Papers › Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability
Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability
Jeremy M. Cohen, Simran Kaur, Yuanzhi Li, J. Zico Kolter, Ameet Talwalkar
We empirically demonstrate that full-batch gradient descent on neural network training objectives typically operates in a regime we call the Edge of Stability. In this regime, the maximum eigenvalue of the training loss Hessian hovers just above the numerical value 2 / (step size), and the training loss behaves non-monotonically over short timescales, yet consistently decreases over long timescales. Since this behavior is inconsistent with several widespread presumptions in the field of optimization, our findings raise questions as to whether these presumptions are relevant to neural network training. We hope that our findings will inspire future efforts aimed at rigorously understanding optimization at the Edge of Stability. Code is available at https://github.com/locuslab/edge-of-stability.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="2103.00065")
Code
Syntology Ran 0 of 2 code samples harvested from 1 repository linked to this paper; 2 have no recorded run.
By repository: found in paper text by Syntology: 1 sample from 1 repository, 0 ran; 1 identical to code first harvested elsewhere. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
2 samples harvested; 0 ran; 0 honoured the contract we drafted; 2 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 1 of the 2 samples is pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from hongyi-zhang/Fixup. Some samples are identical code Syntology first harvested from another repository; for those, this paper's copy is not located and its licence is not recorded. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.
Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.
Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.
d07d18ed4137d374 · report
9b8289076669fe4f · report
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections