Paper Citation Record · LEDGER

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation

As of 17 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2602.00545.

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

pith.paper-citation-record.v1
2602.00545 v3

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T06:08:38.421394Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T07:49:39.417566Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T07:49:50.825137Z

Reference resolution

30 of 30 outbound references displayed

verified exact0
verified fuzzy0
unresolved29
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ea82a3df-6fa8-4f25-8f06-d06b0d2ccf86 · outbound

This paper cites Kakade, and Michael I.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Kakade, and Michael I

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:34.715323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 086a0295-795e-4704-b877-896a7af886f0 · outbound

This paper cites Adahessian: An adaptive second order optimizer for machine learning.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Adahessian: An adaptive second order optimizer for machine learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:34.815215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cb9d17c-2b5d-4eec-bab4-aafb3d5eabbc · outbound

This paper cites Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:34.918720Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02fdbfbe-1239-4b91-9b55-583c553c6fc3 · outbound

This paper cites Adam-mini: Use Fewer Learning Rates To Gain More.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Adam-mini: Use Fewer Learning Rates To Gain More

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:34.989677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c26e057-ae40-468b-9570-316363bdbced · outbound

This paper cites On large-batch training for deep learning: Generalization gap and sharp minima.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation On large-batch training for deep learning: Generalization gap and sharp minima

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.119806Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cce763f2-5f3c-4f68-92e9-f5d0d1bd29ce · outbound

This paper cites Visualizing the loss landscape of neural nets.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Visualizing the loss landscape of neural nets

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.267821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 723a83f3-e465-49d9-829a-ab21dbe0cedb · outbound

This paper cites Vetrov, and Andrew Gordon Wilson.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Vetrov, and Andrew Gordon Wilson

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.383836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ac2bd12-e81d-4ea3-920d-0832023e1b7a · outbound

This paper cites Empirical Analysis of the Hessian of Over-Parametrized Neural Networks.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Empirical Analysis of the Hessian of Over-Parametrized Neural Networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.489446Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1963cdb-9dc5-462b-a400-1451564dd894 · outbound

This paper cites Gradient Descent Happens in a Tiny Subspace.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Gradient Descent Happens in a Tiny Subspace

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.599029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bfe98bc-ee1f-468c-b3ab-fdab3e6dbe40 · outbound

This paper cites An investigation into neural net optimization via hessian eigenvalue density.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation An investigation into neural net optimization via hessian eigenvalue density

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.721476Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13c61a53-9285-49a7-8667-48b8650475dd · outbound

This paper cites Pyhessian: Neural networks through the lens of the hessian.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Pyhessian: Neural networks through the lens of the hessian

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:35.912548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1eb21678-95e1-4800-88ab-ec31de70aa33 · outbound

This paper cites Zico Kolter, and Ameet Talwalkar.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Zico Kolter, and Ameet Talwalkar

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.025930Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e8812bcd-ed1d-4686-acab-a3cc3aa75240 · outbound

This paper cites Does sgd really happen in tiny subspaces?, 2024.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Does sgd really happen in tiny subspaces?, 2024

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.151748Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44f3a387-fb7b-46b0-8f4c-87d584381e4c · outbound

This paper cites an unresolved cited work.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.272830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0525bef-6f93-42a1-98d5-7288e1da05b7 · outbound

This paper cites Models of Heavy-Tailed Mechanistic Universality.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Models of Heavy-Tailed Mechanistic Universality

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.435448Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f95393f-96b1-4b23-90de-db564b316b76 · outbound

This paper cites Geometry of neural network loss surfaces via random matrix theory.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Geometry of neural network loss surfaces via random matrix theory

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.586012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e764501-f90d-4715-83f7-973f7b594962 · outbound

This paper cites A random matrix approach to neural networks.The Annals of Applied Probability, 28(2):1190–1248, 2018.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation A random matrix approach to neural networks.The Annals of Applied Probability, 28(2):1190–1248, 2018

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.806569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6f7e997-b17f-4055-bfe1-799f43810546 · outbound

This paper cites The spectrum of the fisher information matrix of a single-hidden-layer neural network.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation The spectrum of the fisher information matrix of a single-hidden-layer neural network

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:36.924022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac66228c-8fd9-4b7c-838e-9235d87800c5 · outbound

This paper cites Traces of class/cross-class structure in deep network spectra.Journal of Machine Learning Research, 21(252):1–64, 2020.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Traces of class/cross-class structure in deep network spectra.Journal of Machine Learning Research, 21(252):1–64, 2020

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.057937Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 500ce38c-6d20-4996-9f8b-d041cd95cc7f · outbound

This paper cites A convergence analysis of gradient descent for deep linear neural networks.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation A convergence analysis of gradient descent for deep linear neural networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.167556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4429011e-a35a-4ac0-b493-ceb378d6426c · outbound

This paper cites Analytic insights into structure and rank of neural network hessian maps.Advances in Neural Information Processing Systems, 34:23914–23927, 2021.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Analytic insights into structure and rank of neural network hessian maps.Advances in Neural Information Processing Systems, 34:23914–23927, 2021

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.299096Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4052fb58-2015-4457-9490-0ad61b5a1626 · outbound

This paper cites Deep linear network training dynamics from random initialization: Data, width, depth, and hyperparameter transfer.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Deep linear network training dynamics from random initialization: Data, width, depth, and hyperparameter transfer

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.396573Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a6805d3-59a9-4fd9-af4a-e2932bce1e40 · outbound

This paper cites Theoretical characterisation of the gauss-newton conditioning in neural networks.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Theoretical characterisation of the gauss-newton conditioning in neural networks

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.492369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15c883c2-22f0-4a5d-af66-20b3f386a0ee · outbound

This paper cites Depth, not data: An analysis of hessian spectral bifurcation.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Depth, not data: An analysis of hessian spectral bifurcation

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.670741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f15e5f9-9647-4dd7-8007-30310d389f6a · outbound

This paper cites Since the balanced initialization chooses V such that its column space lies within the support ofΣ xx, we haveV ⊤ΣxxV=I d∗.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Since the balanced initialization chooses V such that its column space lies within the support ofΣ xx, we haveV ⊤ΣxxV=I d∗

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.746096Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bee1521-a540-42ad-9b2d-818837a28931 · outbound

This paper cites an unresolved cited work.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:37.873158Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fc68973-64b8-497f-a232-c679e978db27 · outbound

This paper cites Note that ifd L =d ∗ =d 0, thenU∈R dL×dL is a square orthogonal matrix.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Note that ifd L =d ∗ =d 0, thenU∈R dL×dL is a square orthogonal matrix

Reference 27

Resolution: malformed identifier; no resolver link, observed 2026-08-03T06:08:38.015047Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6ba9769-0bf2-4c6a-8539-ab3c4b6b6182 · outbound

This paper cites an unresolved cited work.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:38.152770Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 156245e9-bcfa-4f68-86c8-3dfcb301e220 · outbound

This paper cites an unresolved cited work.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:38.261697Z

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Unavailable: canonical work link unavailable.

Observation bb345218-d900-41d2-9a00-f9ef788526f0 · outbound

This paper cites Furthermore, the eigenvaluesλ i,t fori= 1,.

Depth, Not Data: An Analysis of Hessian Spectral Bifurcation Furthermore, the eigenvaluesλ i,t fori= 1,

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T06:08:38.421394Z

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Pith citing papers

Observation 7cc6ded9-5e9e-4ab0-bfb5-580f6b8e4741 · inbound

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization cites this paper.

RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization Depth, Not Data: An Analysis of Hessian Spectral Bifurcation

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-20T02:04:51.232360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.