{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HUHHKVCQL4VJOWXV6GLWP46HYC","short_pith_number":"pith:HUHHKVCQ","canonical_record":{"source":{"id":"1512.01708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-12-05T22:48:40Z","cross_cats_sorted":["cs.DC","math.OC","stat.ML"],"title_canon_sha256":"a2e949da0a2c79b170cd9d074790008231b4af6bf111fc9aba851951f21d89d0","abstract_canon_sha256":"2df9faf52fe010c9719e6766413ffd96075de10146cf6c1bc60de9a9b9a3efa7"},"schema_version":"1.0"},"canonical_sha256":"3d0e7554505f2a975af5f19767f3c7c08d6044ca100dd0e9736e81fb912083d9","source":{"kind":"arxiv","id":"1512.01708","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01708","created_at":"2026-05-18T00:46:53Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01708v2","created_at":"2026-05-18T00:46:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01708","created_at":"2026-05-18T00:46:53Z"},{"alias_kind":"pith_short_12","alias_value":"HUHHKVCQL4VJ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HUHHKVCQL4VJOWXV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HUHHKVCQ","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HUHHKVCQL4VJOWXV6GLWP46HYC","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01708","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-12-05T22:48:40Z","cross_cats_sorted":["cs.DC","math.OC","stat.ML"],"title_canon_sha256":"a2e949da0a2c79b170cd9d074790008231b4af6bf111fc9aba851951f21d89d0","abstract_canon_sha256":"2df9faf52fe010c9719e6766413ffd96075de10146cf6c1bc60de9a9b9a3efa7"},"schema_version":"1.0"},"canonical_sha256":"3d0e7554505f2a975af5f19767f3c7c08d6044ca100dd0e9736e81fb912083d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:53.746242Z","signature_b64":"rVdW6TRXtL7yoyKb1hNzFSvOrm7xNE/O1Fse2iM+BvqdOZDyFNt3D3Ux+OBp2gV9Hlib2f7pFnPr1jUVsh6RAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d0e7554505f2a975af5f19767f3c7c08d6044ca100dd0e9736e81fb912083d9","last_reissued_at":"2026-05-18T00:46:53.745760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:53.745760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01708","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":"2026-05-18T00:46:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8V+ntwfSwl7BxXUhSwhssGLbQpUv3/VNMPjkenNM6+mXur8axpEIbKqyovWPWPsd6AuJqQd2a5NbJYelYgRTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:02:11.930224Z"},"content_sha256":"57e1a7c60be65183419812ee77b71aba901d6629d606f6bd6d4f9dcc230860d8","schema_version":"1.0","event_id":"sha256:57e1a7c60be65183419812ee77b71aba901d6629d606f6bd6d4f9dcc230860d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HUHHKVCQL4VJOWXV6GLWP46HYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variance Reduction for Distributed Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Gavin Taylor, Soham De, Tom Goldstein","submitted_at":"2015-12-05T22:48:40Z","abstract_excerpt":"Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset) at the end of each epoch. This limits the use of VR methods in practical distributed settings. In this paper, we propose a variance reduction method, called VR-lite, that does not require full gradient computations or extra storage. We explore distributed synchronous and asynchr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01708","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":""},"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":"2026-05-18T00:46:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuLRJ1nbfxsFwHRPi8r15BPXxHKEqCZOhKeYK+uB/+zPODlJTm1TFnVUCAnAMPDKHrUF8FXmQ/o2498D2CjQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:02:11.930688Z"},"content_sha256":"c49b87bfc7efa4042bfa76322ac6a9257b6cdac09a1459ae7831bc3644ac6c87","schema_version":"1.0","event_id":"sha256:c49b87bfc7efa4042bfa76322ac6a9257b6cdac09a1459ae7831bc3644ac6c87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUHHKVCQL4VJOWXV6GLWP46HYC/bundle.json","state_url":"https://pith.science/pith/HUHHKVCQL4VJOWXV6GLWP46HYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUHHKVCQL4VJOWXV6GLWP46HYC/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":"2026-05-26T18:02:11Z","links":{"resolver":"https://pith.science/pith/HUHHKVCQL4VJOWXV6GLWP46HYC","bundle":"https://pith.science/pith/HUHHKVCQL4VJOWXV6GLWP46HYC/bundle.json","state":"https://pith.science/pith/HUHHKVCQL4VJOWXV6GLWP46HYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUHHKVCQL4VJOWXV6GLWP46HYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HUHHKVCQL4VJOWXV6GLWP46HYC","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":"2df9faf52fe010c9719e6766413ffd96075de10146cf6c1bc60de9a9b9a3efa7","cross_cats_sorted":["cs.DC","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-12-05T22:48:40Z","title_canon_sha256":"a2e949da0a2c79b170cd9d074790008231b4af6bf111fc9aba851951f21d89d0"},"schema_version":"1.0","source":{"id":"1512.01708","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01708","created_at":"2026-05-18T00:46:53Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01708v2","created_at":"2026-05-18T00:46:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01708","created_at":"2026-05-18T00:46:53Z"},{"alias_kind":"pith_short_12","alias_value":"HUHHKVCQL4VJ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HUHHKVCQL4VJOWXV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HUHHKVCQ","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:c49b87bfc7efa4042bfa76322ac6a9257b6cdac09a1459ae7831bc3644ac6c87","target":"graph","created_at":"2026-05-18T00:46:53Z","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"},"paper":{"abstract_excerpt":"Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset) at the end of each epoch. This limits the use of VR methods in practical distributed settings. In this paper, we propose a variance reduction method, called VR-lite, that does not require full gradient computations or extra storage. We explore distributed synchronous and asynchr","authors_text":"Gavin Taylor, Soham De, Tom Goldstein","cross_cats":["cs.DC","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-12-05T22:48:40Z","title":"Variance Reduction for Distributed Stochastic Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01708","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":"sha256:57e1a7c60be65183419812ee77b71aba901d6629d606f6bd6d4f9dcc230860d8","target":"record","created_at":"2026-05-18T00:46:53Z","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":"2df9faf52fe010c9719e6766413ffd96075de10146cf6c1bc60de9a9b9a3efa7","cross_cats_sorted":["cs.DC","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-12-05T22:48:40Z","title_canon_sha256":"a2e949da0a2c79b170cd9d074790008231b4af6bf111fc9aba851951f21d89d0"},"schema_version":"1.0","source":{"id":"1512.01708","kind":"arxiv","version":2}},"canonical_sha256":"3d0e7554505f2a975af5f19767f3c7c08d6044ca100dd0e9736e81fb912083d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d0e7554505f2a975af5f19767f3c7c08d6044ca100dd0e9736e81fb912083d9","first_computed_at":"2026-05-18T00:46:53.745760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:53.745760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVdW6TRXtL7yoyKb1hNzFSvOrm7xNE/O1Fse2iM+BvqdOZDyFNt3D3Ux+OBp2gV9Hlib2f7pFnPr1jUVsh6RAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:53.746242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01708","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57e1a7c60be65183419812ee77b71aba901d6629d606f6bd6d4f9dcc230860d8","sha256:c49b87bfc7efa4042bfa76322ac6a9257b6cdac09a1459ae7831bc3644ac6c87"],"state_sha256":"f8a4ee9405a8ceb23ab93df5696a9da0713b2c4ccc23cad19f6d0b1d12563001"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TZ6VnqW5ONfTpEwXZnnC+crfRr4zGsdGEkfjypFrwJel8LBvbqCgGKdk0KByXf6KvlZtLDq/w63MgE7d6U+bDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:02:11.933854Z","bundle_sha256":"63ab5076db421da9d3ef5c86b73636eab1321223b13d9c53346bac25c1f99aaa"}}