{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UQ7R2ALZ4B5DNWAVYAZFT4E7BR","short_pith_number":"pith:UQ7R2ALZ","canonical_record":{"source":{"id":"2410.21676","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-29T02:54:06Z","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"title_canon_sha256":"a6809947abd89815d1dc066c5b170cae4c4f73f5e5a6ef41c87a7486bbfa8139","abstract_canon_sha256":"f98f13a2419d49928022d82e7680a148664675b0e09f57a37b306484a0c54dc1"},"schema_version":"1.0"},"canonical_sha256":"a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f","source":{"kind":"arxiv","id":"2410.21676","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21676","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21676v4","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21676","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"pith_short_12","alias_value":"UQ7R2ALZ4B5D","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"pith_short_16","alias_value":"UQ7R2ALZ4B5DNWAV","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"pith_short_8","alias_value":"UQ7R2ALZ","created_at":"2026-07-05T10:51:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UQ7R2ALZ4B5DNWAVYAZFT4E7BR","target":"record","payload":{"canonical_record":{"source":{"id":"2410.21676","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-29T02:54:06Z","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"title_canon_sha256":"a6809947abd89815d1dc066c5b170cae4c4f73f5e5a6ef41c87a7486bbfa8139","abstract_canon_sha256":"f98f13a2419d49928022d82e7680a148664675b0e09f57a37b306484a0c54dc1"},"schema_version":"1.0"},"canonical_sha256":"a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:27.588381Z","signature_b64":"sXEMtxOplg6ZZ2J4Dg/v8lezxMT0AS+69uGvZKySpfQTkTLQd4nFnpYutI3gthDW9OrUHFoYb7vcqtCc4LlRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f","last_reissued_at":"2026-07-05T10:51:27.587933Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:27.587933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.21676","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:51:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vupvvpmZ9UgArmwo9SKbikoKjRBtETsPXPSVxbvXmn/WhFIl8scWZFpSFO0bXq+m091soIq0TJIw/3mn9Uj4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:05:18.042244Z"},"content_sha256":"d9e1330855410f055ff55cb516bfc6986e85f88058d1e8f2b65be0838fc72bef","schema_version":"1.0","event_id":"sha256:d9e1330855410f055ff55cb516bfc6986e85f88058d1e8f2b65be0838fc72bef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UQ7R2ALZ4B5DNWAVYAZFT4E7BR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Does Critical Batch Size Scale in Pre-training?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Dean Foster, Depen Morwani, Difan Zou, Hanlin Zhang, Jingfeng Wu, Nikhil Vyas, Sham Kakade, Udaya Ghai","submitted_at":"2024-10-29T02:54:06Z","abstract_excerpt":"Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learnin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21676","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/2410.21676/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":"2026-07-05T10:51:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rdHQ1NWep7FIthSGL9KzeO7NynxAOew5gJLjo6y1r99Q9g5TDv0vF+Xw/CV8fHZ8xNHr95cickuXtppFy2aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:05:18.042625Z"},"content_sha256":"b5bcbe7cab8382a01fa52d5f29379a5f6f6eefef307c7bfede844ae74180910c","schema_version":"1.0","event_id":"sha256:b5bcbe7cab8382a01fa52d5f29379a5f6f6eefef307c7bfede844ae74180910c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR/bundle.json","state_url":"https://pith.science/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR/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":"2026-08-04T04:05:18Z","links":{"resolver":"https://pith.science/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR","bundle":"https://pith.science/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR/bundle.json","state":"https://pith.science/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQ7R2ALZ4B5DNWAVYAZFT4E7BR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UQ7R2ALZ4B5DNWAVYAZFT4E7BR","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":"f98f13a2419d49928022d82e7680a148664675b0e09f57a37b306484a0c54dc1","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-29T02:54:06Z","title_canon_sha256":"a6809947abd89815d1dc066c5b170cae4c4f73f5e5a6ef41c87a7486bbfa8139"},"schema_version":"1.0","source":{"id":"2410.21676","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.21676","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"arxiv_version","alias_value":"2410.21676v4","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21676","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"pith_short_12","alias_value":"UQ7R2ALZ4B5D","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"pith_short_16","alias_value":"UQ7R2ALZ4B5DNWAV","created_at":"2026-07-05T10:51:27Z"},{"alias_kind":"pith_short_8","alias_value":"UQ7R2ALZ","created_at":"2026-07-05T10:51:27Z"}],"graph_snapshots":[{"event_id":"sha256:b5bcbe7cab8382a01fa52d5f29379a5f6f6eefef307c7bfede844ae74180910c","target":"graph","created_at":"2026-07-05T10:51:27Z","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/2410.21676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learnin","authors_text":"Dean Foster, Depen Morwani, Difan Zou, Hanlin Zhang, Jingfeng Wu, Nikhil Vyas, Sham Kakade, Udaya Ghai","cross_cats":["cs.AI","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-29T02:54:06Z","title":"How Does Critical Batch Size Scale in Pre-training?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21676","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:d9e1330855410f055ff55cb516bfc6986e85f88058d1e8f2b65be0838fc72bef","target":"record","created_at":"2026-07-05T10:51:27Z","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":"f98f13a2419d49928022d82e7680a148664675b0e09f57a37b306484a0c54dc1","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-29T02:54:06Z","title_canon_sha256":"a6809947abd89815d1dc066c5b170cae4c4f73f5e5a6ef41c87a7486bbfa8139"},"schema_version":"1.0","source":{"id":"2410.21676","kind":"arxiv","version":4}},"canonical_sha256":"a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a43f1d0179e07a36d815c03259f09f0c5ff4d6bcf804a757de6bda1b534edc2f","first_computed_at":"2026-07-05T10:51:27.587933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:27.587933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sXEMtxOplg6ZZ2J4Dg/v8lezxMT0AS+69uGvZKySpfQTkTLQd4nFnpYutI3gthDW9OrUHFoYb7vcqtCc4LlRCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:27.588381Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.21676","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9e1330855410f055ff55cb516bfc6986e85f88058d1e8f2b65be0838fc72bef","sha256:b5bcbe7cab8382a01fa52d5f29379a5f6f6eefef307c7bfede844ae74180910c"],"state_sha256":"0f2ffeae39cdb5fee4156aa566a7595ac8e617c7e42653fb426ce1641fd5f57a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Po11sXhB+w6vPFvM9sBtkPn3A1v/qPMdQOMQoiGstRxGpk4kiOBLiqCbWdmOrY7RxyeLsx5BoEB5B5+87BkzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:05:18.045370Z","bundle_sha256":"aa085964cae27e6e2bedbe3685f417bcf888eaedf4fc6ce246b85e46a6259834"}}