Paper Citation Record · LEDGER

Dyson Brownian motion and random matrix dynamics of weight matrices during learning

As of 16 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2411.13512.

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

pith.paper-citation-record.v1
2411.13512 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T16:28:10.152785Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:28:29.870383Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T23:28:30.153324Z

Reference resolution

24 of 24 outbound references displayed

verified exact2
verified fuzzy9
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2a184ade-cd04-4c37-abfa-8cbf1c0e1b94 · outbound

This paper cites Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics 62 (1955) 548.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics 62 (1955) 548

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.578752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 31a5a5fc-07c5-4f4b-ace1-d7d43752dcd0 · outbound

This paper cites Wigner, Conference on Neutron Physics by Time-of-Flight, p.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Wigner, Conference on Neutron Physics by Time-of-Flight, p

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.562279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d852b51c-c75b-4909-8dbd-48cdc8456e67 · outbound

This paper cites Dyson, Statistical theory of the energy levels of complex systems.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Dyson, Statistical theory of the energy levels of complex systems

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.546864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2173c291-b1ea-4528-b426-142e505b8242 · outbound

This paper cites Dyson, Statistical theory of the energy levels of complex systems.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Dyson, Statistical theory of the energy levels of complex systems

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.530650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation df54a94d-d199-4abe-9102-dc766b4c3cb4 · outbound

This paper cites Dyson, Statistical Theory of the Energy Levels of Complex Systems.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Dyson, Statistical Theory of the Energy Levels of Complex Systems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.513884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c61142f2-afeb-481a-9fc1-fb4c8304485e · outbound

This paper cites Mehta, Random Matrices, Academic Press, New York, 3rd ed.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Mehta, Random Matrices, Academic Press, New York, 3rd ed

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.496628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 69560256-64e2-4d08-8d73-b778d7fd80f8 · outbound

This paper cites Dyson, A Brownian-Motion Model for the Eigenvalues of a Random Matrix, J.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Dyson, A Brownian-Motion Model for the Eigenvalues of a Random Matrix, J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.478779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fac4da33-64f0-481e-901a-f8aa2b2ba9a3 · outbound

This paper cites Stochastic weight matrix dynamics during learning and Dyson Brownian motion.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Stochastic weight matrix dynamics during learning and Dyson Brownian motion

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.069558Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9deb2159-e7f5-49b4-8919-3d6e19bc139f · outbound

This paper cites Pennington and P.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Pennington and P

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.462237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation cbee11c8-0d3c-4c47-89df-a0bce3037c49 · outbound

This paper cites Traditional and Heavy-Tailed Self Regularization in Neural Network Models.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Traditional and Heavy-Tailed Self Regularization in Neural Network Models

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.079370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1405d44f-e2d3-47a3-b562-60c53f0b4e32 · outbound

This paper cites Appearance of Random Matrix Theory in Deep Learning.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Appearance of Random Matrix Theory in Deep Learning

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.084373Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76705b6c-3158-4940-a61d-c91445591d04 · outbound

This paper cites Universal characteristics of deep neural network loss surfaces from random matrix theory.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Universal characteristics of deep neural network loss surfaces from random matrix theory

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-12T16:28:10.379279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 220507a8-8215-4dd9-a9cf-c9b0894454b0 · outbound

This paper cites Couillet and Z.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Couillet and Z

Reference 13

Resolution: verified exact; doi, observed 2026-08-12T16:28:10.201267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c3c8e4f3-d2c3-4930-b7d8-8df556f09bfd · outbound

This paper cites The Universal Statistical Structure and Scaling Laws of Chaos and Turbulence.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning The Universal Statistical Structure and Scaling Laws of Chaos and Turbulence

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.099055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e1e35d7-a77f-4c3a-aee7-2f3711b6723d · outbound

This paper cites A Bayesian Perspective on Generalization and Stochastic Gradient Descent.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning A Bayesian Perspective on Generalization and Stochastic Gradient Descent

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.104356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16f7a9fe-95f7-4417-b9cd-21dab244f9b3 · outbound

This paper cites Don't Decay the Learning Rate, Increase the Batch Size.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Don't Decay the Learning Rate, Increase the Batch Size

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.109495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37c33948-2d4b-4737-97df-2cbfdc27e541 · outbound

This paper cites Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.114425Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95810aa1-75fa-4c2f-a51b-a8168624be6f · outbound

This paper cites Stochastic modified equations and adaptive stochastic gradient algorithms.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Stochastic modified equations and adaptive stochastic gradient algorithms

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.120303Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d38e63c3-a966-48c6-a912-e17ea32240bd · outbound

This paper cites Restricted Boltzmann Machine, recent advances and mean-field theory.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Restricted Boltzmann Machine, recent advances and mean-field theory

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.125607Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4d6327c-4d80-4f7e-bf94-281206de8f8e · outbound

This paper cites Scalar field Restricted Boltzmann Machine as an ultraviolet regulator.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Scalar field Restricted Boltzmann Machine as an ultraviolet regulator

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.131179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 739673fd-573c-415f-a0b4-a8cb53b8f7ae · outbound

This paper cites Attention Is All You Need.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Attention Is All You Need

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.137429Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2a25c50-2489-4781-89a5-93891439fb34 · outbound

This paper cites Karpathy, NanoGPT, https://github.com/karpathy/nanoGPT.git, 2023.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Karpathy, NanoGPT, https://github.com/karpathy/nanoGPT.git, 2023

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T16:28:10.446610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c5a6b1ef-8d46-4c2d-b0e7-777e4395dc57 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Adam: A Method for Stochastic Optimization

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.147716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9acf11b-7954-4e95-9c8f-7a9e80828fa5 · outbound

This paper cites an unresolved cited work.

Dyson Brownian motion and random matrix dynamics of weight matrices during learning Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-12T16:28:10.152785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 6db49146-4169-4690-81e3-a8e35bdde80d · inbound

Random Matrix Theory for Stochastic Gradient Descent cites this paper.

Random Matrix Theory for Stochastic Gradient Descent Dyson Brownian motion and random matrix dynamics of weight matrices during learning

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:28:30.157260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.