{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:YMDGPZLLFCQNGQ7L74RDAWMF3T","short_pith_number":"pith:YMDGPZLL","canonical_record":{"source":{"id":"2309.06497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-12T18:11:10Z","cross_cats_sorted":["cs.DC","cs.MS","math.OC"],"title_canon_sha256":"618edec4cb070839a2daf4bbb58585343bdabb096e6ffee933dad5be1491c7af","abstract_canon_sha256":"59a96b33a0aed909bc606f2d8151b09295c29b45f0323a5319116d29d9606404"},"schema_version":"1.0"},"canonical_sha256":"c30667e56b28a0d343ebff22305985dcd5b09a1775a65219c1fadbe278819e51","source":{"kind":"arxiv","id":"2309.06497","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.06497","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"arxiv_version","alias_value":"2309.06497v1","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.06497","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"pith_short_12","alias_value":"YMDGPZLLFCQN","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"pith_short_16","alias_value":"YMDGPZLLFCQNGQ7L","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"pith_short_8","alias_value":"YMDGPZLL","created_at":"2026-07-05T06:50:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:YMDGPZLLFCQNGQ7L74RDAWMF3T","target":"record","payload":{"canonical_record":{"source":{"id":"2309.06497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-12T18:11:10Z","cross_cats_sorted":["cs.DC","cs.MS","math.OC"],"title_canon_sha256":"618edec4cb070839a2daf4bbb58585343bdabb096e6ffee933dad5be1491c7af","abstract_canon_sha256":"59a96b33a0aed909bc606f2d8151b09295c29b45f0323a5319116d29d9606404"},"schema_version":"1.0"},"canonical_sha256":"c30667e56b28a0d343ebff22305985dcd5b09a1775a65219c1fadbe278819e51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:50:18.476696Z","signature_b64":"7B3voIKvJnWp6cyyeFRGWx9LDigl9d81ZZ4A59LUeuXH0VRqBfOSThz7bGHdn1djymWpvmvYmwIxqb34VBg7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c30667e56b28a0d343ebff22305985dcd5b09a1775a65219c1fadbe278819e51","last_reissued_at":"2026-07-05T06:50:18.476190Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:50:18.476190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.06497","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:50:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OjZqC8i1DRWc7XvnytcXOinfRXxxfjmMMFdprtSiJXGhszYxPx3ELKBDmobZIzpN9A1lmnulvih3UVKPIMaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T07:41:29.021900Z"},"content_sha256":"7a609f888c89df0f113e643d7f53c32301bd8b64273d0de8f4ae42be310dd2ae","schema_version":"1.0","event_id":"sha256:7a609f888c89df0f113e643d7f53c32301bd8b64273d0de8f4ae42be310dd2ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:YMDGPZLLFCQNGQ7L74RDAWMF3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.MS","math.OC"],"primary_cat":"cs.LG","authors_text":"Dheevatsa Mudigere, Hao-Jun Michael Shi, Jose Gallego-Posada, Kaushik Rangadurai, Michael Rabbat, Shintaro Iwasaki, Tsung-Hsien Lee, Zhijing Li","submitted_at":"2023-09-12T18:11:10Z","abstract_excerpt":"Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance optimizations that our implementation leverages to train deep networks at-scale in PyTorch. Our implementation enables fast multi-GPU distributed data-parallel training by distributing the memory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.06497","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/2309.06497/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":"2026-07-05T06:50:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gi9OQQ1muOpPmSxIST8nao21FZiIUMD9jlVlpmcR+Oorqe66ufcpnJHMOVic5/618SmWC1lKvYACGcSEbNcbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-11T07:41:29.022273Z"},"content_sha256":"490a4bdec2d349ed5455dc4bfebe66fc171f56a1c662b52d2c426eed36e6e7ec","schema_version":"1.0","event_id":"sha256:490a4bdec2d349ed5455dc4bfebe66fc171f56a1c662b52d2c426eed36e6e7ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T/bundle.json","state_url":"https://pith.science/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T/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":"2026-07-11T07:41:29Z","links":{"resolver":"https://pith.science/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T","bundle":"https://pith.science/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T/bundle.json","state":"https://pith.science/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMDGPZLLFCQNGQ7L74RDAWMF3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YMDGPZLLFCQNGQ7L74RDAWMF3T","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":"59a96b33a0aed909bc606f2d8151b09295c29b45f0323a5319116d29d9606404","cross_cats_sorted":["cs.DC","cs.MS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-12T18:11:10Z","title_canon_sha256":"618edec4cb070839a2daf4bbb58585343bdabb096e6ffee933dad5be1491c7af"},"schema_version":"1.0","source":{"id":"2309.06497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.06497","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"arxiv_version","alias_value":"2309.06497v1","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.06497","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"pith_short_12","alias_value":"YMDGPZLLFCQN","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"pith_short_16","alias_value":"YMDGPZLLFCQNGQ7L","created_at":"2026-07-05T06:50:18Z"},{"alias_kind":"pith_short_8","alias_value":"YMDGPZLL","created_at":"2026-07-05T06:50:18Z"}],"graph_snapshots":[{"event_id":"sha256:490a4bdec2d349ed5455dc4bfebe66fc171f56a1c662b52d2c426eed36e6e7ec","target":"graph","created_at":"2026-07-05T06:50:18Z","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/2309.06497/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Shampoo is an online and stochastic optimization algorithm belonging to the AdaGrad family of methods for training neural networks. It constructs a block-diagonal preconditioner where each block consists of a coarse Kronecker product approximation to full-matrix AdaGrad for each parameter of the neural network. In this work, we provide a complete description of the algorithm as well as the performance optimizations that our implementation leverages to train deep networks at-scale in PyTorch. Our implementation enables fast multi-GPU distributed data-parallel training by distributing the memory","authors_text":"Dheevatsa Mudigere, Hao-Jun Michael Shi, Jose Gallego-Posada, Kaushik Rangadurai, Michael Rabbat, Shintaro Iwasaki, Tsung-Hsien Lee, Zhijing Li","cross_cats":["cs.DC","cs.MS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-12T18:11:10Z","title":"A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.06497","kind":"arxiv","version":1},"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":"sha256:7a609f888c89df0f113e643d7f53c32301bd8b64273d0de8f4ae42be310dd2ae","target":"record","created_at":"2026-07-05T06:50:18Z","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":"59a96b33a0aed909bc606f2d8151b09295c29b45f0323a5319116d29d9606404","cross_cats_sorted":["cs.DC","cs.MS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-09-12T18:11:10Z","title_canon_sha256":"618edec4cb070839a2daf4bbb58585343bdabb096e6ffee933dad5be1491c7af"},"schema_version":"1.0","source":{"id":"2309.06497","kind":"arxiv","version":1}},"canonical_sha256":"c30667e56b28a0d343ebff22305985dcd5b09a1775a65219c1fadbe278819e51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c30667e56b28a0d343ebff22305985dcd5b09a1775a65219c1fadbe278819e51","first_computed_at":"2026-07-05T06:50:18.476190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:50:18.476190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7B3voIKvJnWp6cyyeFRGWx9LDigl9d81ZZ4A59LUeuXH0VRqBfOSThz7bGHdn1djymWpvmvYmwIxqb34VBg7AA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:50:18.476696Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.06497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a609f888c89df0f113e643d7f53c32301bd8b64273d0de8f4ae42be310dd2ae","sha256:490a4bdec2d349ed5455dc4bfebe66fc171f56a1c662b52d2c426eed36e6e7ec"],"state_sha256":"670fbf431398c541024c9644942820f64223780159ead1a092e8c2c40a291dbd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X7RJMD/FpLro4/NCGgUlllfHqkD0uYikhDBJfEYzO+QW8xZMaCIAtTiLC+oO3zXRwQFXsvgVD5oIPGlslRS0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-11T07:41:29.024398Z","bundle_sha256":"1ac7e858e199ce8fed8bb1f1fa9230b987f153f7cabe19e381bc4d8659f53890"}}