{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HPZ2TYLUIIQHXHRG4FXIOJQXM6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"81483593c864179e7b4f2c20037d60301afd256c002c88ce94643f81ab0195c7","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-04T15:11:36Z","title_canon_sha256":"8d9580df019da6feb4704f296d90c73bb3b3f3d4ba7f32d36c8da0007da41cfc"},"schema_version":"1.0","source":{"id":"2605.02701","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.02701","created_at":"2026-06-24T01:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.02701v2","created_at":"2026-06-24T01:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.02701","created_at":"2026-06-24T01:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"HPZ2TYLUIIQH","created_at":"2026-06-24T01:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"HPZ2TYLUIIQHXHRG","created_at":"2026-06-24T01:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"HPZ2TYLU","created_at":"2026-06-24T01:15:03Z"}],"graph_snapshots":[{"event_id":"sha256:99801e28b65b7075e1fc438add5289b252d32ab3e0017921f908ca96dcffe6f8","target":"graph","created_at":"2026-06-24T01:15:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise."}],"snapshot_sha256":"96ebf94af9d54dbe16776cd7957191b4554cf98e65ef9e822448b55c7138c5e8"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"38d71a1d2f870b1a569ceea4324294941a6ab30a70be072ab9b090cfdf42ae43"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"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"}],"endpoint":"/pith/2605.02701/integrity.json","findings":[],"snapshot_sha256":"3e8a2d53656118744d217047f3ce22c3962004c09c874802f25de159473b9e82","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Davide Nobile, Philipp Grohs","cross_cats":["cs.LG","stat.ML"],"headline":"Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-04T15:11:36Z","title":"Robust and Fast Training via Per-Sample Clipping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.02701","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-08T17:46:07.678858Z","id":"b8af9bf2-6242-46d1-9268-5d799912f7e7","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Per-sample gradient clipping in SGD achieves optimal convergence rates for non-convex problems under heavy-tailed noise.","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.","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."}},"verdict_id":"b8af9bf2-6242-46d1-9268-5d799912f7e7"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:01718097db2c14d89b2d481cd9da4ad3761aa31249bb92560783df34095b8c22","target":"record","created_at":"2026-06-24T01:15:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"81483593c864179e7b4f2c20037d60301afd256c002c88ce94643f81ab0195c7","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-04T15:11:36Z","title_canon_sha256":"8d9580df019da6feb4704f296d90c73bb3b3f3d4ba7f32d36c8da0007da41cfc"},"schema_version":"1.0","source":{"id":"2605.02701","kind":"arxiv","version":2}},"canonical_sha256":"3bf3a9e17442207b9e26e16e87261767bc066827e81d9a2eca60b588c355868c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bf3a9e17442207b9e26e16e87261767bc066827e81d9a2eca60b588c355868c","first_computed_at":"2026-06-24T01:15:03.316448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:03.316448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdGEBgqT97Mvv46qMwoCP4PVclpiyRmeqcUfiypJ+ZDZb4U/dZpq3TPmATdJMH3KNGNfn1ssuDIr0ddb+9V9Cw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:03.316867Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.02701","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01718097db2c14d89b2d481cd9da4ad3761aa31249bb92560783df34095b8c22","sha256:99801e28b65b7075e1fc438add5289b252d32ab3e0017921f908ca96dcffe6f8"],"state_sha256":"e7179b9dece1889ed77fada57808340fc1fad3336fd636c1442e7a7e997f76e1"}