{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:KCMBLR2OLZM23AZXWGEHOJR4XB","short_pith_number":"pith:KCMBLR2O","schema_version":"1.0","canonical_sha256":"509815c74e5e59ad8337b18877263cb87735fa1929c800f4d05d529d6c3b1fe9","source":{"kind":"arxiv","id":"2304.04172","version":2},"attestation_state":"computed","paper":{"title":"$\\mu^2$-SGD: Stable Stochastic Optimization via a Double Momentum Mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Kfir Y. Levy, Tehila Dahan","submitted_at":"2023-04-09T06:18:34Z","abstract_excerpt":"We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of momentum. Then, we design an SGD-style algorithm as well as an accelerated version that make use of this new estimator, and demonstrate the robustness of these new approaches to the choice of the learning rate. Concretely, we show that these approaches obtain the optimal convergence rates for both noiseless and noisy case with the same choice of fixed learning rate."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2304.04172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-04-09T06:18:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"9f9e2e69b7c364e58deedfae03d03bdeb9913a617245c2fc96d3a50303e425f1","abstract_canon_sha256":"2089ccc9abe73bb893216a8e497213ade30e6bac1d312ba522e2cb0980e6767b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:17.546718Z","signature_b64":"rXzZE+Ae+Sf40mxtJgZAHLrU/QcMG4Xu4LzqpR3XV3XH4rgjsH2yMSKOJlgFLEquMFvm8PiWiVZP1UnvQ1jGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"509815c74e5e59ad8337b18877263cb87735fa1929c800f4d05d529d6c3b1fe9","last_reissued_at":"2026-07-05T10:24:17.545607Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:17.545607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mu^2$-SGD: Stable Stochastic Optimization via a Double Momentum Mechanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Kfir Y. Levy, Tehila Dahan","submitted_at":"2023-04-09T06:18:34Z","abstract_excerpt":"We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of momentum. Then, we design an SGD-style algorithm as well as an accelerated version that make use of this new estimator, and demonstrate the robustness of these new approaches to the choice of the learning rate. Concretely, we show that these approaches obtain the optimal convergence rates for both noiseless and noisy case with the same choice of fixed learning rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.04172","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/2304.04172/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2304.04172","created_at":"2026-07-05T10:24:17.545749+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.04172v2","created_at":"2026-07-05T10:24:17.545749+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.04172","created_at":"2026-07-05T10:24:17.545749+00:00"},{"alias_kind":"pith_short_12","alias_value":"KCMBLR2OLZM2","created_at":"2026-07-05T10:24:17.545749+00:00"},{"alias_kind":"pith_short_16","alias_value":"KCMBLR2OLZM23AZX","created_at":"2026-07-05T10:24:17.545749+00:00"},{"alias_kind":"pith_short_8","alias_value":"KCMBLR2O","created_at":"2026-07-05T10:24:17.545749+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.02563","citing_title":"Privacy-Preserving Federated Convex Optimization: Balancing Partial-Participation and Efficiency via Noise Cancellation","ref_index":28,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB","json":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB.json","graph_json":"https://pith.science/api/pith-number/KCMBLR2OLZM23AZXWGEHOJR4XB/graph.json","events_json":"https://pith.science/api/pith-number/KCMBLR2OLZM23AZXWGEHOJR4XB/events.json","paper":"https://pith.science/paper/KCMBLR2O"},"agent_actions":{"view_html":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB","download_json":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB.json","view_paper":"https://pith.science/paper/KCMBLR2O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.04172&json=true","fetch_graph":"https://pith.science/api/pith-number/KCMBLR2OLZM23AZXWGEHOJR4XB/graph.json","fetch_events":"https://pith.science/api/pith-number/KCMBLR2OLZM23AZXWGEHOJR4XB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB/action/storage_attestation","attest_author":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB/action/author_attestation","sign_citation":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB/action/citation_signature","submit_replication":"https://pith.science/pith/KCMBLR2OLZM23AZXWGEHOJR4XB/action/replication_record"}},"created_at":"2026-07-05T10:24:17.545749+00:00","updated_at":"2026-07-05T10:24:17.545749+00:00"}