Paper Citation Record · LEDGER

Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 10 inbound Pith citation observations for arXiv:2407.20199.

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

pith.paper-citation-record.v1
2407.20199 v3

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 10 of 10 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 10 of 10 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T11:19:06.940034Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 1d92bf66-9cac-4000-80d8-58e5e572e237 · inbound

Adaptive kernel predictors from feature-learning infinite limits of neural networks cites this paper.

Adaptive kernel predictors from feature-learning infinite limits of neural networks Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-08T11:19:06.940034Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf772343-b122-42ed-944c-57473aa521d7 · 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 Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:55.768975Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1280246e-07d3-4806-9092-b06d74ad9cd6 · inbound

xRFM: Accurate, scalable, and interpretable feature learning models for tabular data cites this paper.

xRFM: Accurate, scalable, and interpretable feature learning models for tabular data Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 27

Resolution: metadata mismatch; arxiv_id, observed 2026-05-18T23:11:53.953404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ec55a93f-f259-495b-972d-ccfb5607089c · inbound

The Geometric Structure of Models Learning Sparse Data cites this paper.

The Geometric Structure of Models Learning Sparse Data Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 36

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T07:16:28.805391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 08c196f9-a412-42ee-823c-01534798e151 · inbound

The Geometric Structure of Models Learning Sparse Data cites this paper.

The Geometric Structure of Models Learning Sparse Data Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 36

Resolution: metadata mismatch; arxiv_id, observed 2026-05-19T18:02:42.139719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5d0c61b1-9c87-4e21-bf42-f39de688ff63 · inbound

Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data cites this paper.

Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-05-13T05:57:21.853532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 113c5a74-4be8-4fab-a2b5-779e76dac5f6 · 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 Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 191

Resolution: verified exact; arxiv_id, observed 2026-05-20T01:32:56.053375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e2b1529e-1e86-4b86-82c8-bb09519520df · 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 Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 191

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:40:24.794720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0009c740-b9f5-41e2-9c70-d5614b983e95 · inbound

Law of Neural Interaction: Depth-Width Shape, Interaction Efficiency, and Generalization cites this paper.

Law of Neural Interaction: Depth-Width Shape, Interaction Efficiency, and Generalization Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 39

Resolution: malformed identifier; arxiv_id, observed 2026-06-29T14:23:30.983924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8b641fd5-8c62-4355-b149-a2c948b7657a · inbound

K-Inverse-RFM: A Modified RFM that Bridges the Gap to Neural Networks for Data-Corrupted Mathematical Tasks cites this paper.

K-Inverse-RFM: A Modified RFM that Bridges the Gap to Neural Networks for Data-Corrupted Mathematical Tasks Emergence in non-neural models: grokking modular arithmetic via average gradient outer product

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T16:07:08.195458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.