Papers › Sharpness-Aware Minimization Efficiently Selects Flatter Minima Late in Training
Sharpness-Aware Minimization Efficiently Selects Flatter Minima Late in Training
Zhanpeng Zhou, Mingze Wang, Yuchen Mao, Bingrui Li, Junchi Yan
Sharpness-Aware Minimization (SAM) has substantially improved the generalization of neural networks under various settings. Despite the success, its effectiveness remains poorly understood. In this work, we discover an intriguing phenomenon in the training dynamics of SAM, shedding lights on understanding its implicit bias towards flatter minima over Stochastic Gradient Descent (SGD). Specifically, we find that SAM efficiently selects flatter minima late in training. Remarkably, even a few epochs of SAM applied at the end of training yield nearly the same generalization and solution sharpness as full SAM training. Subsequently, we delve deeper into the underlying mechanism behind this phenomenon. Theoretically, we identify two phases in the learning dynamics after applying SAM late in training: i) SAM first escapes the minimum found by SGD exponentially fast; and ii) then rapidly converges to a flatter minimum within the same valley. Furthermore, we empirically investigate the role of SAM during the early training phase. We conjecture that the optimization method chosen in the late phase is more crucial in shaping the final solution's properties. Based on this viewpoint, we extend our findings from SAM to Adversarial Training.
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="2410.10373")
Code
Syntology Ran 1 of 1 code samples harvested from 1 repository linked to this paper; 0 have no recorded run. Of those that ran: 1 ran · our draft was wrong.
By repository: found in paper text by Syntology: 1 sample from 1 repository, 1 ran. 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
1 sample harvested; 1 ran; 0 honoured the contract we drafted; 0 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: 0 of the 1 sample are 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 zzp1012/SAM-in-Late-Phase. “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.
996ab226a85f70fb · report
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
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