{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WG3LB6PM6DSAJDGTFENNTF6E5F","short_pith_number":"pith:WG3LB6PM","canonical_record":{"source":{"id":"1803.08917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-23T17:58:54Z","cross_cats_sorted":["cs.DC","cs.DS","math.OC","stat.ML"],"title_canon_sha256":"f16b9ac9e9d8f7efb74d2a72b8ec70e9f9b6d5f30c9c941428734d555831ab7e","abstract_canon_sha256":"246105f3947c747a3394db07c904f3f63f8df85a9c63691bd1a368c5f0711f2e"},"schema_version":"1.0"},"canonical_sha256":"b1b6b0f9ecf0e4048cd3291ad997c4e9569221ad8b8ea761c7300ef35324d0f2","source":{"kind":"arxiv","id":"1803.08917","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08917","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08917v1","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08917","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"WG3LB6PM6DSA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WG3LB6PM6DSAJDGT","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WG3LB6PM","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WG3LB6PM6DSAJDGTFENNTF6E5F","target":"record","payload":{"canonical_record":{"source":{"id":"1803.08917","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-23T17:58:54Z","cross_cats_sorted":["cs.DC","cs.DS","math.OC","stat.ML"],"title_canon_sha256":"f16b9ac9e9d8f7efb74d2a72b8ec70e9f9b6d5f30c9c941428734d555831ab7e","abstract_canon_sha256":"246105f3947c747a3394db07c904f3f63f8df85a9c63691bd1a368c5f0711f2e"},"schema_version":"1.0"},"canonical_sha256":"b1b6b0f9ecf0e4048cd3291ad997c4e9569221ad8b8ea761c7300ef35324d0f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:18.240004Z","signature_b64":"kAL5Bws5e9bJAbkfSsGaIQPy2hYUJQ1rfWmPp+66+LG6+4bZCP9r/ZTaMmz3avDjEL7svW5iwc/tK0GBjDXwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1b6b0f9ecf0e4048cd3291ad997c4e9569221ad8b8ea761c7300ef35324d0f2","last_reissued_at":"2026-05-18T00:20:18.239351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:18.239351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.08917","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":"2026-05-18T00:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYqFrqksPuneb0mXm4PvewS8hSt5mBtGaf0JQ7BzIa1faKExmLfGWAWRQqbxEHsYROOe48QLL2yb1d8bv4UdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:52:08.814095Z"},"content_sha256":"7e79e2bb3be3f14cc45f37c4a8e1ce91ef93a6ced48281b28b5b569368497bcf","schema_version":"1.0","event_id":"sha256:7e79e2bb3be3f14cc45f37c4a8e1ce91ef93a6ced48281b28b5b569368497bcf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WG3LB6PM6DSAJDGTFENNTF6E5F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Byzantine Stochastic Gradient Descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.DS","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Dan Alistarh, Jerry Li, Zeyuan Allen-Zhu","submitted_at":"2018-03-23T17:58:54Z","abstract_excerpt":"This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of the $m$ machines which allegedly compute stochastic gradients every iteration, an $\\alpha$-fraction are Byzantine, and can behave arbitrarily and adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\\varepsilon$-approximate minimizers of convex functions in $T = \\tilde{O}\\big( \\frac{1}{\\varepsilon^2 m} + \\frac{\\alpha^2}{\\varepsilon^2} \\big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\\big( \\frac{1}{\\varepsilon^2 m} \\big)$ it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08917","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":""},"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":"2026-05-18T00:20:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBiG3NCuk3kqnPuoz8wPSsuCDWDN6uftZuheqmZkXDYndyTMxUDOUGu9sTbCj6RUi4LtMHGvbCrvpuxAPOQRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:52:08.814899Z"},"content_sha256":"a7f2133709a24b6d2f6d1c33d383da2adee659bf25fe0e7c7b3e758c23578d67","schema_version":"1.0","event_id":"sha256:a7f2133709a24b6d2f6d1c33d383da2adee659bf25fe0e7c7b3e758c23578d67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WG3LB6PM6DSAJDGTFENNTF6E5F/bundle.json","state_url":"https://pith.science/pith/WG3LB6PM6DSAJDGTFENNTF6E5F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WG3LB6PM6DSAJDGTFENNTF6E5F/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":"2026-05-26T07:52:08Z","links":{"resolver":"https://pith.science/pith/WG3LB6PM6DSAJDGTFENNTF6E5F","bundle":"https://pith.science/pith/WG3LB6PM6DSAJDGTFENNTF6E5F/bundle.json","state":"https://pith.science/pith/WG3LB6PM6DSAJDGTFENNTF6E5F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WG3LB6PM6DSAJDGTFENNTF6E5F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WG3LB6PM6DSAJDGTFENNTF6E5F","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":"246105f3947c747a3394db07c904f3f63f8df85a9c63691bd1a368c5f0711f2e","cross_cats_sorted":["cs.DC","cs.DS","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-23T17:58:54Z","title_canon_sha256":"f16b9ac9e9d8f7efb74d2a72b8ec70e9f9b6d5f30c9c941428734d555831ab7e"},"schema_version":"1.0","source":{"id":"1803.08917","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08917","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08917v1","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08917","created_at":"2026-05-18T00:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"WG3LB6PM6DSA","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WG3LB6PM6DSAJDGT","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WG3LB6PM","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:a7f2133709a24b6d2f6d1c33d383da2adee659bf25fe0e7c7b3e758c23578d67","target":"graph","created_at":"2026-05-18T00:20:18Z","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"},"paper":{"abstract_excerpt":"This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of the $m$ machines which allegedly compute stochastic gradients every iteration, an $\\alpha$-fraction are Byzantine, and can behave arbitrarily and adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\\varepsilon$-approximate minimizers of convex functions in $T = \\tilde{O}\\big( \\frac{1}{\\varepsilon^2 m} + \\frac{\\alpha^2}{\\varepsilon^2} \\big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\\big( \\frac{1}{\\varepsilon^2 m} \\big)$ it","authors_text":"Dan Alistarh, Jerry Li, Zeyuan Allen-Zhu","cross_cats":["cs.DC","cs.DS","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-23T17:58:54Z","title":"Byzantine Stochastic Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08917","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":"sha256:7e79e2bb3be3f14cc45f37c4a8e1ce91ef93a6ced48281b28b5b569368497bcf","target":"record","created_at":"2026-05-18T00:20:18Z","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":"246105f3947c747a3394db07c904f3f63f8df85a9c63691bd1a368c5f0711f2e","cross_cats_sorted":["cs.DC","cs.DS","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-03-23T17:58:54Z","title_canon_sha256":"f16b9ac9e9d8f7efb74d2a72b8ec70e9f9b6d5f30c9c941428734d555831ab7e"},"schema_version":"1.0","source":{"id":"1803.08917","kind":"arxiv","version":1}},"canonical_sha256":"b1b6b0f9ecf0e4048cd3291ad997c4e9569221ad8b8ea761c7300ef35324d0f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1b6b0f9ecf0e4048cd3291ad997c4e9569221ad8b8ea761c7300ef35324d0f2","first_computed_at":"2026-05-18T00:20:18.239351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:18.239351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kAL5Bws5e9bJAbkfSsGaIQPy2hYUJQ1rfWmPp+66+LG6+4bZCP9r/ZTaMmz3avDjEL7svW5iwc/tK0GBjDXwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:18.240004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08917","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e79e2bb3be3f14cc45f37c4a8e1ce91ef93a6ced48281b28b5b569368497bcf","sha256:a7f2133709a24b6d2f6d1c33d383da2adee659bf25fe0e7c7b3e758c23578d67"],"state_sha256":"744b757c66322298953e6762fde4bb04d80f8fe75463637c0c785f600c7e1aa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tuan2eobfB8N/2QQEKlNTn6NuVs6LbVtftrkR3fTyrdOWrrPAvih/NQ6ZJL5GM9VfNpF4oZmnGHrpHHrs7ugCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:52:08.818742Z","bundle_sha256":"ddca2af2fb675b0571605686d4bf4ec96cfdabdc8cdcc434eb168655efb3d6e4"}}