{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:UAEJ3ARZ3AM55YPURM77NSMXPT","short_pith_number":"pith:UAEJ3ARZ","schema_version":"1.0","canonical_sha256":"a0089d8239d819dee1f48b3ff6c9977cca30bc94baba55f0d3344fa8a348d215","source":{"kind":"arxiv","id":"2409.08770","version":4},"attestation_state":"computed","paper":{"title":"Increasing Both Batch Size and Learning Rate Accelerates Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Hideaki Iiduka, Hikaru Umeda","submitted_at":"2024-09-13T12:24:12Z","abstract_excerpt":"The performance of mini-batch stochastic gradient descent (SGD) strongly depends on setting the batch size and learning rate to minimize the empirical loss in training the deep neural network. In this paper, we present theoretical analyses of mini-batch SGD with four schedulers: (i) constant batch size and decaying learning rate scheduler, (ii) increasing batch size and decaying learning rate scheduler, (iii) increasing batch size and increasing learning rate scheduler, and (iv) increasing batch size and warm-up decaying learning rate scheduler. We show that mini-batch SGD using scheduler (i) "},"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":"2409.08770","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-13T12:24:12Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"765b1398369a6a4f0a3310734847eb9d93f40108f307da55e3d6c730fd8ac29b","abstract_canon_sha256":"4828d6cc03e2945268dff16d864a3bb71c7f00f6ca1494cd9660fe4a8b234bcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:05.441964Z","signature_b64":"EIR901G15lG0uoUppc8mtlk87sRNM6qh6wEBPtMPIRgFHbXH/VM542BpHVNx3ATXKF38XM5+JbhlMgMtGOdxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0089d8239d819dee1f48b3ff6c9977cca30bc94baba55f0d3344fa8a348d215","last_reissued_at":"2026-07-05T10:14:05.441483Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:05.441483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Increasing Both Batch Size and Learning Rate Accelerates Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Hideaki Iiduka, Hikaru Umeda","submitted_at":"2024-09-13T12:24:12Z","abstract_excerpt":"The performance of mini-batch stochastic gradient descent (SGD) strongly depends on setting the batch size and learning rate to minimize the empirical loss in training the deep neural network. In this paper, we present theoretical analyses of mini-batch SGD with four schedulers: (i) constant batch size and decaying learning rate scheduler, (ii) increasing batch size and decaying learning rate scheduler, (iii) increasing batch size and increasing learning rate scheduler, and (iv) increasing batch size and warm-up decaying learning rate scheduler. We show that mini-batch SGD using scheduler (i) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08770","kind":"arxiv","version":4},"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/2409.08770/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":"2409.08770","created_at":"2026-07-05T10:14:05.441539+00:00"},{"alias_kind":"arxiv_version","alias_value":"2409.08770v4","created_at":"2026-07-05T10:14:05.441539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.08770","created_at":"2026-07-05T10:14:05.441539+00:00"},{"alias_kind":"pith_short_12","alias_value":"UAEJ3ARZ3AM5","created_at":"2026-07-05T10:14:05.441539+00:00"},{"alias_kind":"pith_short_16","alias_value":"UAEJ3ARZ3AM55YPU","created_at":"2026-07-05T10:14:05.441539+00:00"},{"alias_kind":"pith_short_8","alias_value":"UAEJ3ARZ","created_at":"2026-07-05T10:14:05.441539+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.06350","citing_title":"Convergence of Riemannian Stochastic Gradient Descents: Varying Batch Sizes And Nonstandard Batch Forming","ref_index":22,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT","json":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT.json","graph_json":"https://pith.science/api/pith-number/UAEJ3ARZ3AM55YPURM77NSMXPT/graph.json","events_json":"https://pith.science/api/pith-number/UAEJ3ARZ3AM55YPURM77NSMXPT/events.json","paper":"https://pith.science/paper/UAEJ3ARZ"},"agent_actions":{"view_html":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT","download_json":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT.json","view_paper":"https://pith.science/paper/UAEJ3ARZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2409.08770&json=true","fetch_graph":"https://pith.science/api/pith-number/UAEJ3ARZ3AM55YPURM77NSMXPT/graph.json","fetch_events":"https://pith.science/api/pith-number/UAEJ3ARZ3AM55YPURM77NSMXPT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT/action/storage_attestation","attest_author":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT/action/author_attestation","sign_citation":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT/action/citation_signature","submit_replication":"https://pith.science/pith/UAEJ3ARZ3AM55YPURM77NSMXPT/action/replication_record"}},"created_at":"2026-07-05T10:14:05.441539+00:00","updated_at":"2026-07-05T10:14:05.441539+00:00"}