Paper Citation Record · LEDGER

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network

As of 17 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2606.05326.

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

pith.paper-citation-record.v1
2606.05326 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T05:00:47.062637Z

measured 32 of 32 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 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

32 of 32 outbound references displayed

verified exact4
verified fuzzy0
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 21f6cb1f-6336-4f55-adec-9b2f04f3573d · outbound

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

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:36:52.024353Z

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 cf64eccf-f097-4247-8d20-d22fcaf15d85 · outbound

This paper cites Proceedings of Machine Learning Research , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Proceedings of Machine Learning Research , year=

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 890df9ad-48a3-4863-a81b-b8230468f921 · outbound

This paper cites International Conference on Learning Representations , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network International Conference on Learning Representations , year=

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e68969d-e890-48d0-8b2b-057afc747c58 · outbound

This paper cites Understanding Edge-of-Stability Training Dynamics with a Minimalist Example.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Understanding Edge-of-Stability Training Dynamics with a Minimalist Example

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:36:52.032960Z

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 2a767a3e-86f4-4a14-b50a-4975be4fde7f · outbound

This paper cites Understanding optimization in deep learning with central flows.arXiv preprint arXiv:2410.24206.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Understanding optimization in deep learning with central flows.arXiv preprint arXiv:2410.24206

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:36:52.030222Z

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 324b420f-ea05-459e-aadd-2bbe40a8cb78 · outbound

This paper cites International Conference on Learning Representations , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network International Conference on Learning Representations , year=

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48e930e3-a136-4af2-8c5f-cdb067bb3434 · outbound

This paper cites Proceedings of the 34th International Conference on Machine Learning (ICML) , volume =.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Proceedings of the 34th International Conference on Machine Learning (ICML) , volume =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 849de1f7-d71d-4ea0-a14e-f1c4dd39f154 · outbound

This paper cites Advances in Neural Information Processing Systems (NeurIPS) , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Advances in Neural Information Processing Systems (NeurIPS) , volume=

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 458d9264-e371-4e40-8abb-1697d27db55c · outbound

This paper cites Proceedings of the 38th International Conference on Machine Learning , pages =.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Proceedings of the 38th International Conference on Machine Learning , pages =

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4be1200a-4a39-4a79-bd93-0c42fcaac78e · outbound

This paper cites Tensor Programs.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Tensor Programs

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8816260-ada5-4e97-9de4-7e3f971c7a24 · outbound

This paper cites 2025 , eprint=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network 2025 , eprint=

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 015a7f0a-d3b7-439a-b8ff-bd1364b1bfad · outbound

This paper cites 2025 , eprint=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network 2025 , eprint=

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aa6f2f3c-22f0-403c-b480-ba3aa238ef98 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Advances in Neural Information Processing Systems , volume=

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a092033-6883-4e51-9002-2f47600a1dc6 · outbound

This paper cites Advances in Neural Information Processing Systems (NeurIPS) , volume =.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Advances in Neural Information Processing Systems (NeurIPS) , volume =

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f4f91bb-4472-4a1f-b86d-dc4705c4fc65 · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network The Thirteenth International Conference on Learning Representations , year=

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae40d5f9-8809-49af-88d4-7b3c8bc811f5 · outbound

This paper cites Proceedings of the 40th International Conference on Machine Learning , pages =.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Proceedings of the 40th International Conference on Machine Learning , pages =

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ebdfe2e-a0a6-48a1-a659-9d420b752db1 · outbound

This paper cites Thirty-seventh Conference on Neural Information Processing Systems , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Thirty-seventh Conference on Neural Information Processing Systems , year=

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4611fac-93ab-4692-8389-620cef5fe0a2 · outbound

This paper cites Understanding Sharpness Dynamics in.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Understanding Sharpness Dynamics in

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e82ae4ca-16f1-43f9-bdf4-8bcf73ac97c9 · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network The Thirteenth International Conference on Learning Representations , year=

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4864ff2d-bc7f-4188-8e72-93cf682f5f46 · outbound

This paper cites an unresolved cited work.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bab3159b-fe89-4887-9e69-d39a61d3d084 · outbound

This paper cites arXiv preprint arXiv:2602.01480 , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network arXiv preprint arXiv:2602.01480 , year=

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-07-02T10:36:52.027282Z

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 1e34975d-b2fe-4dbc-b493-5b78abdbd37b · outbound

This paper cites arXiv preprint , year=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network arXiv preprint , year=

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf4618d8-ea02-4007-b810-cb0ba1b86a4c · outbound

This paper cites Neural Computation , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Neural Computation , volume=

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfa4af3b-8b5f-42cc-87cb-78848a14b80f · outbound

This paper cites 1999 , publisher=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network 1999 , publisher=

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3adb3552-6d3b-4184-9581-8e5342660b46 · outbound

This paper cites 2004 , publisher=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network 2004 , publisher=

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee007e9e-c7b8-4c7d-8d24-0cecb431777d · outbound

This paper cites Proceedings of the National Academy of Sciences , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Proceedings of the National Academy of Sciences , volume=

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b0075e8-9489-47f3-a357-ab8366944fe1 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Advances in Neural Information Processing Systems , volume=

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d36974e-96b0-42a2-9ad6-a16a6b2302de · outbound

This paper cites Journal of Machine Learning Research , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Journal of Machine Learning Research , volume=

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1246042-1df4-4ce5-98a2-7f76c52555b6 · outbound

This paper cites Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence , pages=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence , pages=

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41a89635-7c83-440a-983b-0fb994115b69 · outbound

This paper cites Advances in Neural Information Processing Systems (NeurIPS) , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Advances in Neural Information Processing Systems (NeurIPS) , volume=

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1171bec-2c79-415a-8ef5-6e91eaaa4eaa · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network Advances in Neural Information Processing Systems , volume=

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d01b0523-d9b8-4125-8609-cc13d8cd7633 · outbound

This paper cites 2009 , publisher=.

Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network 2009 , publisher=

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-28T05:00:47.062637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.