Paper Citation Record · LEDGER

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

As of 13 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 11 inbound Pith citation observations for arXiv:2412.17739.

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

pith.paper-citation-record.v1
2412.17739 v4

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T05:18:54.599127Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 11 of 11 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T05:06:51.812677Z

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

25 of 25 outbound references displayed

verified exact2
verified fuzzy5
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

1
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 73abff5e-3522-477e-b544-21dff2d2b9e3 · outbound

This paper cites HoPE: A Novel Positional Encoding Without Long-Term Decay for Enhanced Context Awareness and Extrapolation.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization HoPE: A Novel Positional Encoding Without Long-Term Decay for Enhanced Context Awareness and Extrapolation

Reference 3

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T05:18:55.053956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 252a49c2-5e77-43f6-b769-4af2c14c3beb · outbound

This paper cites Exploring Context Window of Large Language Models via Decomposed Positional Vectors.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Exploring Context Window of Large Language Models via Decomposed Positional Vectors

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.433336Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c97c99b2-db9a-46c9-a41d-c3dee0b9bf4a · outbound

This paper cites SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization SAMSum Corpus: A Human-annotated Dialogue Dataset for Abstractive Summarization

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.455709Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05735c6e-ffab-4b82-b599-dc8df5da9e66 · outbound

This paper cites OLMo: Accelerating the Science of Language Models.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization OLMo: Accelerating the Science of Language Models

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.461609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 217338d6-b10e-44f5-9ae4-bd581cadefb6 · outbound

This paper cites Efficiently Modeling Long Sequences with Structured State Spaces.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Efficiently Modeling Long Sequences with Structured State Spaces

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.467771Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0c11acb-7f8d-4164-b65d-acf589380943 · outbound

This paper cites Efficient Attentions for Long Document Summarization.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Efficient Attentions for Long Document Summarization

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.484670Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 923efcb6-c8e0-4f29-8bc9-897de65c0965 · outbound

This paper cites TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.498681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35a4fd53-5eb2-4c26-90d0-10d52f424946 · outbound

This paper cites Fnet: Mixing tokens with fourier transforms.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Fnet: Mixing tokens with fourier transforms

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:18:55.158159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7e2f3435-9136-4e4e-9e26-e0d05e8bb250 · outbound

This paper cites and Roth, D.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization and Roth, D

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:18:55.140670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8014e8c3-8141-42cd-b60d-01713fade457 · outbound

This paper cites SMR: State Memory Replay for Long Sequence Modeling.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization SMR: State Memory Replay for Long Sequence Modeling

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:18:54.814593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5e2cd189-338c-40b2-9d18-f7139fe6a007 · outbound

This paper cites Encoding word order in complex embeddings.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Encoding word order in complex embeddings

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.566396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b8f4df77-7f58-46a0-9c6f-c77f3c4f229f · outbound

This paper cites Length Generalization of Causal Transformers without Position Encoding.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Length Generalization of Causal Transformers without Position Encoding

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.573270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c48c3e03-ca1d-49f5-8b2e-c60e0507419c · outbound

This paper cites A., Oguz, B., Khabsa, M., Fang, H., Mehdad, Y ., Narang, S., Malik, K., Fan, A., Bhosale, S., Edunov, S., Lewis, M., Wang, S., and Ma, H.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization A., Oguz, B., Khabsa, M., Fang, H., Mehdad, Y ., Narang, S., Malik, K., Fan, A., Bhosale, S., Edunov, S., Lewis, M., Wang, S., and Ma, H

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:18:55.123862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4086da36-a55d-4410-a50f-f5e699e451b8 · outbound

This paper cites XLNet: Generalized Autoregressive Pretraining for Language Understanding.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization XLNet: Generalized Autoregressive Pretraining for Language Understanding

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.593752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation baa77348-5b5f-4f8e-b7c5-a34d96687bf6 · outbound

This paper cites To get the ”Ideal RoPE’s Contribution”, we suppose the Query and Key vectors are equal to 1 constantly (as in the original paper of RoPE (Su et al., 2024).

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization To get the ”Ideal RoPE’s Contribution”, we suppose the Query and Key vectors are equal to 1 constantly (as in the original paper of RoPE (Su et al., 2024)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:18:55.105509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 53a979d7-3cd6-4390-afd0-aada0a796a44 · outbound

This paper cites Multi-News: a Large-Scale Multi-Document Summarization Dataset and Abstractive Hierarchical Model.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Multi-News: a Large-Scale Multi-Document Summarization Dataset and Abstractive Hierarchical Model

Reference 2000

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.439848Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db320341-e811-4ef3-92f8-5c559d73d5f2 · outbound

This paper cites Mixture of In-Context Experts Enhance LLMs' Long Context Awareness.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Mixture of In-Context Experts Enhance LLMs' Long Context Awareness

Reference 2002

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.526861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a74a1207-a15d-4da6-b3a8-e3b3e2945d4c · outbound

This paper cites Hong, X., Jiang, C., Qi, B., Meng, F., Yu, M., Zhou, B., and Zhou, J.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Hong, X., Jiang, C., Qi, B., Meng, F., Yu, M., Zhou, B., and Zhou, J

Reference 2007

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:18:55.173982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bd3bc8fd-24c4-49e3-807e-2783c3a06205 · outbound

This paper cites Self-Attention with Relative Position Representations.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Self-Attention with Relative Position Representations

Reference 2010

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.540598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72feeb7f-2773-4d4f-9e38-7f166988fbd3 · outbound

This paper cites Neurons in Large Language Models: Dead, N-gram, Positional.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Neurons in Large Language Models: Dead, N-gram, Positional

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.553453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f75dc907-df70-48ae-b25b-4bd1b6236c9f · outbound

This paper cites Fourier Head: Helping Large Language Models Learn Complex Probability Distributions.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Fourier Head: Helping Large Language Models Learn Complex Probability Distributions

Reference 2019

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:18:54.996959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e80fcce9-6ab4-42cb-8c1f-367180b1bee7 · outbound

This paper cites LLaMA: Open and Efficient Foundation Language Models.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization LLaMA: Open and Efficient Foundation Language Models

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.546602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b815db7a-f473-409c-8bd8-65ab2aff5842 · outbound

This paper cites LLM Maybe LongLM: Self-Extend LLM Context Window Without Tuning.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization LLM Maybe LongLM: Self-Extend LLM Context Window Without Tuning

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.491009Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d8930d1-f1ef-4e8c-b134-e31a7a766186 · outbound

This paper cites Round and Round We Go! What makes Rotary Positional Encodings useful?.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization Round and Round We Go! What makes Rotary Positional Encodings useful?

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.414888Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6aa34086-b32b-4b3c-bb21-6e6e00f594fd · outbound

This paper cites LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding.

Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T05:18:54.405879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 514b9315-dc90-411a-98be-9b81b6177aa4 · inbound

SeqPE: Transformer with Sequential Position Encoding cites this paper.

SeqPE: Transformer with Sequential Position Encoding Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T00:45:02.940894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07e30fac-3258-49cd-973e-f123b46b2a41 · inbound

CoPE: A Lightweight Complex Positional Encoding cites this paper.

CoPE: A Lightweight Complex Positional Encoding Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-05T17:13:11.792545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4215a694-f9a7-4881-9e3d-4fc0220d2853 · inbound

Mitigating Coordinate Prediction Bias from Positional Encoding Failures cites this paper.

Mitigating Coordinate Prediction Bias from Positional Encoding Failures Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-18T05:12:23.576606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1954f43f-480a-4efb-ba53-c9008c540c5a · inbound

Kimi Linear: An Expressive, Efficient Attention Architecture cites this paper.

Kimi Linear: An Expressive, Efficient Attention Architecture Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-13T23:49:11.154378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 79ff3d99-6ab9-4f86-aa36-c5d1e7382b33 · inbound

UCAN: Unified Convolutional Attention Network for Expansive Receptive Fields in Lightweight Super-Resolution cites this paper.

UCAN: Unified Convolutional Attention Network for Expansive Receptive Fields in Lightweight Super-Resolution Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-15T12:30:35.240254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation be47ecd7-e2c7-489a-b025-2e8b2378082c · 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 Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 7

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T00:49:48.460750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 161dcf8f-9826-479d-90a3-4cddbefb8f67 · inbound

Weierstrass Positional Encoding for Vision Transformers cites this paper.

Weierstrass Positional Encoding for Vision Transformers Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-25T05:50:23.765922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bdca59fe-1cc1-4e18-bb3f-e8a47482b1de · inbound

Mix-MoE: Improving Multilingual Machine Translation of Large Language Models through Mixed MoEs cites this paper.

Mix-MoE: Improving Multilingual Machine Translation of Large Language Models through Mixed MoEs Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-06-30T13:24:40.046732Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 795b498e-3a38-4fde-8a3c-d59354bfb0dd · inbound

LazyAttention: Efficient Retrieval-Augmented Generation with Deferred Positional Encoding cites this paper.

LazyAttention: Efficient Retrieval-Augmented Generation with Deferred Positional Encoding Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 69

Resolution: verified exact; arxiv_id, observed 2026-06-28T07:11:45.570922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 05113f2d-9de5-4c38-a7da-e196b2ea0ef4 · inbound

ClockRoPE: Random Fourier Rotations for Temporal Routine Modeling cites this paper.

ClockRoPE: Random Fourier Rotations for Temporal Routine Modeling Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T17:23:25.469076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfa75425-95e9-4cc8-95a2-268522f777dc · inbound

Addressable Memory for Video World Models cites this paper.

Addressable Memory for Video World Models Fourier Position Embedding: Enhancing Attention's Periodic Extension for Length Generalization

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-10T05:06:51.812677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.