Paper Citation Record · LEDGER

Neural Functions for Learning Periodic Signal

As of 14 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2506.09526.

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

pith.paper-citation-record.v1
2506.09526 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:53:38.128358Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:58:27.801417Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T17:58:28.705397Z

Reference resolution

46 of 46 outbound references displayed

verified exact3
verified fuzzy19
unresolved21
parse uncertain0
malformed identifier3
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 526ebed0-f6c8-4347-ae2a-f46d41d58e5e · outbound

This paper cites Seeing implicit neural representations as fourier series.

Neural Functions for Learning Periodic Signal Seeing implicit neural representations as fourier series

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:46.279439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 495566d5-34ba-434d-ac9e-fcea9c0beb1b · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:45.060936Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ff4e317e-5396-49d8-b325-ad52ff6a793e · outbound

This paper cites DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting.

Neural Functions for Learning Periodic Signal DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:32.948278Z

Source-reported events for the cited work

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Observation 4cfced15-308c-46db-82b7-7d7e74dd9022 · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:43.866829Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b494aa42-d4f9-49b5-a39e-fdd9d6a1337c · outbound

This paper cites Therefore, the window size is a critical hyperparameter in modeling time series.

Neural Functions for Learning Periodic Signal Therefore, the window size is a critical hyperparameter in modeling time series

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:44.335096Z

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Observation 210e0f0e-9726-4ca3-b315-2f24d2d0ad44 · outbound

This paper cites Time2Vec: Learning a Vector Representation of Time.

Neural Functions for Learning Periodic Signal Time2Vec: Learning a Vector Representation of Time

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:33.545278Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b9cdbc3-b132-48b1-9052-c34af5ae70b6 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neural Functions for Learning Periodic Signal Adam: A Method for Stochastic Optimization

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:33.663972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47031cd7-c069-4322-8f3d-341cf518227c · outbound

This paper cites Multi-Time Attention Networks for Irregularly Sampled Time Series.

Neural Functions for Learning Periodic Signal Multi-Time Attention Networks for Irregularly Sampled Time Series

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:34.152740Z

Source-reported events for the cited work

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Observation 5fd93b97-0862-4cb9-b5c3-6c8f821a1b40 · outbound

This paper cites Transformers in Time Series: A Survey.

Neural Functions for Learning Periodic Signal Transformers in Time Series: A Survey

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:34.296829Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8cac6d96-70cb-4bc1-b761-b76765e838ee · outbound

This paper cites Learning Deep Time-index Models for Time Series Forecasting.

Neural Functions for Learning Periodic Signal Learning Deep Time-index Models for Time Series Forecasting

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:53:38.908229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6e4cad5d-8d99-4fed-a104-3f89220aa0e6 · outbound

This paper cites Neural Functional Transformers.

Neural Functions for Learning Periodic Signal Neural Functional Transformers

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:53:38.658927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 52aae692-ef31-4331-8c37-53150f98b365 · outbound

This paper cites Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting.

Neural Functions for Learning Periodic Signal Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:45.528349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 400409b6-9084-416f-8525-262a71f14ba5 · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:45.348749Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5ccf2b33-3c66-4465-96ec-8592785a5163 · outbound

This paper cites Transformers (Vaswani et al., 2017; Zhou et al., 2021; Wu et al., 2021; Liu et al., 2021; Wen et al., 2022; Zhou et al.,.

Neural Functions for Learning Periodic Signal Transformers (Vaswani et al., 2017; Zhou et al., 2021; Wu et al., 2021; Liu et al., 2021; Wen et al., 2022; Zhou et al.,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:44.778989Z

Source-reported events for the cited work

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Observation 372e170a-3ffb-4a83-acbf-e851cdbde097 · outbound

This paper cites modulation.

Neural Functions for Learning Periodic Signal modulation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:44.560393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ace65fae-0cd0-4a13-a074-5ab4d983103f · outbound

This paper cites E.2 nth ORDER DERIVATIVE PENALTY We propose an additional penalty term for use in the training process of INR to represent smooth dynamics and prevent overfitting.

Neural Functions for Learning Periodic Signal E.2 nth ORDER DERIVATIVE PENALTY We propose an additional penalty term for use in the training process of INR to represent smooth dynamics and prevent overfitting

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:44.055349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e105c473-7dc5-42b9-a910-784a842100e4 · outbound

This paper cites Results of interpolation task with an ODE (Figures 11(a)-(b)) and extracted factors during training (Figure 11(c)).

Neural Functions for Learning Periodic Signal Results of interpolation task with an ODE (Figures 11(a)-(b)) and extracted factors during training (Figure 11(c))

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:43.657721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b0a86067-cf38-4194-9adf-1c617972a966 · outbound

This paper cites We experiment with the condition of the Equation 4 and are able to directly obtain the analytical solution u(x, y) = sin(a1πx) sin(a2πy).

Neural Functions for Learning Periodic Signal We experiment with the condition of the Equation 4 and are able to directly obtain the analytical solution u(x, y) = sin(a1πx) sin(a2πy)

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:43.429839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 57aa7ad6-1ed4-4274-b20a-a7e91e52cbf4 · outbound

This paper cites • Long-term time series – ETTh1 and ETTh2 (Zhou et al.,.

Neural Functions for Learning Periodic Signal • Long-term time series – ETTh1 and ETTh2 (Zhou et al.,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:42.868607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b01e4ef1-da25-4a15-b25f-67d026c4152b · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:42.586733Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 07eb669c-1d5c-4da2-9f5e-71623f0dcd2b · outbound

This paper cites It contains the information of patients with influenza-like illness spanning from 2002 to.

Neural Functions for Learning Periodic Signal It contains the information of patients with influenza-like illness spanning from 2002 to

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:42.348237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 13d443e4-9cef-4c09-bc0e-e4be56696af6 · outbound

This paper cites Figures 16(a)-(f) represent the results after training for 1,000 epochs, while Figures 16(g)-(l) depict the results after training for 10,000 epochs.

Neural Functions for Learning Periodic Signal Figures 16(a)-(f) represent the results after training for 1,000 epochs, while Figures 16(g)-(l) depict the results after training for 10,000 epochs

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:42.090056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8ba6c318-9fed-457e-998f-81d37fc07c0c · outbound

This paper cites On the other hand, all INR models demonstrate successfully precise learning of the training range (x ∈ [1.0, 1.5], y∈ [1.0, 1.5]) within just 1,000 epoch.

Neural Functions for Learning Periodic Signal On the other hand, all INR models demonstrate successfully precise learning of the training range (x ∈ [1.0, 1.5], y∈ [1.0, 1.5]) within just 1,000 epoch

Reference 35

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T04:53:41.817510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2362d78c-79cc-42cf-be1d-972f0105c9cd · outbound

This paper cites We compare NeRT to Linear and Cubic only for the interpolation task, since those numerical methods are not able to extrapolate.

Neural Functions for Learning Periodic Signal We compare NeRT to Linear and Cubic only for the interpolation task, since those numerical methods are not able to extrapolate

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:41.602250Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f878ade2-c8c1-4fa1-91d7-4dbd42eec445 · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:40.689166Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 879176b8-70f4-44ca-9cf0-8241c4212f77 · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 42

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T04:53:40.409893Z

Source-reported events for the cited work

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Observation e4505dc6-facd-4119-9ba9-f857975e2afd · outbound

This paper cites The best results are reported in boldface.

Neural Functions for Learning Periodic Signal The best results are reported in boldface

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:40.256612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 850cbd6f-efb2-4b9a-ba71-9462bfe57c37 · outbound

This paper cites For example, NeRT shows an MSE of 0.1257 in ETTh1 with a drop ratio of 70%, while baselines exhibit errors from 0.1978 in minimum to 0.4256 in maximum.

Neural Functions for Learning Periodic Signal For example, NeRT shows an MSE of 0.1257 in ETTh1 with a drop ratio of 70%, while baselines exhibit errors from 0.1978 in minimum to 0.4256 in maximum

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:40.032116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c68a12c5-b53b-42cc-abae-f6b9911e45b2 · outbound

This paper cites Figures (a), (b) and (c) show the results for interpolation, extrapolation, and both interpolation and extrapolation, respectively.

Neural Functions for Learning Periodic Signal Figures (a), (b) and (c) show the results for interpolation, extrapolation, and both interpolation and extrapolation, respectively

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:39.812773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f23fdd8a-59cb-41ce-90f7-4ec5c92d6b8f · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:39.610384Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 24c6b659-9f25-48e4-835e-c1a6aa54d94b · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:40.880165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 93b99b36-c3bb-48d7-83c1-6340033b0ce3 · outbound

This paper cites For NeRT, since it is not trained for each window combination, we report the average cost required for training one sample, with total amount in the parentheses.

Neural Functions for Learning Periodic Signal For NeRT, since it is not trained for each window combination, we report the average cost required for training one sample, with total amount in the parentheses

Reference 96

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T04:53:38.461639Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation da766282-4f43-4e7d-80cf-3a88ad9ecb06 · outbound

This paper cites Additionally, Figure 24 shows how the models predict n values given the input window size m on the Traffic dataset, where n = 96 and m = 48 in this setting.

Neural Functions for Learning Periodic Signal Additionally, Figure 24 shows how the models predict n values given the input window size m on the Traffic dataset, where n = 96 and m = 48 in this setting

Reference 192

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:41.131259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f83481ed-2e9e-4f39-b18a-ef7b1ab3cdca · outbound

This paper cites Baselines To evaluate the performance of NeRT, we compare it with eight existing time series baselines.

Neural Functions for Learning Periodic Signal Baselines To evaluate the performance of NeRT, we compare it with eight existing time series baselines

Reference 720

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:41.326793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2549fa22-25ff-453f-8ce7-c713a6eb1c4b · outbound

This paper cites Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism.

Neural Functions for Learning Periodic Signal Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism

Reference 1963

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Observation 81f12839-582f-4f3c-a5ed-babeb6ca4066 · outbound

This paper cites Deep Learning on Implicit Neural Representations of Shapes.

Neural Functions for Learning Periodic Signal Deep Learning on Implicit Neural Representations of Shapes

Reference 1994

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:32.839242Z

Source-reported events for the cited work

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Observation c68e824a-4d04-4854-bdaf-2b343f1564c0 · outbound

This paper cites Neural tangent kernel: Convergence and generalization in neural networks.

Neural Functions for Learning Periodic Signal Neural tangent kernel: Convergence and generalization in neural networks

Reference 1997

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:46.002776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 18312f75-ead1-497c-8663-a11d2df61af1 · outbound

This paper cites A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction.

Neural Functions for Learning Periodic Signal A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction

Reference 2000

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:33.874143Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8520b7a-4f24-47a2-8e9f-aecebb3f07a7 · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 2014

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:43.239224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4889cc77-6e4e-4cf8-a68d-d0c8a304e81c · outbound

This paper cites an unresolved cited work.

Neural Functions for Learning Periodic Signal Unresolved cited work

Reference 2016

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:53:43.017804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 874bc680-c215-4458-9f43-334655fdfbff · outbound

This paper cites On the spectral bias of neural networks.

Neural Functions for Learning Periodic Signal On the spectral bias of neural networks

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:53:45.762690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 92cf5462-bf68-49c0-bc24-db2481ea76c7 · outbound

This paper cites Time-Series Anomaly Detection with Implicit Neural Representation.

Neural Functions for Learning Periodic Signal Time-Series Anomaly Detection with Implicit Neural Representation

Reference 2018

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:53:39.341760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8bc8ea26-3b23-414f-93a8-5b84c3a148a7 · outbound

This paper cites Generalized Teacher Forcing for Learning Chaotic Dynamics.

Neural Functions for Learning Periodic Signal Generalized Teacher Forcing for Learning Chaotic Dynamics

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:33.038391Z

Source-reported events for the cited work

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Observation c5e327b6-0ebc-4e4b-b52c-6ea7da6090ca · outbound

This paper cites Are Transformers Effective for Time Series Forecasting?.

Neural Functions for Learning Periodic Signal Are Transformers Effective for Time Series Forecasting?

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:34.533452Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4e0459f-8cc6-415c-a78e-a0ed86951e77 · outbound

This paper cites Koopman-informed recurrent neural networks.

Neural Functions for Learning Periodic Signal Koopman-informed recurrent neural networks

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:32.573268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a9007ee-99b1-4647-b2cb-a492a04b0a84 · outbound

This paper cites Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction.

Neural Functions for Learning Periodic Signal Almost-Linear RNNs Yield Highly Interpretable Symbolic Codes in Dynamical Systems Reconstruction

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T04:53:32.658151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation dc916282-d006-473d-8f6e-7815af92f012 · inbound

ELMZip: Onboard Satellite Image Compression via Extreme Learning Machines for Efficient Downlink cites this paper.

ELMZip: Onboard Satellite Image Compression via Extreme Learning Machines for Efficient Downlink Neural Functions for Learning Periodic Signal

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-10T17:58:28.711739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.