{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GKQRL3ZICVGMELX2GRGBT6RS3F","short_pith_number":"pith:GKQRL3ZI","canonical_record":{"source":{"id":"2303.01215","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-02T12:56:52Z","cross_cats_sorted":[],"title_canon_sha256":"41efef0d453fa96f694e3b97dc90a776cd097d2f5145514022f2b66f67efb113","abstract_canon_sha256":"c81d660c6af4d3e7861fda4dc40d36909f491c6e6765eb7bb1e0cc7751323fb5"},"schema_version":"1.0"},"canonical_sha256":"32a115ef28154cc22efa344c19fa32d94605a87068cd658dd01d136ceff833d8","source":{"kind":"arxiv","id":"2303.01215","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01215","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01215v2","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01215","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"GKQRL3ZICVGM","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"GKQRL3ZICVGMELX2","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"GKQRL3ZI","created_at":"2026-07-05T05:49:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GKQRL3ZICVGMELX2GRGBT6RS3F","target":"record","payload":{"canonical_record":{"source":{"id":"2303.01215","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-02T12:56:52Z","cross_cats_sorted":[],"title_canon_sha256":"41efef0d453fa96f694e3b97dc90a776cd097d2f5145514022f2b66f67efb113","abstract_canon_sha256":"c81d660c6af4d3e7861fda4dc40d36909f491c6e6765eb7bb1e0cc7751323fb5"},"schema_version":"1.0"},"canonical_sha256":"32a115ef28154cc22efa344c19fa32d94605a87068cd658dd01d136ceff833d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:49:33.493597Z","signature_b64":"cQkDNLB7Mdu7QJEKqyUyDoHwlAwVMEMyuKPoMZHz97NIACG4+7tUA3Z7DKR9s/yBpHF2DfUHtwNdU/2J8zQDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32a115ef28154cc22efa344c19fa32d94605a87068cd658dd01d136ceff833d8","last_reissued_at":"2026-07-05T05:49:33.493117Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:49:33.493117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.01215","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FJ+NdeiS5GKjt0ExPb7suIge4CgrMrS2ubY+hzYRogM38HpcgqWfhMmLMVbZyTF5L8WXV6CCsdjHkBKNjBK4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:10:04.371112Z"},"content_sha256":"539fd9bbf2e8d2ad43c9d6d5e216124b7eaba1ff8434063e855570aa48e138fa","schema_version":"1.0","event_id":"sha256:539fd9bbf2e8d2ad43c9d6d5e216124b7eaba1ff8434063e855570aa48e138fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GKQRL3ZICVGMELX2GRGBT6RS3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Why (and When) does Local SGD Generalize Better than SGD?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Kaifeng Lyu, Longbo Huang, Sanjeev Arora, Xinran Gu","submitted_at":"2023-03-02T12:56:52Z","abstract_excerpt":"Local SGD is a communication-efficient variant of SGD for large-scale training, where multiple GPUs perform SGD independently and average the model parameters periodically. It has been recently observed that Local SGD can not only achieve the design goal of reducing the communication overhead but also lead to higher test accuracy than the corresponding SGD baseline (Lin et al., 2020b), though the training regimes for this to happen are still in debate (Ortiz et al., 2021). This paper aims to understand why (and when) Local SGD generalizes better based on Stochastic Differential Equation (SDE) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01215","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/2303.01215/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DJKEuNxS//SsLLEtjwQCs8m+h/wIk+/Hxiu8JQ+NscfcAY7VjjdUYOLDmtZUlYiKYgRfIy2vmNO6Jk5OI/BDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:10:04.371996Z"},"content_sha256":"de0fbdbd3d37561857d8313f1aa9c107a7e1fdb7c2ed08afb773829417fe1e4f","schema_version":"1.0","event_id":"sha256:de0fbdbd3d37561857d8313f1aa9c107a7e1fdb7c2ed08afb773829417fe1e4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKQRL3ZICVGMELX2GRGBT6RS3F/bundle.json","state_url":"https://pith.science/pith/GKQRL3ZICVGMELX2GRGBT6RS3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKQRL3ZICVGMELX2GRGBT6RS3F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T03:10:04Z","links":{"resolver":"https://pith.science/pith/GKQRL3ZICVGMELX2GRGBT6RS3F","bundle":"https://pith.science/pith/GKQRL3ZICVGMELX2GRGBT6RS3F/bundle.json","state":"https://pith.science/pith/GKQRL3ZICVGMELX2GRGBT6RS3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKQRL3ZICVGMELX2GRGBT6RS3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GKQRL3ZICVGMELX2GRGBT6RS3F","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":"c81d660c6af4d3e7861fda4dc40d36909f491c6e6765eb7bb1e0cc7751323fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-02T12:56:52Z","title_canon_sha256":"41efef0d453fa96f694e3b97dc90a776cd097d2f5145514022f2b66f67efb113"},"schema_version":"1.0","source":{"id":"2303.01215","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01215","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01215v2","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01215","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"GKQRL3ZICVGM","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"GKQRL3ZICVGMELX2","created_at":"2026-07-05T05:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"GKQRL3ZI","created_at":"2026-07-05T05:49:33Z"}],"graph_snapshots":[{"event_id":"sha256:de0fbdbd3d37561857d8313f1aa9c107a7e1fdb7c2ed08afb773829417fe1e4f","target":"graph","created_at":"2026-07-05T05:49:33Z","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/2303.01215/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Local SGD is a communication-efficient variant of SGD for large-scale training, where multiple GPUs perform SGD independently and average the model parameters periodically. It has been recently observed that Local SGD can not only achieve the design goal of reducing the communication overhead but also lead to higher test accuracy than the corresponding SGD baseline (Lin et al., 2020b), though the training regimes for this to happen are still in debate (Ortiz et al., 2021). This paper aims to understand why (and when) Local SGD generalizes better based on Stochastic Differential Equation (SDE) ","authors_text":"Kaifeng Lyu, Longbo Huang, Sanjeev Arora, Xinran Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-02T12:56:52Z","title":"Why (and When) does Local SGD Generalize Better than SGD?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01215","kind":"arxiv","version":2},"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":"sha256:539fd9bbf2e8d2ad43c9d6d5e216124b7eaba1ff8434063e855570aa48e138fa","target":"record","created_at":"2026-07-05T05:49:33Z","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":"c81d660c6af4d3e7861fda4dc40d36909f491c6e6765eb7bb1e0cc7751323fb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-02T12:56:52Z","title_canon_sha256":"41efef0d453fa96f694e3b97dc90a776cd097d2f5145514022f2b66f67efb113"},"schema_version":"1.0","source":{"id":"2303.01215","kind":"arxiv","version":2}},"canonical_sha256":"32a115ef28154cc22efa344c19fa32d94605a87068cd658dd01d136ceff833d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32a115ef28154cc22efa344c19fa32d94605a87068cd658dd01d136ceff833d8","first_computed_at":"2026-07-05T05:49:33.493117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:49:33.493117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQkDNLB7Mdu7QJEKqyUyDoHwlAwVMEMyuKPoMZHz97NIACG4+7tUA3Z7DKR9s/yBpHF2DfUHtwNdU/2J8zQDBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:49:33.493597Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.01215","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:539fd9bbf2e8d2ad43c9d6d5e216124b7eaba1ff8434063e855570aa48e138fa","sha256:de0fbdbd3d37561857d8313f1aa9c107a7e1fdb7c2ed08afb773829417fe1e4f"],"state_sha256":"c70f8515fe542688941f6b1b70691ce63a13326232fec6e0d93b7cbfe3d06c86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b7+SgCGqVNzGpzf2XRw50/MIalnIPvs4Sj/oS30kFaf2TAoKBLcNNkGKuzQsveE/ad3nNzK/oHeCGGkjLVcYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T03:10:04.377180Z","bundle_sha256":"cc0ff16b5df173ebdfb4e0c9a9e1727acc9e0a24dddc4e0a14af36b64a28246c"}}