Paper Citation Record · LEDGER

When do complex-valued neural networks help? A study of representation, geometry, and optimization

As of 14 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2605.27673.

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

pith.paper-citation-record.v1
2605.27673 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T18:45:27.282354Z

measured 30 of 30 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 2026-08-01T05:07:54.611065Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

verified exact7
verified fuzzy0
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 67c3f2cd-86e9-4974-8fda-2e2b1c59c6fa · outbound

This paper cites Charles Clancy.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Charles Clancy

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

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Observation 68193f87-5318-4f3c-8c29-ff7aa8cbfa84 · outbound

This paper cites Understanding and improving convolutional neural networks via concatenated rectified linear units.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Understanding and improving convolutional neural networks via concatenated rectified linear units

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Observation b7221820-7401-46a5-befd-5a1d3d52bad8 · outbound

This paper cites Decoupled Weight Decay Regularization.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Decoupled Weight Decay Regularization

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.700128Z

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 ea1e2a57-c9cb-4563-a090-b4abac0fd8d4 · outbound

This paper cites Springer, 2006.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Springer, 2006

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Observation 07f56d95-cbd3-42d6-948a-cb0c83662521 · outbound

This paper cites Deep Complex Networks.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Deep Complex Networks

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.697136Z

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 1c5e0049-8eab-426d-b156-781a64bde254 · outbound

This paper cites Better than real: Complex-valued neural nets for mri fingerprinting.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Better than real: Complex-valued neural nets for mri fingerprinting

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Observation ed0de6b1-9ea3-4ad4-b692-5034635441cd · outbound

This paper cites Analysis of deep complex-valued convolutionalneuralnetworksformrireconstructionandphase-focusedapplications.Magneticresonance in medicine, 86(2):1093–1109, 2021.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Analysis of deep complex-valued convolutionalneuralnetworksformrireconstructionandphase-focusedapplications.Magneticresonance in medicine, 86(2):1093–1109, 2021

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Observation 4e7289d6-9cdf-4401-92c9-3e937a767b5e · outbound

This paper cites Unitary evolution recurrent neural networks.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Unitary evolution recurrent neural networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fb2c910-e513-47fd-9b42-7e88c2136dbc · outbound

This paper cites Full-capacity unitary recurrent neural networks.Advances in neural information processing systems, 29, 2016.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Full-capacity unitary recurrent neural networks.Advances in neural information processing systems, 29, 2016

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 187da629-1f70-41fe-be5a-f94a7e3c5245 · outbound

This paper cites Group equivariant convolutional networks.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Group equivariant convolutional networks

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

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Observation e9e452ed-561e-447d-9ada-91518fde4004 · outbound

This paper cites Steerable CNNs.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Steerable CNNs

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.691765Z

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 03a53eca-fff7-4426-aabe-b8199c218948 · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.694725Z

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 08e50f47-e4bc-4760-beb1-f3386cbff7d1 · outbound

This paper cites Generale(2)-equivariantsteerablecnns.Advancesinneuralinformation processing systems, 32, 2019.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Generale(2)-equivariantsteerablecnns.Advancesinneuralinformation processing systems, 32, 2019

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Observation 3ad6d09c-f724-4bad-a24e-48a4cc312c09 · outbound

This paper cites Harmonic networks: Deep translation and rotation equivariance.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Harmonic networks: Deep translation and rotation equivariance

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Unavailable: canonical work link unavailable.

Observation 3482b372-2947-40f6-9261-52d75fdc0cfe · outbound

This paper cites Springer, 2011.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Springer, 2011

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2e4a3b9-3402-4a4f-aeae-803740e88b0a · outbound

This paper cites On Complex Valued Convolutional Neural Networks.

When do complex-valued neural networks help? A study of representation, geometry, and optimization On Complex Valued Convolutional Neural Networks

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.682996Z

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 f6604aaa-1a91-4fbe-96af-f085cd9e125a · outbound

This paper cites A complex gradient operator and its application in adaptive array theory.

When do complex-valued neural networks help? A study of representation, geometry, and optimization A complex gradient operator and its application in adaptive array theory

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80c5b49c-20b7-44f5-bb25-dcdc6f6e3a92 · outbound

This paper cites The Complex Gradient Operator and the CR-Calculus.

When do complex-valued neural networks help? A study of representation, geometry, and optimization The Complex Gradient Operator and the CR-Calculus

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.686170Z

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 cb47fe68-fb5a-42a3-8f7f-db6717ed581d · outbound

This paper cites Convolutionalradiomodulationrecognition networks.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Convolutionalradiomodulationrecognition networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f62af8f-a19c-424f-a22f-5976b5d2d365 · outbound

This paper cites Modulation pattern detection using complex convolutions in deep learning.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Modulation pattern detection using complex convolutions in deep learning

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Unavailable: canonical work link unavailable.

Observation 41e52481-cede-4186-95ca-cd8a993599a5 · outbound

This paper cites Complex-valued networks for automatic modulation classification.IEEE Transactions on Vehicular Technology, 69(9):10085–10089, 2020.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Complex-valued networks for automatic modulation classification.IEEE Transactions on Vehicular Technology, 69(9):10085–10089, 2020

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

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Observation 116537f7-7eb3-4a76-bdd8-a3bdeee91a5d · outbound

This paper cites an unresolved cited work.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a491abd7-814c-49d5-af0e-c50ed85f88de · outbound

This paper cites Deep learning with convolutional neural networks for eeg decoding and visualization.Human brain mapping, 38(11):5391–5420, 2017.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Deep learning with convolutional neural networks for eeg decoding and visualization.Human brain mapping, 38(11):5391–5420, 2017

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4331b3c-58f9-42aa-9f57-eb35a8a87e3a · outbound

This paper cites Eegnet: acompactconvolutionalneuralnetworkforeeg-basedbrain–computerinterfaces.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Eegnet: acompactconvolutionalneuralnetworkforeeg-basedbrain–computerinterfaces

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 331db8e6-7db9-4fbb-8fc5-ce1d32a589a1 · outbound

This paper cites Measuring phase- amplitude coupling between neuronal oscillations of different frequencies.Journal of neurophysiology, 104(2):1195–1210, 2010.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Measuring phase- amplitude coupling between neuronal oscillations of different frequencies.Journal of neurophysiology, 104(2):1195–1210, 2010

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c7c072aa-69ff-483b-9f8f-04767d7534dd · outbound

This paper cites Deep reinforcement learning that matters.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Deep reinforcement learning that matters

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Observation d9ee8436-9f74-4f54-ac66-1d48a0ad924e · outbound

This paper cites Are gans created equal? a large-scale study.Advances in neural information processing systems, 31, 2018.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Are gans created equal? a large-scale study.Advances in neural information processing systems, 31, 2018

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

Source-reported events for the cited work

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Observation 3c99588c-8aa1-48f0-a58d-32d658983659 · outbound

This paper cites On the State of the Art of Evaluation in Neural Language Models.

When do complex-valued neural networks help? A study of representation, geometry, and optimization On the State of the Art of Evaluation in Neural Language Models

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-06-29T18:53:51.689041Z

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 15065440-7f8a-4ed9-a627-a64b960dcc56 · outbound

This paper cites Accounting for variance in machine learning benchmarks.Proceedings of machine learning and systems, 3:747–769, 2021.

When do complex-valued neural networks help? A study of representation, geometry, and optimization Accounting for variance in machine learning benchmarks.Proceedings of machine learning and systems, 3:747–769, 2021

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-29T18:45:27.282354Z

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Pith citing papers

Observation e9103f76-a576-4cb9-a69e-638b17b915fc · inbound

IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data cites this paper.

IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data When do complex-valued neural networks help? A study of representation, geometry, and optimization

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-01T05:07:54.611065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.