Paper Citation Record · LEDGER

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization

As of 7 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2507.22090.

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

pith.paper-citation-record.v1
2507.22090 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:39:11.694265Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

47 of 47 outbound references displayed

verified exact9
verified fuzzy16
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f8012c82-7e0a-4186-b24a-9512c31fda49 · outbound

This paper cites Learning Activation Functions to Improve Deep Neural Networks.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Learning Activation Functions to Improve Deep Neural Networks

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:07.140374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 002e5468-6f4f-4edb-8821-c57bc3685015 · outbound

This paper cites & Prevete, R.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Prevete, R

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:17.655232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d3c642c3-1e8a-4451-b888-eef108e8fd55 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:07.285193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1352200-5678-499d-99ba-d8be0f93f2d8 · outbound

This paper cites Gomez, Łukasz Kaiser, and Illia Polosukhin.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Gomez, Łukasz Kaiser, and Illia Polosukhin

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:17.511608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a9fe7327-e0e7-41c1-a2c6-158277c0645f · outbound

This paper cites Activation functions and their characteristics in deep neural networks,.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Activation functions and their characteristics in deep neural networks,

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:07.595597Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8abd9c4-27fa-4f64-8c54-2484df16201e · outbound

This paper cites & Bengio, Y.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Bengio, Y

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:17.365672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bebb8c47-3e94-4947-94f2-be23cf8ed030 · outbound

This paper cites & Pandey, A.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Pandey, A

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:17.219357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8d1f3d72-7477-477e-81d7-fec55466919a · outbound

This paper cites https://www.kaggle.com/c/boston-housing.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization https://www.kaggle.com/c/boston-housing

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:17.090686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4258d684-6491-4a1d-990d-d910467a1b98 · outbound

This paper cites Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs).

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:07.927596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f76a24d-24ad-45b3-bfe0-53f60080f5f1 · outbound

This paper cites Approximation by superpositions of a sigmoidal function.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Approximation by superpositions of a sigmoidal function

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:08.020177Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d134107-9f64-4892-9811-f053bc61f45a · outbound

This paper cites The impact of activation functions on training and performance of a deep neural network,.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization The impact of activation functions on training and performance of a deep neural network,

Reference 11

Resolution: verified exact; raw_fallback, observed 2026-08-06T12:39:13.969094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8bba6a91-50e7-460c-9d85-a207dcd73b8e · outbound

This paper cites & Zhou, J.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Zhou, J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:16.914744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 15fc05f6-d392-4457-abbd-781b573e100e · outbound

This paper cites R., Singh, S.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization R., Singh, S

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:08.347492Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd0afa1a-6ccb-4bfe-a54d-9b1238d2d198 · outbound

This paper cites & Doya, K.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Doya, K

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:08.435753Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37373d57-6cf2-4ab4-8fcf-32580335255e · outbound

This paper cites O., Ante, J.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization O., Ante, J

Reference 15

Resolution: verified exact; doi, observed 2026-08-06T12:39:12.943488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 42f20c68-aaa0-49fd-99af-508b518fd411 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 16

Resolution: verified exact; doi, observed 2026-08-06T12:39:12.773661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e1cee271-e645-401f-996a-21f09504f20c · outbound

This paper cites and Bengio, Y.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization and Bengio, Y

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:16.607421Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 521ec621-b3cc-4d52-80d1-caedfc4cd93f · outbound

This paper cites and Bengio, Y.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization and Bengio, Y

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:16.386439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 48812abe-3348-4211-ba70-8085f1d3218c · outbound

This paper cites & Courville, A.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Courville, A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:16.242116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 91276b8c-136a-4964-8d51-ac5285df4d06 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:39:16.088868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation fae27df8-f25a-4fe0-85eb-c7035bd8d454 · outbound

This paper cites https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:15.918287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bb50c474-12e0-49d8-a0b5-880a7269d3d6 · outbound

This paper cites How important are activation functions in regression and classification? A survey, performance comparison, and future directions.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization How important are activation functions in regression and classification? A survey, performance comparison, and future directions

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:09.308337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22aa2863-5397-41a4-9917-fa31e54aef3c · outbound

This paper cites Delving Deep into Rectifiers: Surpassing Human -Level Performance on ImageNet Classification,.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Delving Deep into Rectifiers: Surpassing Human -Level Performance on ImageNet Classification,

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:09.415877Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04b96588-0219-4309-8720-51877d41a378 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 24

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T12:39:13.732792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 10c4d71c-440d-409b-bd0c-caf51effe283 · outbound

This paper cites Multiple data-driven missing imputation.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Multiple data-driven missing imputation

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:39:13.478770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 291d13ce-a8c7-45a3-8c66-db1ccc9a91cc · outbound

This paper cites Three Decades of Activations: A Comprehensive Survey of 400 Activation Functions for Neural Networks.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Three Decades of Activations: A Comprehensive Survey of 400 Activation Functions for Neural Networks

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:09.621769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59caa939-3ad9-424e-88b6-aebf3b4c69c1 · outbound

This paper cites Computational aspects of critical infrastructures security.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Computational aspects of critical infrastructures security

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:15.748949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8eeb3dca-4813-45f5-9ef9-f47caf9a10bd · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:39:15.558983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 632694e1-5550-4461-a983-637702ebf33f · outbound

This paper cites & Hinton, G.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Hinton, G

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:09.981341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a5f2ade-f77d-42e9-881b-a32de900c5a0 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:39:15.437168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8fa44c4d-f895-42ed-b9a8-e070d7a47548 · outbound

This paper cites & Goldstein, T.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Goldstein, T

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:15.307280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 78a5e84b-3f29-40fd-ad0c-b17ad0df0af6 · outbound

This paper cites and Ng, A.Y.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization and Ng, A.Y

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:15.167658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 61cca31d-20d3-4f10-bc7d-97b012fa3db1 · outbound

This paper cites & Vrahatis, A.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Vrahatis, A

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:15.052260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1531dcea-7460-4fc7-8200-072f619dd095 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 34

Resolution: verified exact; raw_fallback, observed 2026-08-06T12:39:13.334220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1af972da-eb98-4630-9b01-52330caba868 · outbound

This paper cites Mish: A Self Regularized Non-Monotonic Activation Function.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Mish: A Self Regularized Non-Monotonic Activation Function

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:10.624184Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9eab66df-4753-417c-a776-fbad359746b0 · outbound

This paper cites https://www.kaggle.com/datasets/hojjatk/mnist-dataset.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization https://www.kaggle.com/datasets/hojjatk/mnist-dataset

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:14.905277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6a95ff7d-f372-4828-b11d-8306559ed1e1 · outbound

This paper cites & Bengio, Y.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization & Bengio, Y

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:39:14.752679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3ef7bdde-8e1b-4ae2-9c4d-6ce790441629 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:39:14.586186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation acf01ff9-a0d8-4e1a-b114-911998e5961c · outbound

This paper cites Searching for Activation Functions.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Searching for Activation Functions

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:11.059693Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aa340219-6b9d-4379-a119-454b6cef424b · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 40

Resolution: verified exact; doi, observed 2026-08-06T12:39:12.530711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 41043d23-924d-4a31-bb7a-de7446b0d048 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 41

Resolution: verified exact; doi, observed 2026-08-06T12:39:12.337885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7c1957a6-6fe2-4818-91c3-b792a9082c8b · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:39:14.402039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3149e844-bb4c-49a6-bc57-741cdeb6bfd2 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 43

Resolution: verified exact; doi, observed 2026-08-06T12:39:12.081398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d405a5da-74f3-4e79-8fce-076ad7c6d5c4 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:39:14.189422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 375931ce-1305-4413-8894-6862fcbbd770 · outbound

This paper cites an unresolved cited work.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Unresolved cited work

Reference 45

Resolution: verified exact; doi, observed 2026-08-06T12:39:11.805686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bd2514c5-8e79-4d62-ac71-d078f415b486 · outbound

This paper cites Empirical Evaluation of Rectified Activations in Convolutional Network.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization Empirical Evaluation of Rectified Activations in Convolutional Network

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:11.550783Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83d9e9be-3243-4e90-8799-802d852ae993 · outbound

This paper cites https://doi.org/10.1007/978-3-642-35289-8_3.

Hybrid activation functions for deep neural networks: S3 and S4 -- a novel approach to gradient flow optimization https://doi.org/10.1007/978-3-642-35289-8_3

Reference 7700

Resolution: unresolved; no resolver link, observed 2026-08-06T12:39:10.146480Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.