{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:X3R4246LZHXBRKDGXVXQMOTAAR","short_pith_number":"pith:X3R4246L","schema_version":"1.0","canonical_sha256":"bee3cd73cbc9ee18a866bd6f063a600444d901964bcd31f4f89ebd08e4495173","source":{"kind":"arxiv","id":"2412.11341","version":1},"attestation_state":"computed","paper":{"title":"Coupling-based Convergence Diagnostic and Stepsize Scheme for Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Qiaomin Xie, Xiang Li","submitted_at":"2024-12-15T23:50:23Z","abstract_excerpt":"The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient phase. However, when reaching stationarity, the iterates oscillate around the optimum without making further progress. In this paper, we study the convergence diagnostics for SGD with constant stepsize, aiming to develop an effective dynamic stepsize scheme. We propose a novel coupling-based convergence diagnostic procedure, which monitors the distance of two co"},"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":"2412.11341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-15T23:50:23Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"c0d950b4c8aea71bd9f4a964170fcbfd3b74b3673661528c135eada3f56fb133","abstract_canon_sha256":"18d4fa4cff94bafe246cbb163b76c659b08b30ddc6ef6a8628ac5d26305d33e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:21.399502Z","signature_b64":"ijka9koOwUzh93FjOUbGuQ+PJt4yj5APbr3w8SCEu38fTV9cc8leJsufkFfm/rrK4LWhhN+qEUsh6s4RH+R2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bee3cd73cbc9ee18a866bd6f063a600444d901964bcd31f4f89ebd08e4495173","last_reissued_at":"2026-06-30T01:17:21.398865Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:21.398865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coupling-based Convergence Diagnostic and Stepsize Scheme for Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Qiaomin Xie, Xiang Li","submitted_at":"2024-12-15T23:50:23Z","abstract_excerpt":"The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient phase. However, when reaching stationarity, the iterates oscillate around the optimum without making further progress. In this paper, we study the convergence diagnostics for SGD with constant stepsize, aiming to develop an effective dynamic stepsize scheme. We propose a novel coupling-based convergence diagnostic procedure, which monitors the distance of two co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11341","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/2412.11341/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":"2412.11341","created_at":"2026-06-30T01:17:21.398948+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.11341v1","created_at":"2026-06-30T01:17:21.398948+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11341","created_at":"2026-06-30T01:17:21.398948+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3R4246LZHXB","created_at":"2026-06-30T01:17:21.398948+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3R4246LZHXBRKDG","created_at":"2026-06-30T01:17:21.398948+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3R4246L","created_at":"2026-06-30T01:17:21.398948+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR","json":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR.json","graph_json":"https://pith.science/api/pith-number/X3R4246LZHXBRKDGXVXQMOTAAR/graph.json","events_json":"https://pith.science/api/pith-number/X3R4246LZHXBRKDGXVXQMOTAAR/events.json","paper":"https://pith.science/paper/X3R4246L"},"agent_actions":{"view_html":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR","download_json":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR.json","view_paper":"https://pith.science/paper/X3R4246L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.11341&json=true","fetch_graph":"https://pith.science/api/pith-number/X3R4246LZHXBRKDGXVXQMOTAAR/graph.json","fetch_events":"https://pith.science/api/pith-number/X3R4246LZHXBRKDGXVXQMOTAAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR/action/storage_attestation","attest_author":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR/action/author_attestation","sign_citation":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR/action/citation_signature","submit_replication":"https://pith.science/pith/X3R4246LZHXBRKDGXVXQMOTAAR/action/replication_record"}},"created_at":"2026-06-30T01:17:21.398948+00:00","updated_at":"2026-06-30T01:17:21.398948+00:00"}