Paper Citation Record · LEDGER

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training

As of 8 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2607.20811.

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

pith.paper-citation-record.v1
2607.20811 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T09:35:49.102437Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

46 of 46 outbound references displayed

verified exact9
verified fuzzy0
unresolved37
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External citation measurements

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Outbound references

Observation ae072385-bf2d-4022-81c3-aae877a395e3 · outbound

This paper cites Training neural networks is er-complete.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Training neural networks is er-complete

Reference 1

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Observation 9a7b369c-0452-40b9-a678-0425e9a4ea23 · outbound

This paper cites Understanding deep neural networks with rectified linear units.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Understanding deep neural networks with rectified linear units

Reference 2

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Observation a5113a64-3800-4161-bcbb-b48149bebd35 · outbound

This paper cites Training Fully Connected Neural Networks is $\exists\mathbb{R}$-Complete.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Training Fully Connected Neural Networks is $\exists\mathbb{R}$-Complete

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-01T09:39:30.122621Z

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Observation b1804776-8c3a-4201-ab33-ca25f0c07767 · outbound

This paper cites an unresolved cited work.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Unresolved cited work

Reference 4

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This paper cites S., and Lan, G.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training S., and Lan, G

Reference 5

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Observation 3ef63f07-bdc6-433e-88f6-5af906e1c719 · outbound

This paper cites Parameterized algorithms for milps with small treedepth.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Parameterized algorithms for milps with small treedepth

Reference 6

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Observation 480a02d8-f08c-4cc8-8aef-323c7aacad8e · outbound

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Unresolved cited work

Reference 7

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Observation 75edbd21-070d-483c-934e-afe434664c76 · outbound

This paper cites On the expressive power of deep learning: A tensor analysis.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training On the expressive power of deep learning: A tensor analysis

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T09:35:45.529971Z

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Observation 3b43a22b-b8cb-4fc3-ba09-175058cc9e2e · outbound

This paper cites The monadic second-order logic of graphs.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training The monadic second-order logic of graphs

Reference 9

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Observation 5c6969fb-fd1f-43c7-863c-60110f08b09a · outbound

This paper cites and Engelfriet, J.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Engelfriet, J

Reference 10

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Observation 18021a30-f25e-41fe-b2d3-aedd9272902b · outbound

This paper cites and Pillow, J.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Pillow, J

Reference 11

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Observation 656f7ed1-64c5-43af-88f6-a0d9de52e056 · outbound

This paper cites V., Panolan, F., and Simonov, K.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training V., Panolan, F., and Simonov, K

Reference 12

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Observation fe6d5c87-db88-4788-8cf3-24386f73cd04 · outbound

This paper cites S., Wang, G., and Xie, Y.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training S., Wang, G., and Xie, Y

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T09:35:45.845867Z

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Observation 4755f18d-95a8-4fce-9a07-bd224bf62701 · outbound

This paper cites Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Graph Theory, 4th Edition, volume 173 of Graduate texts in mathematics

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T09:35:45.900512Z

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Observation d1a6e25c-ad50-4ea2-aa91-ff24a400748c · outbound

This paper cites Constructing arrangements of lines and hyperplanes with applications.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Constructing arrangements of lines and hyperplanes with applications

Reference 15

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Observation bc3e5329-187c-4102-85f4-0b420e566392 · outbound

This paper cites and Shamir, O.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Shamir, O

Reference 16

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Observation cae4065b-fe21-4187-8783-0c568d9009b8 · outbound

This paper cites and Tardos, \'E.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Tardos, \'E

Reference 17

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Observation 9e1cf20e-0e31-4d07-b46c-ce032c4ecc1b · outbound

This paper cites Training Neural Networks is NP-Hard in Fixed Dimension.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Training Neural Networks is NP-Hard in Fixed Dimension

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-01T09:39:29.936815Z

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Observation f1acd42a-e94d-4f8d-a476-d9fbc60af31a · outbound

This paper cites The computational complexity of relu network training parameterized by data dimensionality.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training The computational complexity of relu network training parameterized by data dimensionality

Reference 19

Resolution: verified exact; doi, observed 2026-08-01T09:39:29.878872Z

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Observation 705f7b99-ef02-49c1-894a-fbe7158826f5 · outbound

This paper cites and Korchemna, V.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Korchemna, V

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T09:35:46.405167Z

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Observation c7a817af-650e-4131-a92a-3d079a6482ff · outbound

This paper cites and Ordyniak, S.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Ordyniak, S

Reference 21

Resolution: verified exact; doi, observed 2026-08-01T09:39:29.770625Z

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Observation b4c396ab-91b4-4d3a-96e0-60c88380339c · outbound

This paper cites A., Ordyniak, S., and Szeider, S.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training A., Ordyniak, S., and Szeider, S

Reference 22

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Observation 900d8007-06af-488a-9596-bca29e2cbddb · outbound

This paper cites The complexity of k-means clustering when little is known.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training The complexity of k-means clustering when little is known

Reference 23

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Observation fe29e983-90b3-426f-9a6e-f1157de25846 · outbound

This paper cites Adaptive convolutional relus.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Adaptive convolutional relus

Reference 24

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Observation 2f653c03-a5db-4878-9a46-1af6add504b8 · outbound

This paper cites R., Manurangsi, P., and Reichman, D.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training R., Manurangsi, P., and Reichman, D

Reference 25

Resolution: verified exact; doi, observed 2026-08-01T09:39:29.607970Z

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Observation e07b97f3-78fb-420d-afda-d175dc927743 · outbound

This paper cites Deep Learning.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Deep Learning

Reference 26

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Observation d3c7f9ea-bdd0-4e72-99c4-1811a6e3442a · outbound

This paper cites and Komusiewicz, C.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Komusiewicz, C

Reference 27

Resolution: verified exact; doi, observed 2026-08-01T09:39:29.513206Z

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Observation 9a6ab800-bbfe-46a5-8871-4ab2960af4ac · outbound

This paper cites Lower bounds on the depth of integral relu neural networks via lattice polytopes.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Lower bounds on the depth of integral relu neural networks via lattice polytopes

Reference 28

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Unresolved cited work

Reference 29

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Observation 43952d8f-6335-419c-9e34-5b293ce59705 · outbound

This paper cites and Telle, J.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Telle, J

Reference 30

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This paper cites Facets of neural network complexity.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Facets of neural network complexity

Reference 31

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training D., and Skutella, M

Reference 32

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This paper cites Minkowski's convex body theorem and integer programming.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Minkowski's convex body theorem and integer programming

Reference 33

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Observation c4ded68b-c582-4b82-acd4-d9ac6674d37b · outbound

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training K., Tarasov, S

Reference 34

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Unresolved cited work

Reference 35

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This paper cites Bounds for the computational power and learning complexity of analog neural nets.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Bounds for the computational power and learning complexity of analog neural nets

Reference 36

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training On the complexity of polyhedral separability

Reference 37

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Observation 7d82307d-7546-49fe-a36a-c45e09d986e7 · outbound

This paper cites and Szeider, S.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Szeider, S

Reference 38

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Observation 01aba5b3-3e2e-4e9b-8fe1-7aebbdd43301 · outbound

This paper cites Methods for quadratic programming: A survey.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Methods for quadratic programming: A survey

Reference 39

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This paper cites Effect of activation functions on the training of overparametrized neural nets.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Effect of activation functions on the training of overparametrized neural nets

Reference 40

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Seymour, P

Reference 41

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training Unresolved cited work

Reference 42

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training V., Golovach, P

Reference 43

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This paper cites A Decision Method for Elementary Algebra and Geometry: Prepared for Publication with the Assistance of J.C.C.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training A Decision Method for Elementary Algebra and Geometry: Prepared for Publication with the Assistance of J.C.C

Reference 44

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This paper cites benefits of depth in neural networks.

New Complexity-Theoretic Frontiers of Tractability for Neural Network Training benefits of depth in neural networks

Reference 45

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New Complexity-Theoretic Frontiers of Tractability for Neural Network Training and Reinsel, G

Reference 46

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