Paper Citation Record · LEDGER

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer

As of 9 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 4 inbound Pith citation observations for arXiv:2502.02531.

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

pith.paper-citation-record.v1
2502.02531 v3

Coverage vector

measured 53 of 53 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T11:54:36.999715Z

measured 57 of 57 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-22T10:25:54.649302Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T10:26:24.100616Z

Reference resolution

53 of 53 outbound references displayed

verified exact0
verified fuzzy25
unresolved27
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5eb35ad6-997a-48be-a296-59725bf22aec · outbound

This paper cites write newline.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer write newline

Reference 1

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Observation bf6a0a3e-984e-4ad9-bb98-5825e86a2882 · outbound

This paper cites GPT-4 Technical Report.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer GPT-4 Technical Report

Reference 2

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Observation 18fab8f8-e431-488d-8ab6-661036f0506d · outbound

This paper cites and Pennington, J.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Pennington, J

Reference 3

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Observation 3974edb7-3f78-4252-871e-453a708d4599 · outbound

This paper cites and Pennington, J.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Pennington, J

Reference 4

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Observation 4491be3e-df65-413b-b1cb-83b4a084524b · outbound

This paper cites S., Saxe, A.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer S., Saxe, A

Reference 5

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Observation 888c9cdf-5189-4f96-88ea-3fe798a179af · outbound

This paper cites Out-of-equilibrium dynamical mean-field equations for the perceptron model.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Out-of-equilibrium dynamical mean-field equations for the perceptron model

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.874794Z

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Observation fb4eb0b4-15c8-457a-98f3-eb03bae36086 · outbound

This paper cites Local kernel renormalization as a mechanism for feature learning in overparametrized convolutional neural networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Local kernel renormalization as a mechanism for feature learning in overparametrized convolutional neural networks

Reference 7

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Observation f6d688ed-e99c-49e9-aa59-e53305ba142e · outbound

This paper cites Neural networks as kernel learners: The silent alignment effect.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Neural networks as kernel learners: The silent alignment effect

Reference 8

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Observation e355e0f3-a00b-4864-8445-674f9d001585 · outbound

This paper cites Predictive power of a bayesian effective action for fully connected one hidden layer neural networks in the proportional limit.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Predictive power of a bayesian effective action for fully connected one hidden layer neural networks in the proportional limit

Reference 9

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Observation cf1dc6c6-0932-4ef7-9b4d-a0dbd131e1bf · outbound

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

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Feature learning in finite-width Bayesian deep linear networks with multiple outputs and convolutional layers

Reference 10

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Observation c09b42b8-6058-441a-a813-1c79c1436f24 · outbound

This paper cites Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks

Reference 11

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Observation 91f53ded-6e7d-4d80-bab1-cb29eff73b45 · outbound

This paper cites Dynamics of Finite Width Kernel and Prediction Fluctuations in Mean Field Neural Networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Dynamics of Finite Width Kernel and Prediction Fluctuations in Mean Field Neural Networks

Reference 12

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Observation f1aa050a-3461-4a3a-a485-ffb0c08bc2e9 · outbound

This paper cites A Dynamical Model of Neural Scaling Laws.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer A Dynamical Model of Neural Scaling Laws

Reference 13

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Observation e0677a36-301e-4be4-a930-f0e5157640d7 · outbound

This paper cites How Feature Learning Can Improve Neural Scaling Laws.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer How Feature Learning Can Improve Neural Scaling Laws

Reference 14

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Observation 8dd11ef5-724c-4372-ac3a-392f2a3b2628 · outbound

This paper cites B., Hanin, B., and Pehlevan, C.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer B., Hanin, B., and Pehlevan, C

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.817724Z

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Observation 30be389f-6e5d-497e-a1f4-e8621dcec3b2 · outbound

This paper cites Dimension free ridge regression.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Dimension free ridge regression

Reference 16

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Source-reported events for the cited work

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Observation 39b2a6c4-6922-4c15-af54-acdc5d92246c · outbound

This paper cites Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 17

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Observation 6cb14acb-408e-4921-b419-20817423b660 · outbound

This paper cites and Sompolinsky, H.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Sompolinsky, H

Reference 18

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Observation cb4c6b9c-4353-4c3d-839f-4a67beb73df9 · outbound

This paper cites Bayes-optimal learning of deep random networks of extensive-width.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Bayes-optimal learning of deep random networks of extensive-width

Reference 19

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Observation bb4af645-3e8a-4f5f-9739-ba494ca1c375 · outbound

This paper cites Error scaling laws for kernel classification under source and capacity conditions.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Error scaling laws for kernel classification under source and capacity conditions

Reference 20

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Observation e05c33be-1290-497a-924c-41480ba3a4fd · outbound

This paper cites How two-layer neural networks learn, one (giant) step at a time.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer How two-layer neural networks learn, one (giant) step at a time

Reference 21

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Observation 487aad8a-f5b0-4bc3-aceb-248014afba66 · outbound

This paper cites From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks

Reference 22

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Observation b1a0c616-1509-45ba-b17c-5370de4eaec0 · outbound

This paper cites and Gur-Ari, G.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Gur-Ari, G

Reference 23

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Observation 4b4a5173-09bc-4304-a3f9-615fcbe86358 · outbound

This paper cites Double trouble in double descent: Bias and variance (s) in the lazy regime.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Double trouble in double descent: Bias and variance (s) in the lazy regime

Reference 24

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Observation a7e52749-50eb-49f8-8199-6388b3bf013b · outbound

This paper cites Scaling Exponents Across Parameterizations and Optimizers.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Scaling Exponents Across Parameterizations and Optimizers

Reference 25

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Observation 51d65a98-8151-425a-9436-df7dddd7fb5e · outbound

This paper cites Rigorous dynamical mean field theory for stochastic gradient descent methods.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Rigorous dynamical mean field theory for stochastic gradient descent methods

Reference 26

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Observation fa877548-18b0-4e8a-9a07-1b3a8ba427f6 · outbound

This paper cites Finite Depth and Width Corrections to the Neural Tangent Kernel.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Finite Depth and Width Corrections to the Neural Tangent Kernel

Reference 27

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Observation 69b556e7-2555-4f97-a301-e677cd4c1b19 · outbound

This paper cites Bayesian Inference with Deep Weakly Nonlinear Networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Bayesian Inference with Deep Weakly Nonlinear Networks

Reference 28

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Observation b4495b4e-ae97-43c0-9450-55b568f14903 · outbound

This paper cites Training Compute-Optimal Large Language Models.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Training Compute-Optimal Large Language Models

Reference 29

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Observation 9be7a1d6-12c7-4620-9ff0-b1498b2a381a · outbound

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Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Lu, Y

Reference 30

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Observation cb006b81-e733-46e9-a44b-8c727f47f8ea · outbound

This paper cites Neural tangent kernel: Convergence and generalization in neural networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Neural tangent kernel: Convergence and generalization in neural networks

Reference 31

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Observation ff950a05-9e44-4e4d-b021-616f3aefd125 · outbound

This paper cites Get rich quick: exact solutions reveal how unbalanced initializations promote rapid feature learning.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Get rich quick: exact solutions reveal how unbalanced initializations promote rapid feature learning

Reference 32

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Observation cb9b95c5-7286-4f86-b37f-a1be6128f2ca · outbound

This paper cites Wide neural networks of any depth evolve as linear models under gradient descent.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Wide neural networks of any depth evolve as linear models under gradient descent

Reference 33

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Observation fef3fdc1-d76b-49cd-b92e-d5cd1c7143cf · outbound

This paper cites and Sompolinsky, H.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Sompolinsky, H

Reference 34

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Observation e533b552-3d57-4592-8a3a-c2b56294f779 · outbound

This paper cites S., Krzakala, F., Urbani, P., and Zdeborova, L.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer S., Krzakala, F., Urbani, P., and Zdeborova, L

Reference 35

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Observation c410c5fe-855b-48e4-bb62-93685066eb7d · outbound

This paper cites C., Siggia, E., and Rose, H.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer C., Siggia, E., and Rose, H

Reference 36

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Observation 4074d9ba-0652-4f7f-8a0c-f8163ccd94a5 · outbound

This paper cites and Montanari, A.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Montanari, A

Reference 37

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Observation 0ad92422-bac8-4d8b-9cbb-5d8e2e0527ca · outbound

This paper cites Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit

Reference 38

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Observation c8e199a5-0987-45b1-beaa-7d09c68b14ed · outbound

This paper cites and Urbani, P.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Urbani, P

Reference 39

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Observation 0d56aadf-0172-48a3-bf55-453600e41fc9 · outbound

This paper cites Dynamical mean-field theory for stochastic gradient descent in gaussian mixture classification.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Dynamical mean-field theory for stochastic gradient descent in gaussian mixture classification

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.594154Z

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Observation 289b2551-a682-4c73-9c82-303688f13aa2 · outbound

This paper cites Super Consistency of Neural Network Landscapes and Learning Rate Transfer.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Super Consistency of Neural Network Landscapes and Learning Rate Transfer

Reference 41

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Observation 909e0d77-9f8e-4372-ab69-3498556f84ce · outbound

This paper cites A statistical mechanics framework for bayesian deep neural networks beyond the infinite-width limit.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer A statistical mechanics framework for bayesian deep neural networks beyond the infinite-width limit

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.578804Z

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Observation 0b9f5d02-a367-447e-8c95-4e115429eca3 · outbound

This paper cites 4+3 Phases of Compute-Optimal Neural Scaling Laws.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer 4+3 Phases of Compute-Optimal Neural Scaling Laws

Reference 43

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Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Unresolved cited work

Reference 44

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Observation dd3a2e97-1875-44d4-8a2b-56b426e8e51d · outbound

This paper cites A., Yaida, S., and Hanin, B.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer A., Yaida, S., and Hanin, B

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.563851Z

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Observation 5bc77b0f-2c30-4669-8522-aa2f2e219d45 · outbound

This paper cites and Vanden-Eijnden, E.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Vanden-Eijnden, E

Reference 46

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Source-reported events for the cited work

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Observation 4fce7627-0883-44ff-95e8-ef9cc212008f · outbound

This paper cites Exact solutions to the nonlinear dynamics of learning in deep linear neural networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-09T11:54:36.972330Z

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Observation 53bc0647-54a0-4ec2-86e9-2f2472422dc4 · outbound

This paper cites C., Xu, J., Haas, M., and Cevher, V.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer C., Xu, J., Haas, M., and Cevher, V

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.540836Z

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Observation 2cfc7ce2-5863-46df-a64d-8d1d718484a9 · outbound

This paper cites and Hu, E.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer and Hu, E

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-09T11:54:36.981463Z

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Observation a8bf1cc5-f80f-4f56-bf33-f97752193d7b · outbound

This paper cites J., Babuschkin, I., Sidor, S., Liu, X., Farhi, D., Ryder, N., Pachocki, J., Chen, W., and Gao, J.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer J., Babuschkin, I., Sidor, S., Liu, X., Farhi, D., Ryder, N., Pachocki, J., Chen, W., and Gao, J

Reference 50

Resolution: unresolved; no resolver link, observed 2026-08-09T11:54:36.985871Z

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Observation b7c6b5ed-b662-47d4-aeac-825a38105945 · outbound

This paper cites Tensor Programs VI: Feature Learning in Infinite-Depth Neural Networks.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Tensor Programs VI: Feature Learning in Infinite-Depth Neural Networks

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-09T11:54:36.990546Z

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Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer Unresolved cited work

Reference 52

Resolution: unresolved; raw_fallback, observed 2026-08-09T11:54:37.508761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d741f9d7-7f6f-4a17-aa21-e2aafadbe8bd · outbound

This paper cites A., Tong, W.

Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer A., Tong, W

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T11:54:37.494758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation 3f788870-ad61-4919-b3a2-181940488d87 · inbound

There Will Be a Scientific Theory of Deep Learning cites this paper.

There Will Be a Scientific Theory of Deep Learning Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer

Reference 22

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T15:21:08.980824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 64686c53-6c31-48df-85d3-0635d4454f8d · inbound

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer cites this paper.

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer

Reference 64

Resolution: verified exact; arxiv_id, observed 2026-05-11T03:05:53.487859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cc0eec55-8df5-4051-a7eb-4bd5f1761e89 · inbound

Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer cites this paper.

Reference 69

Resolution: verified exact; arxiv_id, observed 2026-05-22T10:26:24.104396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ac9810ea-8128-4c8c-b11f-5b109f14e692 · inbound

How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization cites this paper.

How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization Deep Linear Network Training Dynamics from Random Initialization: Data, Width, Depth, and Hyperparameter Transfer

Reference 66

Resolution: metadata mismatch; arxiv_id, observed 2026-05-15T04:49:44.858804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.