Paper Citation Record · LEDGER

Grokking Modular Polynomials

As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 13 inbound Pith citation observations for arXiv:2406.03495.

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

pith.paper-citation-record.v1
2406.03495 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 13 of 13 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 13 of 13 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T18:32:14.645620Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T19:08:49.918323Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation bfb1fbbb-74cd-44c4-82c7-91221e920893 · inbound

(How) Can Transformers Predict Pseudo-Random Numbers? cites this paper.

(How) Can Transformers Predict Pseudo-Random Numbers? Grokking Modular Polynomials

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T18:32:14.645620Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Mechanistic Insights into Grokking from the Embedding Layer cites this paper.

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 1a5f812d-08d5-4a78-83e0-206dd977c582 · inbound

Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks cites this paper.

Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks Grokking Modular Polynomials

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:56.187966Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9204c1b0-623d-4178-9221-ff3448285cf5 · inbound

Learning words in groups: fusion algebras, tensor ranks and grokking cites this paper.

Learning words in groups: fusion algebras, tensor ranks and grokking Grokking Modular Polynomials

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T22:57:12.084835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d99fd05a-69c1-42ad-b69b-95fe8bce8ad4 · inbound

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

Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking Grokking Modular Polynomials

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:14:22.032793Z

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 1671c171-2ba0-4148-ae78-93f3e467af22 · inbound

Learning Large-Scale Modular Addition with an Auxiliary Modulus cites this paper.

Learning Large-Scale Modular Addition with an Auxiliary Modulus Grokking Modular Polynomials

Reference 8

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T04:10:59.322631Z

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 d5752ad1-0796-42f3-be5e-5359d7958015 · inbound

Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent cites this paper.

Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent Grokking Modular Polynomials

Reference 199

Resolution: verified exact; arxiv_id, observed 2026-05-20T01:32:56.067252Z

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 f7562153-87d6-477d-bbd6-8b1696dac9e2 · inbound

Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent cites this paper.

Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent Grokking Modular Polynomials

Reference 199

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:40:24.708227Z

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 34109042-3461-4e3e-b68e-fa2db88f7cdf · inbound

Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention cites this paper.

Why Larger Models Learn More: Effects of Capacity, Interference, and Rare-Task Retention Grokking Modular Polynomials

Reference 103

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T08:43:15.243320Z

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 1b83f5e2-9032-4023-ada4-f80c7cd0aa01 · 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 Grokking Modular Polynomials

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-07-02T12:06:56.086673Z

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 c8df9e15-8d35-4647-b3e5-ef2f6e7c77f5 · inbound

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication cites this paper.

The Discrete-Log Clock: How a Transformer Learns Modular Multiplication Grokking Modular Polynomials

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-03T19:08:49.920050Z

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 f14ece75-50a9-4476-bf4b-c901dd234078 · inbound

Grokking Is Conditional and Fragile: A Fully-Tractable, Multi-Seed Study at 12K Parameters cites this paper.

Grokking Is Conditional and Fragile: A Fully-Tractable, Multi-Seed Study at 12K Parameters Grokking Modular Polynomials

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T08:46:29.099447Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 97f906b3-6a31-4418-937f-376213a08d6e · inbound

Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations cites this paper.

Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations Grokking Modular Polynomials

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T03:55:34.633765Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.