Paper Citation Record · LEDGER

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization

As of 20 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 1 inbound Pith citation observation for arXiv:2504.14762.

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

pith.paper-citation-record.v1
2504.14762 v2

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:45:08.047257Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:37:56.587227Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T16:37:56.828002Z

Reference resolution

25 of 25 outbound references displayed

verified exact0
verified fuzzy14
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3d53bb51-d233-4d2b-a7fd-353b3668f141 · outbound

This paper cites A convergence theory for deep learning via over-parameterization.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization A convergence theory for deep learning via over-parameterization

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.319775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 31398bbc-c717-4c77-9186-0f0c49d21c67 · outbound

This paper cites On warm-starting neural network training.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization On warm-starting neural network training

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.307362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c5c9f8c0-3825-4a09-9817-6a5a642c8c46 · outbound

This paper cites Understanding dropout.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Understanding dropout

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.296053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 63886882-0e17-4b88-a023-caaa14371ad5 · outbound

This paper cites an unresolved cited work.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:45:08.284617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7851a7e6-db32-4039-81b4-7b24d8805c42 · outbound

This paper cites Graduate Texts in Mathematics 184.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Graduate Texts in Mathematics 184

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.273552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2c292f07-b9a7-4756-9b3f-648531231251 · outbound

This paper cites The lottery ticket hypothesis for pre-trained bert networks.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization The lottery ticket hypothesis for pre-trained bert networks

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.262486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 61b05afc-9d86-40b4-adce-2aed155af085 · outbound

This paper cites The geometry of relu networks through the relu transition graph, 2025.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization The geometry of relu networks through the relu transition graph, 2025

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:07.977949Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d7d4f05-dfdb-4f20-b07a-babc23697c10 · outbound

This paper cites Neural networks as universal finite-state machines: A constructive deterministic finite automaton theory, 2025.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Neural networks as universal finite-state machines: A constructive deterministic finite automaton theory, 2025

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:07.981676Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4d2518d-15f6-45e8-8eda-14797a6da220 · outbound

This paper cites Essentially no barriers in neural network energy landscape.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Essentially no barriers in neural network energy landscape

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.238019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3b37ac38-efcd-4b63-a147-e4ef54eb5434 · outbound

This paper cites an unresolved cited work.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:07.989204Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f8dd878-0d46-4ee1-b384-ad1dbd2266cf · outbound

This paper cites Deep ensembles: A loss landscape perspective, 12 2019.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Deep ensembles: A loss landscape perspective, 12 2019

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.220138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 73d5274a-9395-455c-8497-bb709d8e6566 · outbound

This paper cites Dropout as a bayesian approximation: Representing model uncertainty in deep learning.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Dropout as a bayesian approximation: Representing model uncertainty in deep learning

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.207618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fe076946-c3c8-4f8f-927a-1fbcd842778c · outbound

This paper cites Loss surfaces, mode connectivity, and fast ensembling of dnns.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Loss surfaces, mode connectivity, and fast ensembling of dnns

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.194761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 62c56d51-8186-4e55-b737-c5094cbc87e4 · outbound

This paper cites Approximating continuous functions by relu nets of minimal width, 2018.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Approximating continuous functions by relu nets of minimal width, 2018

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:08.004443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e9ecc0d-512b-466e-ad54-1c98247384be · outbound

This paper cites Deep residual learning for im- age recognition.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Deep residual learning for im- age recognition

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:08.008309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f508ac12-0e11-4422-a1f6-4ca9eaaf4f4e · outbound

This paper cites Flat minima.Neural Computation, 9(1):1–42, 01 1997.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Flat minima.Neural Computation, 9(1):1–42, 01 1997

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.168878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6b69a704-53bb-4fc0-bb52-944b49e5c599 · outbound

This paper cites Variational dropout and the local reparam- eterization trick.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Variational dropout and the local reparam- eterization trick

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.157632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3addbe76-e5e0-461e-be52-1e2cd78f0f8f · outbound

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

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Learning multiple layers of features from tiny images

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:08.019226Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e3652286-e578-4b7a-9ddd-9bafff1df5f5 · outbound

This paper cites an unresolved cited work.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-16T11:45:08.139101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 73700cb0-bfa1-4c4a-a784-dad50e44ded3 · outbound

This paper cites McAllester.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization McAllester

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:08.029396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 009871b3-f81a-4d49-be86-a64bd0446176 · outbound

This paper cites In search of the real inductive bias: On the role of implicit regularization in deep learning, 2015.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization In search of the real inductive bias: On the role of implicit regularization in deep learning, 2015

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.120490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d6e60487-ff99-4057-9eef-8794e9d5ce41 · outbound

This paper cites Pytorch: An imperative style, high- performance deep learning library.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Pytorch: An imperative style, high- performance deep learning library

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.108375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 715ba6c0-e2f5-4ecc-adbe-25c5540c2cfb · outbound

This paper cites Dropout: A simple way to prevent neural networks from overfitting.Journal of Machine Learning Research, 15(56):1929–1958, 2014.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Dropout: A simple way to prevent neural networks from overfitting.Journal of Machine Learning Research, 15(56):1929–1958, 2014

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:08.040118Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4906cc45-7f15-42e2-9b73-f88577efd511 · outbound

This paper cites Dropout training as adaptive regularization.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Dropout training as adaptive regularization

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-16T11:45:08.043617Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7980cdbf-3e66-4d76-bb6c-860d0c2301dd · outbound

This paper cites Lee, Martin J.

A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization Lee, Martin J

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:45:08.080462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 8110ae7b-4b0c-4b79-af1f-d0faf002571a · inbound

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs cites this paper.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:37:56.831894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.