Paper Citation Record · LEDGER

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks

As of 17 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 2 inbound Pith citation observations for arXiv:2505.11589.

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

pith.paper-citation-record.v1
2505.11589 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:56:01.586850Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T22:37:13.002522Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T13:55:45.491954Z

Reference resolution

43 of 43 outbound references displayed

verified exact5
verified fuzzy21
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6269d8ed-3079-47fb-b2a8-2c6e418d81f5 · outbound

This paper cites https://www.hhs.gov/hipaa/, 1996.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks https://www.hhs.gov/hipaa/, 1996

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.399063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation bbc023e2-6063-4462-b5de-c3c9ca54d8b2 · outbound

This paper cites http://data.europa.eu/eli/reg/2016/679/oj, 2016.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks http://data.europa.eu/eli/reg/2016/679/oj, 2016

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.386379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 45becb5b-ef18-4a06-80a9-9422e6440a16 · outbound

This paper cites Stabilizing Inputs to Approximated Nonlinear Functions for Inference with Homomorphic Encryption in Deep Neural Networks.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Stabilizing Inputs to Approximated Nonlinear Functions for Inference with Homomorphic Encryption in Deep Neural Networks

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:56:02.083376Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6d70c6ef-0e97-4b08-bd7c-dfb0fa1c215f · outbound

This paper cites On Polynomial Approximations for Privacy-Preserving and Verifiable ReLU Networks.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks On Polynomial Approximations for Privacy-Preserving and Verifiable ReLU Networks

Reference 4

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Source-reported events for the cited work

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Observation 1933d993-922f-4f87-9ffd-222e273cecd9 · outbound

This paper cites OpenFHE : Open-source fully homomorphic encryption library.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks OpenFHE : Open-source fully homomorphic encryption library

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.373484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e82395b3-af08-4beb-b608-a579d44141c8 · outbound

This paper cites A methodology for training homomorphic encryption friendly neural networks.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks A methodology for training homomorphic encryption friendly neural networks

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.360046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ca3b1825-4386-4f80-a6b4-9e7d9ecdc46d · outbound

This paper cites Training Large Scale Polynomial CNNs for E2E Inference over Homomorphic Encryption.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Training Large Scale Polynomial CNNs for E2E Inference over Homomorphic Encryption

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.434090Z

Source-reported events for the cited work

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Observation 22cea893-1478-4bf7-979c-ffc69a0afcb9 · outbound

This paper cites nGraph-HE2: A High-Throughput Framework for Neural Network Inference on Encrypted Data.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks nGraph-HE2: A High-Throughput Framework for Neural Network Inference on Encrypted Data

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:56:02.039047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9a62f445-ecfe-4f6d-88c6-f6a963c21af8 · outbound

This paper cites Low latency privacy preserving inference.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Low latency privacy preserving inference

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.347400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 85f94d51-e455-4c01-9579-f5c5422cd696 · outbound

This paper cites Capture-24: A large dataset of wrist-worn activity tracker data collected in the wild for human activity recognition.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Capture-24: A large dataset of wrist-worn activity tracker data collected in the wild for human activity recognition

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.335001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6ed75fd9-519e-4d44-9f72-8e1b00b3fe4a · outbound

This paper cites Homomorphic encryption for arithmetic of approximate numbers.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Homomorphic encryption for arithmetic of approximate numbers

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.321794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1b53140e-0f4c-4d09-bb17-cfc1ea9bfcec · outbound

This paper cites Chrysos, Stylianos Moschoglou, Giorgos Bouritsas, Yannis Panagakis, Jiankang Deng, and Stefanos Zafeiriou.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Chrysos, Stylianos Moschoglou, Giorgos Bouritsas, Yannis Panagakis, Jiankang Deng, and Stefanos Zafeiriou

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.309291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 10e910a1-c9c3-48cb-92c5-332219328e4f · outbound

This paper cites The mnist database of handwritten digit images for machine learning research.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks The mnist database of handwritten digit images for machine learning research

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.460583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f01026af-98ca-4500-bb08-220f82579667 · outbound

This paper cites Cryptonets: applying neural networks to encrypted data with high throughput and accuracy.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Cryptonets: applying neural networks to encrypted data with high throughput and accuracy

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.286420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1220f43c-6dfe-4a1d-8a4f-2244adeac1e0 · outbound

This paper cites Scalable Interpretability via Polynomials.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Scalable Interpretability via Polynomials

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:56:01.671588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b4d8d4d6-7fa3-45cf-b232-91ac52aea5f1 · outbound

This paper cites A new remez-type algorithm for best polynomial approximation.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks A new remez-type algorithm for best polynomial approximation

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.270758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 345f5721-91fc-4b75-ab88-2cf69efa5bff · outbound

This paper cites Interpretable polynomial neural ordinary differential equations.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Interpretable polynomial neural ordinary differential equations

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.257432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6ec59626-46dc-4d54-8a2d-ad235dabd788 · outbound

This paper cites Polynomial activation functions.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Polynomial activation functions

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.245413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0a986940-2b8d-400e-bc2f-06d11a822ec4 · outbound

This paper cites Improved polynomial neural networks with normalised activations.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Improved polynomial neural networks with normalised activations

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.487179Z

Source-reported events for the cited work

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Observation df023d95-682f-4520-8ab6-cf6cf7ac29a9 · outbound

This paper cites Zhang, Shaoqing Ren, and Jian Sun.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Zhang, Shaoqing Ren, and Jian Sun

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.233995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9fcb701d-abca-4e7f-b29a-a2d1290effac · outbound

This paper cites CryptoDL: Deep Neural Networks over Encrypted Data.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks CryptoDL: Deep Neural Networks over Encrypted Data

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.496232Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92c0ea08-3000-448e-8145-558f1533941c · outbound

This paper cites Stinchcombe, and Halbert L.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Stinchcombe, and Halbert L

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.501340Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43198825-9346-49bd-9e99-ab9d085bcf54 · outbound

This paper cites Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.505131Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce8660ca-23f4-47d7-bc74-6fd7ec1b8d9f · outbound

This paper cites Highly accurate cnn inference using approximate activation functions over homomorphic encryption.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Highly accurate cnn inference using approximate activation functions over homomorphic encryption

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.213419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b6e45fd2-e068-4512-b0fa-a7e039dd9ded · outbound

This paper cites GAZELLE : A low latency framework for secure neural network inference.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks GAZELLE : A low latency framework for secure neural network inference

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.201135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2d3cfee1-3304-4cf7-8910-0a90666052c1 · outbound

This paper cites Universal Approximation with Deep Narrow Networks.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Universal Approximation with Deep Narrow Networks

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.516594Z

Source-reported events for the cited work

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Observation 5ef0a224-1688-4933-8160-9287a9387f06 · outbound

This paper cites On the expressive power of deep polynomial neural networks.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks On the expressive power of deep polynomial neural networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.181922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8acb6cfc-d6cf-4f32-b524-35991fb715c7 · outbound

This paper cites Learning multiple layers of features from tiny images.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Learning multiple layers of features from tiny images

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.525314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90ee0873-8d47-44ac-9e61-3634ff5757b9 · outbound

This paper cites Cifar-100 (canadian institute for advanced research).

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Cifar-100 (canadian institute for advanced research)

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.530380Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e659526e-56e2-4568-a644-aa55d79313bd · outbound

This paper cites Precise approximation of convolutional neural networks for homomorphically encrypted data.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Precise approximation of convolutional neural networks for homomorphically encrypted data

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.152908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 72fb29c9-c677-4f07-b6d8-dc6114069799 · outbound

This paper cites Optimized layerwise approximation for efficient private inference on fully homomorphic encryption, 2024.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Optimized layerwise approximation for efficient private inference on fully homomorphic encryption, 2024

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.538726Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01ba7b84-619e-491e-b9fc-05d80238c51a · outbound

This paper cites Decoupled weight decay regularization.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Decoupled weight decay regularization

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.140037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1965d21a-4a76-47aa-8de3-e829b9d02901 · outbound

This paper cites an unresolved cited work.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-08-15T20:56:01.652973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a173cf94-5214-4a20-afeb-da4f50ba2bb5 · outbound

This paper cites Trefethen.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Trefethen

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.127993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 058db889-b768-4322-9bf4-6baf69b74958 · outbound

This paper cites AESPA: Accuracy Preserving Low-degree Polynomial Activation for Fast Private Inference.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks AESPA: Accuracy Preserving Low-degree Polynomial Activation for Fast Private Inference

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.555163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11a1a3bd-27e0-46fc-ac32-e24d189e7635 · outbound

This paper cites Self-learning activation functions to increase accuracy of privacy-preserving convolutional neural networks with homomorphic encryption.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Self-learning activation functions to increase accuracy of privacy-preserving convolutional neural networks with homomorphic encryption

Reference 36

Resolution: verified exact; doi, observed 2026-08-15T20:56:01.640324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation fde89be1-e3d2-4b01-a1cc-1d57ef8dc496 · outbound

This paper cites Human Activity Recognition Using Smartphones.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Human Activity Recognition Using Smartphones

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.563473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e8bcd8b-218e-4b4c-bb0d-dccd6668fbc1 · outbound

This paper cites Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.567406Z

Source-reported events for the cited work

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Observation 0580d3f4-ea2f-4a55-8e8a-e5f6042864c4 · outbound

This paper cites Ppolynets: Achieving high prediction accuracy and efficiency with parametric polynomial activations.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Ppolynets: Achieving high prediction accuracy and efficiency with parametric polynomial activations

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.571267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 251aeaad-5bda-4e85-841e-83a8330b2242 · outbound

This paper cites Extrapolation of polynomial nets and their generalization guarantees, 2022.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Extrapolation of polynomial nets and their generalization guarantees, 2022

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.115641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e5525528-f5d7-487b-9dc4-6903c5c3e269 · outbound

This paper cites Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms, 2017.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms, 2017

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.579335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74eb3189-1c9d-404d-8d73-7fc855f1b184 · outbound

This paper cites Polynomial activation neural networks: Modeling, stability analysis and coverage bp-training.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Polynomial activation neural networks: Modeling, stability analysis and coverage bp-training

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T20:56:01.583044Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d107f10-fa5e-41a5-a054-c0500f1da844 · outbound

This paper cites Converting transformers to polynomial form for secure inference over homomorphic encryption, 2023.

A Training Framework for Optimal and Stable Training of Polynomial Neural Networks Converting transformers to polynomial form for secure inference over homomorphic encryption, 2023

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:56:02.097091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation 98e168f1-a45d-418f-b5fa-6d4ac9fea195 · inbound

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects cites this paper.

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects A Training Framework for Optimal and Stable Training of Polynomial Neural Networks

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-12T07:41:31.829274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c0a246ae-8607-4986-988b-b36017419078 · inbound

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects cites this paper.

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects A Training Framework for Optimal and Stable Training of Polynomial Neural Networks

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-01T13:55:45.493334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.