{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TKWKBMET7S2KQQDQCGT4P7ZNM2","short_pith_number":"pith:TKWKBMET","canonical_record":{"source":{"id":"1709.08728","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-25T21:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"f487fcb360f07d72d80176a814adf8d7a0b006dd6826401ce62dc6956ca15ce0","abstract_canon_sha256":"2e5e7dddf96528feed182edc8bc0a72bbc6d58412014363b61927d0a0c14e753"},"schema_version":"1.0"},"canonical_sha256":"9aaca0b093fcb4a8407011a7c7ff2d669a576743298536921ea78ebe187402d7","source":{"kind":"arxiv","id":"1709.08728","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08728","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08728v4","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08728","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"TKWKBMET7S2K","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TKWKBMET7S2KQQDQ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TKWKBMET","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TKWKBMET7S2KQQDQCGT4P7ZNM2","target":"record","payload":{"canonical_record":{"source":{"id":"1709.08728","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-25T21:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"f487fcb360f07d72d80176a814adf8d7a0b006dd6826401ce62dc6956ca15ce0","abstract_canon_sha256":"2e5e7dddf96528feed182edc8bc0a72bbc6d58412014363b61927d0a0c14e753"},"schema_version":"1.0"},"canonical_sha256":"9aaca0b093fcb4a8407011a7c7ff2d669a576743298536921ea78ebe187402d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:44.486484Z","signature_b64":"POvoXZ8hcce/0R+H7OE924VSMykaWNRYaLYk8GicIagJY/EN4Kbo2h5EnKr/I/4VuKPbWEJYzVTPRVrQ2h+WCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aaca0b093fcb4a8407011a7c7ff2d669a576743298536921ea78ebe187402d7","last_reissued_at":"2026-05-17T23:51:44.485778Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:44.485778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.08728","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":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bzs3VwC7bodrh4ZjUxXUhV5AAYGIrx3c7NWdPfyUAno3Gb9Jk7Vme9yLWwZfyVsAkDC1dZrWFD2H65rkYluqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:11:55.556009Z"},"content_sha256":"c3bd2acdfde550a9fd30b882de93c720bdafa8560680259143b519bde4b8493d","schema_version":"1.0","event_id":"sha256:c3bd2acdfde550a9fd30b882de93c720bdafa8560680259143b519bde4b8493d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TKWKBMET7S2KQQDQCGT4P7ZNM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Nonconvex Optimization with Large Minibatches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nathan Srebro, Weiran Wang","submitted_at":"2017-09-25T21:20:32Z","abstract_excerpt":"We study stochastic optimization of nonconvex loss functions, which are typical objectives for training neural networks. We propose stochastic approximation algorithms which optimize a series of regularized, nonlinearized losses on large minibatches of samples, using only first-order gradient information. Our algorithms provably converge to an approximate critical point of the expected objective with faster rates than minibatch stochastic gradient descent, and facilitate better parallelization by allowing larger minibatches."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08728","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":""},"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":"2026-05-17T23:51:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3rYguosDhmq2fJCOXb66S3km7aCwHlPB+bWAU34Nl02hAfUXVGWVrzJvrOsf4ukfhFvMg5yTddqfJp1sSPGiCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:11:55.556623Z"},"content_sha256":"40f44b7d5f6fba235e9d83af9009cd8ba35559481220e90f2fd939659af48db9","schema_version":"1.0","event_id":"sha256:40f44b7d5f6fba235e9d83af9009cd8ba35559481220e90f2fd939659af48db9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2/bundle.json","state_url":"https://pith.science/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2/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":"2026-06-05T04:11:55Z","links":{"resolver":"https://pith.science/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2","bundle":"https://pith.science/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2/bundle.json","state":"https://pith.science/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKWKBMET7S2KQQDQCGT4P7ZNM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TKWKBMET7S2KQQDQCGT4P7ZNM2","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":"2e5e7dddf96528feed182edc8bc0a72bbc6d58412014363b61927d0a0c14e753","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-25T21:20:32Z","title_canon_sha256":"f487fcb360f07d72d80176a814adf8d7a0b006dd6826401ce62dc6956ca15ce0"},"schema_version":"1.0","source":{"id":"1709.08728","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.08728","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1709.08728v4","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08728","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"TKWKBMET7S2K","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TKWKBMET7S2KQQDQ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TKWKBMET","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:40f44b7d5f6fba235e9d83af9009cd8ba35559481220e90f2fd939659af48db9","target":"graph","created_at":"2026-05-17T23:51:44Z","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":"We study stochastic optimization of nonconvex loss functions, which are typical objectives for training neural networks. We propose stochastic approximation algorithms which optimize a series of regularized, nonlinearized losses on large minibatches of samples, using only first-order gradient information. Our algorithms provably converge to an approximate critical point of the expected objective with faster rates than minibatch stochastic gradient descent, and facilitate better parallelization by allowing larger minibatches.","authors_text":"Nathan Srebro, Weiran Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-25T21:20:32Z","title":"Stochastic Nonconvex Optimization with Large Minibatches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08728","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:c3bd2acdfde550a9fd30b882de93c720bdafa8560680259143b519bde4b8493d","target":"record","created_at":"2026-05-17T23:51:44Z","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":"2e5e7dddf96528feed182edc8bc0a72bbc6d58412014363b61927d0a0c14e753","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-25T21:20:32Z","title_canon_sha256":"f487fcb360f07d72d80176a814adf8d7a0b006dd6826401ce62dc6956ca15ce0"},"schema_version":"1.0","source":{"id":"1709.08728","kind":"arxiv","version":4}},"canonical_sha256":"9aaca0b093fcb4a8407011a7c7ff2d669a576743298536921ea78ebe187402d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aaca0b093fcb4a8407011a7c7ff2d669a576743298536921ea78ebe187402d7","first_computed_at":"2026-05-17T23:51:44.485778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:44.485778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"POvoXZ8hcce/0R+H7OE924VSMykaWNRYaLYk8GicIagJY/EN4Kbo2h5EnKr/I/4VuKPbWEJYzVTPRVrQ2h+WCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:44.486484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.08728","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3bd2acdfde550a9fd30b882de93c720bdafa8560680259143b519bde4b8493d","sha256:40f44b7d5f6fba235e9d83af9009cd8ba35559481220e90f2fd939659af48db9"],"state_sha256":"dbb1a5f40bce4e44b1999f6e940785d4710971c7ee2122389af5df0cdeeef68e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34XD+l7VFRAF+dPATI1l+QAJLvQpDVHjT0dDv9B5jXpcwkRnzL2eUXcu6+NzWCLy1KwqjyQTXYC49+Z/y8VSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:11:55.559722Z","bundle_sha256":"02735aaa6a59c61eef19c5c7653a49151f4e7f7eaac7795d3fc9d8d1d2009041"}}