Paper Citation Record · LEDGER

Proportional infinite-width infinite-depth limit for deep linear neural networks

As of 13 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 4 inbound Pith citation observations for arXiv:2411.15267.

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

pith.paper-citation-record.v1
2411.15267 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T15:05:40.879958Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T09:36:54.155047Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T12:45:44.976159Z

Reference resolution

36 of 36 outbound references displayed

verified exact2
verified fuzzy12
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation dd0a00d8-e03e-48f0-914b-cc8aa24e47bb · outbound

This paper cites Local Kernel Renormalization as a mechanism for feature learning in overparametrized Convolutional Neural Networks.

Proportional infinite-width infinite-depth limit for deep linear neural networks Local Kernel Renormalization as a mechanism for feature learning in overparametrized Convolutional Neural Networks

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.710001Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03361589-4e1e-481b-b54c-d088f265e4f9 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.499481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b1d0c7ad-0156-421b-a500-1d11d4788ce2 · outbound

This paper cites Feature learning in finite-width Bayesian deep linear networks with multiple outputs and convolutional layers.

Proportional infinite-width infinite-depth limit for deep linear neural networks Feature learning in finite-width Bayesian deep linear networks with multiple outputs and convolutional layers

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.721116Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40077ef5-764e-403d-bdad-265e5e88c5ae · outbound

This paper cites Infinitely wide limits for deep Stable neural networks: sub-linear, linear and super-linear activation functions.

Proportional infinite-width infinite-depth limit for deep linear neural networks Infinitely wide limits for deep Stable neural networks: sub-linear, linear and super-linear activation functions

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-12T15:05:41.010962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 517cccd1-d1a3-481c-94dd-0250d3ab9282 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.482859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d33485cb-9400-4a60-bb05-4fd05351725d · outbound

This paper cites and Bach, F.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Bach, F

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.467459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 162afd48-0188-485c-b171-378a63eea285 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.451716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c354028d-2ea7-4338-9d61-38719a83fef1 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.436472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cf8c1982-4a26-4f9a-b45d-4a220fa05183 · outbound

This paper cites Matthews, A.

Proportional infinite-width infinite-depth limit for deep linear neural networks Matthews, A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.421567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 837dc0d9-3a41-4b9b-9475-a53e51c8fb65 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.405088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6a6ac3b4-187f-4de0-a2b5-03415bdf0963 · outbound

This paper cites Quantitative CLTs in Deep Neural Networks.

Proportional infinite-width infinite-depth limit for deep linear neural networks Quantitative CLTs in Deep Neural Networks

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.761888Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e18a11d-beec-4e92-9d89-412e7ca92412 · outbound

This paper cites Large-width asymptotics for ReLU neural networks with $\alpha$-Stable initializations.

Proportional infinite-width infinite-depth limit for deep linear neural networks Large-width asymptotics for ReLU neural networks with $\alpha$-Stable initializations

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-12T15:05:40.970631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a4459453-7391-46fc-beb1-f45fccff1386 · outbound

This paper cites E., and Aitchison, L.

Proportional infinite-width infinite-depth limit for deep linear neural networks E., and Aitchison, L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.388269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7649d7fc-8ca1-4fd3-ac59-510238b7962a · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.776317Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f834a14-9901-4045-95e5-d6445480568a · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.372265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a1b4532d-6fa1-4376-8759-73419fac5569 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.355689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cf041b6a-b5a9-4fdb-a2af-4d5bf14451c7 · outbound

This paper cites and Zlokapa, A.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Zlokapa, A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.339201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 5722727b-4655-4c7d-974e-88363e870aed · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.322706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e12cacbe-358a-4b22-9170-f5dcfa29a3e1 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.303841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7110dce9-ce6c-4f94-b5bf-ef8a44fa47fe · outbound

This paper cites and Shreve, S.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Shreve, S

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.286945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f5fcc66e-2127-4598-8d7e-9850f2940da7 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.269655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 95739927-d124-4f15-a4d4-a67d0b5dab79 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.253066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a2da3b25-81b5-4130-8e86-ae612da2f390 · outbound

This paper cites The large learning rate phase of deep learning: the catapult mechanism.

Proportional infinite-width infinite-depth limit for deep linear neural networks The large learning rate phase of deep learning: the catapult mechanism

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.818846Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b2629e8-731c-4313-96c1-f5c7345288e0 · outbound

This paper cites and Sompolinsky, H.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Sompolinsky, H

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.236737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation df1db75f-1ff2-4d0a-97a3-8af6935111aa · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.828479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b817fe34-2d72-46a1-9859-38644204ca0c · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.209661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2c781661-7781-4fef-942b-851ff1fe9715 · outbound

This paper cites A., Pennington, J., and Sohl-dickstein, J.

Proportional infinite-width infinite-depth limit for deep linear neural networks A., Pennington, J., and Sohl-dickstein, J

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.194162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation db1e2108-07c0-4cc7-aeb7-922b8791167b · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.177334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 82b897fa-95bd-4e53-9583-ddf47c98022a · outbound

This paper cites and Vanden-Eijnden, E.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Vanden-Eijnden, E

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.160353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f19449a7-70bd-4a56-88be-57509c2ec259 · outbound

This paper cites M., McClelland, J.

Proportional infinite-width infinite-depth limit for deep linear neural networks M., McClelland, J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.144263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8ce159fd-3554-489b-8a50-217f9ebda150 · outbound

This paper cites M., McClelland, J.

Proportional infinite-width infinite-depth limit for deep linear neural networks M., McClelland, J

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.126979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 322dabf1-f578-4a3b-ad76-847746722c2d · outbound

This paper cites and Spiliopoulos, K.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Spiliopoulos, K

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.111201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6263c103-2046-477c-a23a-fac1c310b486 · outbound

This paper cites Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processes.

Proportional infinite-width infinite-depth limit for deep linear neural networks Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processes

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-12T15:05:40.865469Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc80af75-8971-41c3-873d-2dbaad7bf5be · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.094647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 86d3e2db-f3ae-434f-991c-4ed664e809fc · outbound

This paper cites and Hu, E.

Proportional infinite-width infinite-depth limit for deep linear neural networks and Hu, E

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T15:05:41.078254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e9d0532d-2a36-4587-b11f-9595a01e6380 · outbound

This paper cites an unresolved cited work.

Proportional infinite-width infinite-depth limit for deep linear neural networks Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-12T15:05:41.061861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation a96e1a70-a7fa-46f0-86d6-50d78a46b783 · inbound

Large deviation principles for convolutional Bayesian neural networks cites this paper.

Large deviation principles for convolutional Bayesian neural networks Proportional infinite-width infinite-depth limit for deep linear neural networks

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-15T14:03:39.869199Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fed401a-734c-434e-8f67-1414c29a93ec · inbound

Bayesian Inference with Shaped Deep Non-linear MLPs cites this paper.

Bayesian Inference with Shaped Deep Non-linear MLPs Proportional infinite-width infinite-depth limit for deep linear neural networks

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T20:42:37.105524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f64594c9-097b-4b2c-9f58-640d6d4ed791 · inbound

Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product cites this paper.

Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product Proportional infinite-width infinite-depth limit for deep linear neural networks

Reference 60

Resolution: verified exact; arxiv_id, observed 2026-07-01T12:45:44.977904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7659bc2c-b226-408c-b51d-04903f765440 · inbound

Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product cites this paper.

Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product Proportional infinite-width infinite-depth limit for deep linear neural networks

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-02T09:36:54.155047Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.