{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WNZRLVQFHM25OZEJ76VR6XNS5S","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":"30c76313c7d8151de2e789436e01bf532447284417a11fb66f137ca0cbd75959","cross_cats_sorted":["cond-mat.dis-nn","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-09-19T15:23:07Z","title_canon_sha256":"6e11c5653c3cad823a7fa4924bbe26962af4adc6fccfe62f6ebbe3a8ccda657b"},"schema_version":"1.0","source":{"id":"2309.10688","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.10688","created_at":"2026-07-05T07:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"2309.10688v4","created_at":"2026-07-05T07:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.10688","created_at":"2026-07-05T07:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"WNZRLVQFHM25","created_at":"2026-07-05T07:50:03Z"},{"alias_kind":"pith_short_16","alias_value":"WNZRLVQFHM25OZEJ","created_at":"2026-07-05T07:50:03Z"},{"alias_kind":"pith_short_8","alias_value":"WNZRLVQF","created_at":"2026-07-05T07:50:03Z"}],"graph_snapshots":[{"event_id":"sha256:8122511dd7f939848b7d4a861eb6aea931a61fffa561140800a67292b990b077","target":"graph","created_at":"2026-07-05T07:50:03Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.10688/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modern deep networks are trained with stochastic gradient descent (SGD) whose key hyperparameters are the number of data considered at each step or batch size $B$, and the step size or learning rate $\\eta$. For small $B$ and large $\\eta$, SGD corresponds to a stochastic evolution of the parameters, whose noise amplitude is governed by the ''temperature'' $T\\equiv \\eta/B$. Yet this description is observed to break down for sufficiently large batches $B\\geq B^*$, or simplifies to gradient descent (GD) when the temperature is sufficiently small. Understanding where these cross-overs take place re","authors_text":"Antonio Sclocchi, Matthieu Wyart","cross_cats":["cond-mat.dis-nn","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-09-19T15:23:07Z","title":"On the different regimes of Stochastic Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.10688","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:522fd72966a400e7bfc71b418cb0c95bf95aa77f9d7b66f40d352c3a54542e91","target":"record","created_at":"2026-07-05T07:50:03Z","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":"30c76313c7d8151de2e789436e01bf532447284417a11fb66f137ca0cbd75959","cross_cats_sorted":["cond-mat.dis-nn","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-09-19T15:23:07Z","title_canon_sha256":"6e11c5653c3cad823a7fa4924bbe26962af4adc6fccfe62f6ebbe3a8ccda657b"},"schema_version":"1.0","source":{"id":"2309.10688","kind":"arxiv","version":4}},"canonical_sha256":"b37315d6053b35d76489ffab1f5db2eca2305a81d227d4e02dbd0d1a7719268c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b37315d6053b35d76489ffab1f5db2eca2305a81d227d4e02dbd0d1a7719268c","first_computed_at":"2026-07-05T07:50:03.438528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:50:03.438528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cCaZFJ4iOqhwUyKrCoC/GHR8PiY6txyb20rZXtjicjr9mcOLYp+CxVzlMfuebulwJLdam1ZCLimJyKQlOtUUAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:50:03.439004Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.10688","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:522fd72966a400e7bfc71b418cb0c95bf95aa77f9d7b66f40d352c3a54542e91","sha256:8122511dd7f939848b7d4a861eb6aea931a61fffa561140800a67292b990b077"],"state_sha256":"0c3eedb0b26e0a86da7e78775b60a9a445134378da1bb4640498b54526a004ca"}