Paper Citation Record · LEDGER

Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

As of 20 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2402.09469.

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

pith.paper-citation-record.v1
2402.09469 v4

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 6 of 6 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:56:34.205833Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-23T03:12:28.775466Z

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 475f8bbe-670a-4978-9d92-64691aaeddc1 · inbound

Numerical Pruning for Efficient Autoregressive Models cites this paper.

Numerical Pruning for Efficient Autoregressive Models Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Reference 59

Resolution: unresolved; no resolver link, observed 2026-08-11T14:11:27.013958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b12cf0fd-259b-4a4a-8706-a65b8c672175 · inbound

LazyDiT: Lazy Learning for the Acceleration of Diffusion Transformers cites this paper.

LazyDiT: Lazy Learning for the Acceleration of Diffusion Transformers Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-11T14:11:39.496594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb542a59-e055-4bf5-b0c5-a5da46059bf9 · inbound

Video Latent Flow Matching: Optimal Polynomial Projections for Video Interpolation and Extrapolation cites this paper.

Video Latent Flow Matching: Optimal Polynomial Projections for Video Interpolation and Extrapolation Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-09T18:51:12.545706Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6892761-25c6-47f5-9fe8-51370119a235 · inbound

FoNE: Precise Single-Token Number Embeddings via Fourier Features cites this paper.

FoNE: Precise Single-Token Number Embeddings via Fourier Features Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-23T03:12:28.778958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1df9b6d3-71d8-490e-8675-3548304193f4 · inbound

Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transform cites this paper.

Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transform Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Reference 106

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:34.205833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ba5a09e-d4d9-447a-bb1a-139e4e042d31 · inbound

Convergent Evolution: How Different Language Models Learn Similar Number Representations cites this paper.

Convergent Evolution: How Different Language Models Learn Similar Number Representations Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs

Reference 9

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T00:49:48.456285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.