{"paper":{"title":"Robust and Fast Training via Per-Sample Clipping","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise.","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Davide Nobile, Philipp Grohs","submitted_at":"2026-05-04T15:11:36Z","abstract_excerpt":"We propose a robust gradient estimator based on per-sample gradient clipping and analyze its properties both theoretically and empirically. We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal in-expectation convergence rates for non-convex optimization problems under heavy-tailed gradient noise. Moreover, we establish high-probability convergence guarantees that match the in-expectation rates up to polylogarithmic factors in the failure probability. We complement our theoretical results with multiple numerical experiments. In particular, we demonstrate tha"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal in-expectation convergence rates for non-convex optimization problems under heavy-tailed gradient noise. Moreover, we establish high-probability convergence guarantees that match the in-expectation rates up to polylogarithmic factors in the failure probability.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis requires that gradient noise follows a heavy-tailed distribution with specific moment bounds; if real gradients during training do not satisfy these tail conditions, the claimed optimal rates may not apply.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Per-sample clipped SGD achieves optimal in-expectation and high-probability convergence rates for non-convex optimization under heavy-tailed gradient noise while outperforming standard SGD and batch clipping on CIFAR-100.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"96ebf94af9d54dbe16776cd7957191b4554cf98e65ef9e822448b55c7138c5e8"},"source":{"id":"2605.02701","kind":"arxiv","version":2},"verdict":{"id":"b8af9bf2-6242-46d1-9268-5d799912f7e7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T17:46:07.678858Z","strongest_claim":"We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal in-expectation convergence rates for non-convex optimization problems under heavy-tailed gradient noise. Moreover, we establish high-probability convergence guarantees that match the in-expectation rates up to polylogarithmic factors in the failure probability.","one_line_summary":"Per-sample clipped SGD achieves optimal in-expectation and high-probability convergence rates for non-convex optimization under heavy-tailed gradient noise while outperforming standard SGD and batch clipping on CIFAR-100.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis requires that gradient noise follows a heavy-tailed distribution with specific moment bounds; if real gradients during training do not satisfy these tail conditions, the claimed optimal rates may not apply.","pith_extraction_headline":"Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02701/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T15:35:00.150278Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T02:31:22.692424Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T16:05:45.875652Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"3e8a2d53656118744d217047f3ce22c3962004c09c874802f25de159473b9e82"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"38d71a1d2f870b1a569ceea4324294941a6ab30a70be072ab9b090cfdf42ae43"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}