Paper Citation Record · LEDGER

The Complexity Dynamics of Grokking

As of 20 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 7 inbound Pith citation observations for arXiv:2412.09810.

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

pith.paper-citation-record.v1
2412.09810 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T16:48:12.689120Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T10:50:30.330031Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-11T00:47:42.265531Z

Reference resolution

34 of 34 outbound references displayed

verified exact3
verified fuzzy6
unresolved25
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 33fb1481-cd85-4a5c-bc8b-bfead2a34cfb · outbound

This paper cites write newline.

The Complexity Dynamics of Grokking write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.603234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a83def1f-57f4-4bdb-bd9c-be0a887e2f19 · outbound

This paper cites write newline.

The Complexity Dynamics of Grokking write newline

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.606969Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c30836bb-bcac-43b6-9ab0-71f0af930bac · outbound

This paper cites write newline.

The Complexity Dynamics of Grokking write newline

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.609540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a3cc2bd-6251-48d9-be78-5cb61be4d38b · outbound

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

The Complexity Dynamics of Grokking Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.612104Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df29f097-dc90-43e9-bda1-a2888eb46b75 · outbound

This paper cites Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton.

The Complexity Dynamics of Grokking Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.614692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7fc0bae-a3f3-4910-bcab-ac1c69709130 · outbound

This paper cites Rissanen , title Modeling by shortest data description* , journal Autom.

The Complexity Dynamics of Grokking Rissanen , title Modeling by shortest data description* , journal Autom

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:48:12.921904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 528ea8b2-4d22-41d0-8706-2ff3c8249c24 · outbound

This paper cites an unresolved cited work.

The Complexity Dynamics of Grokking Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:48:12.914105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3743e39a-dbf8-41c8-bb32-a31767b9826e · outbound

This paper cites an unresolved cited work.

The Complexity Dynamics of Grokking Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:48:12.907310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 10f4730f-f72e-4d89-bf98-50d1f9fee588 · outbound

This paper cites an unresolved cited work.

The Complexity Dynamics of Grokking Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:48:12.900468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e2cbd5a9-b8ef-45c8-b730-b58b245bf57b · outbound

This paper cites an unresolved cited work.

The Complexity Dynamics of Grokking Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:48:12.893888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c721e66f-59fe-4d01-a9f8-c01ee2c5c9dc · outbound

This paper cites Towards Understanding Grokking: An Effective Theory of Representation Learning.

The Complexity Dynamics of Grokking Towards Understanding Grokking: An Effective Theory of Representation Learning

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.628443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f86104b7-cdbd-43ac-a086-0451ce08dbd7 · outbound

This paper cites Omnigrok: Grokking Beyond Algorithmic Data.

The Complexity Dynamics of Grokking Omnigrok: Grokking Beyond Algorithmic Data

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.632173Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e94c250-b9ed-4ea3-b16a-753d635ebf64 · outbound

This paper cites Explaining grokking through circuit efficiency.

The Complexity Dynamics of Grokking Explaining grokking through circuit efficiency

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.635277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd6f56ad-74a7-49cc-abcd-ab029a910450 · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

The Complexity Dynamics of Grokking Progress measures for grokking via mechanistic interpretability

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.638214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c423517e-f78c-4fb7-a497-1574f595414c · outbound

This paper cites Nakkiran , author G.

The Complexity Dynamics of Grokking Nakkiran , author G

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:48:12.887692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2eb41484-530c-44e4-9e3b-3d0e5b75ebd6 · outbound

This paper cites Scaling Laws for Neural Language Models.

The Complexity Dynamics of Grokking Scaling Laws for Neural Language Models

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.644187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21435634-a6d3-4801-a980-9b085aa7b028 · outbound

This paper cites Scaling Laws for Autoregressive Generative Modeling.

The Complexity Dynamics of Grokking Scaling Laws for Autoregressive Generative Modeling

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.647249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2edaf089-c6de-4441-868d-68936cbec5de · outbound

This paper cites Non-Vacuous Generalization Bounds for Large Language Models.

The Complexity Dynamics of Grokking Non-Vacuous Generalization Bounds for Large Language Models

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.650055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb48dff9-5e11-4778-93e5-114514cb544e · outbound

This paper cites The No Free Lunch Theorem, Kolmogorov Complexity, and the Role of Inductive Biases in Machine Learning.

The Complexity Dynamics of Grokking The No Free Lunch Theorem, Kolmogorov Complexity, and the Role of Inductive Biases in Machine Learning

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.652898Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e7d29ee-2ecb-4024-a7e5-81edc91cbb6c · outbound

This paper cites Langford , author M.

The Complexity Dynamics of Grokking Langford , author M

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:48:12.881422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 83197d43-bd7b-462e-9558-0e1047943d44 · outbound

This paper cites Li , author P.

The Complexity Dynamics of Grokking Li , author P

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:48:12.875087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 30295f48-4c16-4c6f-a6b5-42ea4ec109a8 · outbound

This paper cites Blau , author T.

The Complexity Dynamics of Grokking Blau , author T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:48:12.868526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d8b6bb88-74d4-4ec6-9706-cc9c7faade91 · outbound

This paper cites an unresolved cited work.

The Complexity Dynamics of Grokking Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:48:12.861832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ae7c99a6-b438-48cc-b2db-c4a672e1ce66 · outbound

This paper cites Mixed Precision Training.

The Complexity Dynamics of Grokking Mixed Precision Training

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.665891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de86783e-ed87-4c5b-a6ab-c9f09739b0f6 · outbound

This paper cites The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits.

The Complexity Dynamics of Grokking The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.668249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 65d2c1ce-c6c7-4b9e-91a7-72c665e571d7 · outbound

This paper cites an unresolved cited work.

The Complexity Dynamics of Grokking Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-11T16:48:12.855091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5548ac89-4497-4483-bf75-4f0ee09a105b · outbound

This paper cites LoRA: Low-Rank Adaptation of Large Language Models.

The Complexity Dynamics of Grokking LoRA: Low-Rank Adaptation of Large Language Models

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.672581Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c989bc5b-7073-42dd-b9cc-22f53becab67 · outbound

This paper cites QLoRA: Efficient Finetuning of Quantized LLMs.

The Complexity Dynamics of Grokking QLoRA: Efficient Finetuning of Quantized LLMs

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.674825Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74e9d158-280d-4b10-bca9-67401b4c79c7 · outbound

This paper cites Measuring the Intrinsic Dimension of Objective Landscapes.

The Complexity Dynamics of Grokking Measuring the Intrinsic Dimension of Objective Landscapes

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.677099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f6dd97f-1f7c-4697-970b-027d6de68625 · outbound

This paper cites Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning.

The Complexity Dynamics of Grokking Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-11T16:48:12.679940Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2022e735-33e3-4598-8a5b-d6fbb77814e6 · outbound

This paper cites Roy , author M.

The Complexity Dynamics of Grokking Roy , author M

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:48:12.846908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8d6a5e3e-9604-409e-a992-52af5a72d45f · outbound

This paper cites Ebtekar , author M.

The Complexity Dynamics of Grokking Ebtekar , author M

Reference 32

Resolution: verified exact; doi, observed 2026-08-11T16:48:12.728529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1a1d2958-14c4-4d89-b873-f2e4c7a69041 · outbound

This paper cites Baez , author M.

The Complexity Dynamics of Grokking Baez , author M

Reference 33

Resolution: verified exact; doi, observed 2026-08-11T16:48:12.719971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3833acb9-57b8-4f8f-a638-dbe3f1eaebd5 · outbound

This paper cites Kolchinsky , author D.

The Complexity Dynamics of Grokking Kolchinsky , author D

Reference 34

Resolution: verified exact; doi, observed 2026-08-11T16:48:12.711984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 3ce1a1a6-583a-409e-a2e4-b64e46338660 · inbound

Unifying Two Types of Scaling Laws from the Perspective of Conditional Kolmogorov Complexity cites this paper.

Unifying Two Types of Scaling Laws from the Perspective of Conditional Kolmogorov Complexity The Complexity Dynamics of Grokking

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T20:56:20.942932Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 526f62ac-0da1-4080-a59e-50dc51476ce2 · inbound

Compositional Generalization via Forced Rendering of Disentangled Latents cites this paper.

Compositional Generalization via Forced Rendering of Disentangled Latents The Complexity Dynamics of Grokking

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-09T22:31:17.317028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8bfb5cfe-7e14-4285-b099-106506d729dd · inbound

Grokking vs. Learning: Same Features, Different Encodings cites this paper.

Grokking vs. Learning: Same Features, Different Encodings The Complexity Dynamics of Grokking

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-09T14:44:27.013833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06225137-1a24-4b5e-8e9b-66396ee83cb4 · inbound

NeuralGrok: Accelerate Grokking by Neural Gradient Transformation cites this paper.

NeuralGrok: Accelerate Grokking by Neural Gradient Transformation The Complexity Dynamics of Grokking

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T10:50:30.330031Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d49d725-10f8-4629-9d37-103edb2dd138 · inbound

Reinforcement Learning for Reasoning in Large Language Models with One Training Example cites this paper.

Reinforcement Learning for Reasoning in Large Language Models with One Training Example The Complexity Dynamics of Grokking

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-05-15T19:51:04.983727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a3f8f410-1d6c-4881-bf08-9a9af42aed18 · inbound

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

Model Capacity Determines Grokking through Competing Memorisation and Generalisation Speeds The Complexity Dynamics of Grokking

Reference 40

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:56:21.709805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ec834ab3-76ea-4e03-a1d4-056ad0216a62 · 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 The Complexity Dynamics of Grokking

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-07-11T00:47:42.289616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.