357fe54ed9 · outbound

This paper cites Grokking at the Edge of Numerical Stability.

Mechanistic Insights into Grokking from the Embedding Layer Grokking at the Edge of Numerical Stability

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:32.966025Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 934c21f7-3b4a-432d-ae6c-16d98684e37a · outbound

This paper cites Explaining grokking through circuit efficiency.

Mechanistic Insights into Grokking from the Embedding Layer Explaining grokking through circuit efficiency

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:33.018742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f68dad0-555d-49be-a7f5-b6cf1d835efa · outbound

This paper cites an unresolved cited work.

Mechanistic Insights into Grokking from the Embedding Layer Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:33.088522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation befd7f07-cf2f-4dd4-837c-c158b116bf73 · outbound

This paper cites Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model.

Mechanistic Insights into Grokking from the Embedding Layer Let Me Grok for You: Accelerating Grokking via Embedding Transfer from a Weaker Model

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:33.165073Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 64a87adb-cb78-467d-980d-9ca0ad804177 · outbound

This paper cites Yang and E.

Mechanistic Insights into Grokking from the Embedding Layer Yang and E

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:34.955379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a46dae56-8ffe-4a9d-972c-b3508831d25c · outbound

This paper cites Zhang, S.

Mechanistic Insights into Grokking from the Embedding Layer Zhang, S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:34.789016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8db54ecc-4645-45b5-aa8f-62252775bc69 · outbound

This paper cites Why Transformers Need Adam: A Hessian Perspective.

Mechanistic Insights into Grokking from the Embedding Layer Why Transformers Need Adam: A Hessian Perspective

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T15:20:33.396451Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 63cf471c-575a-4285-8928-cd5f11de9c27 · outbound

This paper cites an unresolved cited work.

Mechanistic Insights into Grokking from the Embedding Layer Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:20:34.646298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 94d77c88-887a-4b30-a7c5-afbfd1704530 · outbound

This paper cites an unresolved cited work.

Mechanistic Insights into Grokking from the Embedding Layer Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:20:34.462892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0cb443d6-bec1-4308-ab18-747d43efe9dd · outbound

This paper cites Figure 9 shows the maximum eigenvalues of the Hessian with respect to E and W during training.

Mechanistic Insights into Grokking from the Embedding Layer Figure 9 shows the maximum eigenvalues of the Hessian with respect to E and W during training

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:20:34.254769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation 62ecb233-e66f-4453-a930-9227882a6184 · inbound

Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction cites this paper.

Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction Mechanistic Insights into Grokking from the Embedding Layer

Reference 57

Resolution: verified exact; arxiv_id, observed 2026-07-02T12:06:56.081199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1b04501c-70a7-4c5e-8e6e-8f0b3f04c833 · inbound

Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic cites this paper.

Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic Mechanistic Insights into Grokking from the Embedding Layer

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-02T23:57:28.749482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 19c113ba-196b-4a86-8859-7cab247f68bd · 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 Mechanistic Insights into Grokking from the Embedding Layer

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-07-11T00:47:42.552783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.