{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sharpness-aware-minimization-and-the-edge-of","title":"Sharpness-Aware Minimization and the Edge of Stability","arxiv_id":"2309.12488","date":"2023-09-21","proceeding":null,"authors":["Philip M. Long","Peter L. Bartlett"],"abstract":"Recent experiments have shown that, often, when training a neural network with gradient descent (GD) with a step size $\\eta$, the operator norm of the Hessian of the loss grows until it approximately reaches $2/\\eta$, after which it fluctuates around this value. The quantity $2/\\eta$ has been called the \"edge of stability\" based on consideration of a local quadratic approximation of the loss. We perform a similar calculation to arrive at an \"edge of stability\" for Sharpness-Aware Minimization (SAM), a variant of GD which has been shown to improve its generalization. Unlike the case for GD, the resulting SAM-edge depends on the norm of the gradient. Using three deep learning training tasks, we see empirically that SAM operates on the edge of stability identified by this analysis.","url_abs":"https://arxiv.org/abs/2309.12488v6","url_pdf":"https://arxiv.org/pdf/2309.12488v6.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sharpness-aware-minimization-and-the-edge-of","repo_url":"https://github.com/google-deepmind/sam_edge","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[],"methods":[{"method_slug":"sam","method_name":"SAM"},{"method_slug":"sharpness-aware-minimization","method_name":"Sharpness-Aware Minimization"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2309.12488","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2309.12488"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/google-deepmind/sam_edge","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"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"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"143a32689176be43","entry":"test_error_fn","repo":"google-deepmind/sam_edge","repo_kind":"official","path":"image_classification.py","file_url":"https://github.com/google-deepmind/sam_edge/blob/HEAD/image_classification.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"Apache-2.0","inline_ok":true,"mcp_get_code":{"code_sha256":"143a32689176be43"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}