Paper Citation Record · LEDGER

Random Matrix Theory for Stochastic Gradient Descent

As of 12 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2412.20496.

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

pith.paper-citation-record.v1
2412.20496 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:28:29.910469Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

26 of 26 outbound references displayed

verified exact4
verified fuzzy11
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6089b4a9-5fc6-4761-9b6b-b29d81c70382 · outbound

This paper cites Machine learning and the physical sciences.

Random Matrix Theory for Stochastic Gradient Descent Machine learning and the physical sciences

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.613387Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8328b243-39fb-4031-afab-862be59c7ddb · outbound

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

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

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.618836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd68be48-a4a9-4b57-8d64-6264d884c59a · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Wigner,Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics 62(1955) 548

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.713111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation af0c86ac-4062-4930-a617-ac54c77cb83f · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Wigner,Conference on Neutron Physics by Time-of-Flight, p

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.698820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 30a6c6e8-4443-4ace-b2dd-a2e34e762309 · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Dyson,Statistical theory of the energy levels of complex systems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.685806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d99e7409-7f9e-4764-9344-24a1dde9a0db · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Dyson,Statistical theory of the energy levels of complex systems

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.672054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7e5a285f-9cf8-49ae-ac63-2bcca123822c · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Dyson,Statistical Theory of the Energy Levels of Complex Systems

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.642536Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75d1b192-6563-4b90-a5ac-a310d0845d1a · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Dyson,A Brownian-Motion Model for the Eigenvalues of a Random Matrix, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.653040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5be17bfb-a670-40a9-a38c-6e600a531b79 · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Mehta,Random Matrices, Academic Press, New York, 3rd ed

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.639847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation db6e851d-868b-4491-9710-422ebac0848d · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Traditional and Heavy-Tailed Self Regularization in Neural Network Models

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.668149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09f95c5e-559e-4280-a923-29b80a7bca90 · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Appearance of Random Matrix Theory in Deep Learning

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.746912Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e14ae5e-2fe6-4c8a-9ee6-8f59ecdc3f0e · outbound

This paper cites Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour.

Random Matrix Theory for Stochastic Gradient Descent Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.822946Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44128a12-7b6b-40b7-b165-94d13b4e16d4 · outbound

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

Random Matrix Theory for Stochastic Gradient Descent A Bayesian Perspective on Generalization and Stochastic Gradient Descent

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.857819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4d4bd3b-ba18-493e-ae28-7ab8f2fd6627 · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Don't Decay the Learning Rate, Increase the Batch Size

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.861538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4db84599-6cd3-4fdd-9ec1-60a6fd87ef4a · outbound

This paper cites Stochastic natural gradient descent draws posterior samples in function space.

Random Matrix Theory for Stochastic Gradient Descent Stochastic natural gradient descent draws posterior samples in function space

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:28:30.175791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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

This paper cites Dyson Brownian motion and random matrix dynamics of weight matrices during learning.

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 2026-08-12T06:34:41.77262+00:00.

Observation 6623dc00-3d59-4ca7-b475-0f1c2d73c23d · outbound

This paper cites Mandt, M.D.

Random Matrix Theory for Stochastic Gradient Descent Mandt, M.D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.590276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1d2af006-3339-4cdb-9268-c9ef3a052146 · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Stochastic modified equations and adaptive stochastic gradient algorithms

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.878141Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 574837fe-b827-4eb4-8fe9-f145bc1434b5 · outbound

This paper cites Fluctuation-dissipation relations for stochastic gradient descent.

Random Matrix Theory for Stochastic Gradient Descent Fluctuation-dissipation relations for stochastic gradient descent

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.881681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3d1a7b6-0e19-4af4-9c4c-efc9cb3b72d5 · outbound

This paper cites Smolensky,Chapter 6: Information processing in dynamical systems: Foundations of harmony theory, inParallel Distributed Processing: Volume 1, D.

Random Matrix Theory for Stochastic Gradient Descent Smolensky,Chapter 6: Information processing in dynamical systems: Foundations of harmony theory, inParallel Distributed Processing: Volume 1, D

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.408975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 79601bbc-f0e9-44a2-abb9-bce5d58a1167 · outbound

This paper cites Hinton,Training Products of Experts by Minimizing Contrastive Divergence,Neural Computation 14(2002) 1771.

Random Matrix Theory for Stochastic Gradient Descent Hinton,Training Products of Experts by Minimizing Contrastive Divergence,Neural Computation 14(2002) 1771

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.322809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dd562bc2-10f6-4d75-b2c3-e422525d335b · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Restricted Boltzmann Machine, recent advances and mean-field theory

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:28:30.116524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation abe8ed9d-685c-4f4e-8298-9b423ba980ca · outbound

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

Random Matrix Theory for Stochastic Gradient Descent Scalar field Restricted Boltzmann Machine as an ultraviolet regulator

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T23:28:29.898270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6fd0ae5-26d3-4ddc-b75f-1297d8efe006 · outbound

This paper cites Bahri, J.

Random Matrix Theory for Stochastic Gradient Descent Bahri, J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.310214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7265edc5-efa4-45d7-8175-336bb58d2ecf · outbound

This paper cites Goldt, M.S.

Random Matrix Theory for Stochastic Gradient Descent Goldt, M.S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:28:30.295808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a6144477-72c0-47ab-997e-576fe07619fa · outbound

This paper cites an unresolved cited work.

Random Matrix Theory for Stochastic Gradient Descent Unresolved cited work

Reference 26

Resolution: verified exact; doi, observed 2026-08-10T23:28:30.035604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.