{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7UPZMEOA6OEWXEMGUMKX7TW54E","short_pith_number":"pith:7UPZMEOA","schema_version":"1.0","canonical_sha256":"fd1f9611c0f3896b9186a3157fcedde11539203d33285a77188f4f3cbc36d6f4","source":{"kind":"arxiv","id":"2308.06775","version":1},"attestation_state":"computed","paper":{"title":"Stochastic Gradient Descent in the Viewpoint of Graduated Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Da Li, Jingjing Wu, Qingrun Zhang","submitted_at":"2023-08-13T14:02:35Z","abstract_excerpt":"Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex optimization problems. Instead of the actual optimization problem, a series of smoothed optimization problems that can be achieved in various ways are solved in the graduated optimization approach. In this work, a formal formulation of the graduated optimization is provided based on the nonnegative approximate identity, which generalizes the idea of Gaussian "},"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":"2308.06775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-08-13T14:02:35Z","cross_cats_sorted":[],"title_canon_sha256":"2eb5f3f6f36f8d5993ddfa4e181766fadce9e02bede56805079a1052e73e47bb","abstract_canon_sha256":"2af86bab38a1b5099ab89f6b5e0172d2a41ca425be4b6495284b0933ac86aa80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:44.942280Z","signature_b64":"RYGdmSXefx3yTXRLwr//9XV5B7xw7xlByUKDXT8hyUBAEm8e/rsi/AS8a+1E8zxw5Rdn+Kv8IW+GrOiOnmbZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd1f9611c0f3896b9186a3157fcedde11539203d33285a77188f4f3cbc36d6f4","last_reissued_at":"2026-07-05T06:40:44.941925Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:44.941925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Gradient Descent in the Viewpoint of Graduated Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Da Li, Jingjing Wu, Qingrun Zhang","submitted_at":"2023-08-13T14:02:35Z","abstract_excerpt":"Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex optimization problems. Instead of the actual optimization problem, a series of smoothed optimization problems that can be achieved in various ways are solved in the graduated optimization approach. In this work, a formal formulation of the graduated optimization is provided based on the nonnegative approximate identity, which generalizes the idea of Gaussian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.06775","kind":"arxiv","version":1},"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/2308.06775/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":"2308.06775","created_at":"2026-07-05T06:40:44.941973+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.06775v1","created_at":"2026-07-05T06:40:44.941973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.06775","created_at":"2026-07-05T06:40:44.941973+00:00"},{"alias_kind":"pith_short_12","alias_value":"7UPZMEOA6OEW","created_at":"2026-07-05T06:40:44.941973+00:00"},{"alias_kind":"pith_short_16","alias_value":"7UPZMEOA6OEWXEMG","created_at":"2026-07-05T06:40:44.941973+00:00"},{"alias_kind":"pith_short_8","alias_value":"7UPZMEOA","created_at":"2026-07-05T06:40:44.941973+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.11501","citing_title":"Explicit and Implicit Graduated Optimization in Deep Neural Networks","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E","json":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E.json","graph_json":"https://pith.science/api/pith-number/7UPZMEOA6OEWXEMGUMKX7TW54E/graph.json","events_json":"https://pith.science/api/pith-number/7UPZMEOA6OEWXEMGUMKX7TW54E/events.json","paper":"https://pith.science/paper/7UPZMEOA"},"agent_actions":{"view_html":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E","download_json":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E.json","view_paper":"https://pith.science/paper/7UPZMEOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.06775&json=true","fetch_graph":"https://pith.science/api/pith-number/7UPZMEOA6OEWXEMGUMKX7TW54E/graph.json","fetch_events":"https://pith.science/api/pith-number/7UPZMEOA6OEWXEMGUMKX7TW54E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E/action/storage_attestation","attest_author":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E/action/author_attestation","sign_citation":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E/action/citation_signature","submit_replication":"https://pith.science/pith/7UPZMEOA6OEWXEMGUMKX7TW54E/action/replication_record"}},"created_at":"2026-07-05T06:40:44.941973+00:00","updated_at":"2026-07-05T06:40:44.941973+00:00"}