Paper Citation Record · LEDGER

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More

As of 7 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 1 inbound Pith citation observation for arXiv:2506.06940.

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

pith.paper-citation-record.v1
2506.06940 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:56:05.359947Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T23:15:59.394256Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

15 of 15 outbound references displayed

verified exact0
verified fuzzy12
unresolved1
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 57021063-48e9-4dd8-bcaa-693a84e6bff9 · outbound

This paper cites We denote o⋆ i =w ⊤ i u⋆ for each i∈[r].

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More We denote o⋆ i =w ⊤ i u⋆ for each i∈[r]

Reference 1

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:56:05.390139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c9607362-8ff4-4080-bf02-cab7602f9dff · outbound

This paper cites LeCun, Y ., Bottou, L., Orr, G.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More LeCun, Y ., Bottou, L., Orr, G

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.435482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation db526dc8-46a0-4183-8429-101f1fc489e6 · outbound

This paper cites cc/paper_files/paper/2019/file/ bce9abf229ffd7e570818476ee5d7dde-Paper.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More cc/paper_files/paper/2019/file/ bce9abf229ffd7e570818476ee5d7dde-Paper

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.428718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f6d2fb13-91e3-4b39-84d1-5e91ed18c1e7 · outbound

This paper cites Pesme, S., Pillaud-Vivien, L., and Flammarion, N.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Pesme, S., Pillaud-Vivien, L., and Flammarion, N

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.420575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e378db56-cf5f-4ee7-b504-f89e79530c72 · outbound

This paper cites an unresolved cited work.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:56:05.404717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 78cefd46-bf30-4718-aa9b-195cb00bd873 · outbound

This paper cites We denote o⋆ i =w ⊤ i u⋆ for each i∈[r].

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More We denote o⋆ i =w ⊤ i u⋆ for each i∈[r]

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.382431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6c8c8745-d3f8-4b38-878d-5d416f5572ac · outbound

This paper cites URL https://proceedings.mlr.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More URL https://proceedings.mlr

Reference 2010

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.471644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 15d5f353-21bb-4c23-ac1e-f06bc335a8e7 · outbound

This paper cites URL https://aclanthology.org/D13-1170/.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More URL https://aclanthology.org/D13-1170/

Reference 2013

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.412200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 25b92df4-d1ce-45f9-95ce-025e80c7b54a · outbound

This paper cites cc/paper_files/paper/2018/file/ 5a4be1fa34e62bb8a6ec6b91d2462f5a-Paper.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More cc/paper_files/paper/2018/file/ 5a4be1fa34e62bb8a6ec6b91d2462f5a-Paper

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.465832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f03537a0-f4fa-4bd1-96a0-4ce98b1736e2 · outbound

This paper cites Jastrz˛ ebski, S., Szymczak, M., Fort, S., Arpit, D., Tabor, J., Cho, K., and Geras, K.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Jastrz˛ ebski, S., Szymczak, M., Fort, S., Arpit, D., Tabor, J., Cho*, K., and Geras*, K

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.458591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation eb2f51d7-1fa3-48df-9280-50faa3cb1738 · outbound

This paper cites Kalra, D.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Kalra, D

Reference 2020

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.450695Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 506a4f3d-2f50-40da-b3d1-3a559477c7ff · outbound

This paper cites Cohen, J., Kaur, S., Li, Y ., Kolter, J.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Cohen, J., Kaur, S., Li, Y ., Kolter, J

Reference 2022

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.478251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2afe7010-4b8c-4c38-859a-27f08ed4e1d6 · outbound

This paper cites Ahn, K., Zhang, J., and Sra, S.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Ahn, K., Zhang, J., and Sra, S

Reference 2023

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.484663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ca1b26d-130c-4b74-903f-f9b80bb6c001 · outbound

This paper cites Zhu, X., Wang, Z., Wang, X., Zhou, M., and Ge, R.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Zhu, X., Wang, Z., Wang, X., Zhou, M., and Ge, R

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:56:05.397358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a77e5499-e7fc-43b0-a7e3-8c9187c68212 · outbound

This paper cites Knyazev, A.

Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More Knyazev, A

Reference 2025

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:56:05.442880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 2a3e6cbe-1499-4dd6-be23-28137c1257eb · inbound

Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway cites this paper.

Gradient Descent with Large Step Size Restores Symmetry in Deep Linear Networks with Multi-Pathway Understanding Sharpness Dynamics in NN Training with a Minimalist Example: The Effects of Dataset Difficulty, Depth, Stochasticity, and More

Reference 40

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:22:46.402929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.