{"paper":{"title":"Minor First, Major Last: A Depth-Induced Implicit Bias of Sharpness-Aware Minimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Chaewon Moon, Chulhee Yun, Dongkuk Si","submitted_at":"2026-03-09T12:09:14Z","abstract_excerpt":"We study the implicit bias of Sharpness-Aware Minimization (SAM) when training $L$-layer linear diagonal networks on linearly separable binary classification. For linear models ($L=1$), both $\\ell_\\infty$- and $\\ell_2$-SAM recover the $\\ell_2$ max-margin classifier, matching gradient descent (GD). However, for depth $L = 2$, the behavior changes drastically -- even on a single-example dataset. For $\\ell_\\infty$-SAM, the limit direction depends critically on initialization and can converge to $\\mathbf{0}$ or to any standard basis vector, in stark contrast to GD, whose limit aligns with the basi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.08290","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.08290/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}