{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:GGFRGXWXDBAT354LVGYGXQLTPB","short_pith_number":"pith:GGFRGXWX","canonical_record":{"source":{"id":"2206.02275","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-05T21:32:33Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"cd64b0521f35d33b586da78729c5d2d50110ea7f364b42bb66b5de1ddbf5c15b","abstract_canon_sha256":"049c68c78f9b6f85264a1b6b400f22b164091a02184cbc46f72e92783f53d43e"},"schema_version":"1.0"},"canonical_sha256":"318b135ed718413df78ba9b06bc1737846e5a5e7b561007f69e31d3baf3e0e24","source":{"kind":"arxiv","id":"2206.02275","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.02275","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"2206.02275v1","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.02275","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"GGFRGXWXDBAT","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"pith_short_16","alias_value":"GGFRGXWXDBAT354L","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"pith_short_8","alias_value":"GGFRGXWX","created_at":"2026-07-05T04:29:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:GGFRGXWXDBAT354LVGYGXQLTPB","target":"record","payload":{"canonical_record":{"source":{"id":"2206.02275","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-05T21:32:33Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"cd64b0521f35d33b586da78729c5d2d50110ea7f364b42bb66b5de1ddbf5c15b","abstract_canon_sha256":"049c68c78f9b6f85264a1b6b400f22b164091a02184cbc46f72e92783f53d43e"},"schema_version":"1.0"},"canonical_sha256":"318b135ed718413df78ba9b06bc1737846e5a5e7b561007f69e31d3baf3e0e24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:29:16.017122Z","signature_b64":"YEEUr2Zv6lRVwqNtvRtbjLs2b1kEEVf7hz9oln+7i1CTPZzAwsx3qVMJ4UUdkZWpeW5re9vNTywAHMRc9wTTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"318b135ed718413df78ba9b06bc1737846e5a5e7b561007f69e31d3baf3e0e24","last_reissued_at":"2026-07-05T04:29:16.016712Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:29:16.016712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.02275","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":"2026-07-05T04:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pWyEDFPTbLppy46gTYJNkOu858OZuK6G8wMg9vyqDs2EQ9icfOjQnmQT8QZCpojFOqQQd5nKb6HfstTFyICoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T13:54:46.938489Z"},"content_sha256":"f73a0866a8c865c121ffdf4343e013a625d8579590abc0a06c4b82f7fa77d120","schema_version":"1.0","event_id":"sha256:f73a0866a8c865c121ffdf4343e013a625d8579590abc0a06c4b82f7fa77d120"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:GGFRGXWXDBAT354LVGYGXQLTPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharper Rates and Flexible Framework for Nonconvex SGD with Client and Data Sampling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexander Tyurin, Konstantin Burlachenko, Lukang Sun, Peter Richt\\'arik","submitted_at":"2022-06-05T21:32:33Z","abstract_excerpt":"We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient evaluations of individual functions is $\\mathcal{O}\\left(n + n^{1/2}\\varepsilon^{-1}\\right)$, attained by the optimal SGD methods $\\small\\sf\\color{green}{SPIDER}$(arXiv:1807.01695) and $\\small\\sf\\color{green}{PAGE}$(arXiv:2008.10898), for example, where $\\varepsilon$ is the error tolerance. However, i) the big-$\\mathcal{O}$ notation hides crucial dependencies on th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.02275","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/2206.02275/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":"2026-07-05T04:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QxI5nyL/4REkpWZnwc8/Kp5bLa2QCPevJbf1b46elWKCWrWz/2yytePy7zPdLb09smiquMp/VCq+/Uh5ByAxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T13:54:46.938873Z"},"content_sha256":"01bfc1a22990140fefe8854c743059e724e516c6ae16609cf0cb70a391f8e8aa","schema_version":"1.0","event_id":"sha256:01bfc1a22990140fefe8854c743059e724e516c6ae16609cf0cb70a391f8e8aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGFRGXWXDBAT354LVGYGXQLTPB/bundle.json","state_url":"https://pith.science/pith/GGFRGXWXDBAT354LVGYGXQLTPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGFRGXWXDBAT354LVGYGXQLTPB/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":"2026-07-17T13:54:46Z","links":{"resolver":"https://pith.science/pith/GGFRGXWXDBAT354LVGYGXQLTPB","bundle":"https://pith.science/pith/GGFRGXWXDBAT354LVGYGXQLTPB/bundle.json","state":"https://pith.science/pith/GGFRGXWXDBAT354LVGYGXQLTPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGFRGXWXDBAT354LVGYGXQLTPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GGFRGXWXDBAT354LVGYGXQLTPB","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":"049c68c78f9b6f85264a1b6b400f22b164091a02184cbc46f72e92783f53d43e","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-05T21:32:33Z","title_canon_sha256":"cd64b0521f35d33b586da78729c5d2d50110ea7f364b42bb66b5de1ddbf5c15b"},"schema_version":"1.0","source":{"id":"2206.02275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.02275","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"2206.02275v1","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.02275","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"GGFRGXWXDBAT","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"pith_short_16","alias_value":"GGFRGXWXDBAT354L","created_at":"2026-07-05T04:29:16Z"},{"alias_kind":"pith_short_8","alias_value":"GGFRGXWX","created_at":"2026-07-05T04:29:16Z"}],"graph_snapshots":[{"event_id":"sha256:01bfc1a22990140fefe8854c743059e724e516c6ae16609cf0cb70a391f8e8aa","target":"graph","created_at":"2026-07-05T04:29:16Z","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/2206.02275/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We revisit the classical problem of finding an approximately stationary point of the average of $n$ smooth and possibly nonconvex functions. The optimal complexity of stochastic first-order methods in terms of the number of gradient evaluations of individual functions is $\\mathcal{O}\\left(n + n^{1/2}\\varepsilon^{-1}\\right)$, attained by the optimal SGD methods $\\small\\sf\\color{green}{SPIDER}$(arXiv:1807.01695) and $\\small\\sf\\color{green}{PAGE}$(arXiv:2008.10898), for example, where $\\varepsilon$ is the error tolerance. However, i) the big-$\\mathcal{O}$ notation hides crucial dependencies on th","authors_text":"Alexander Tyurin, Konstantin Burlachenko, Lukang Sun, Peter Richt\\'arik","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-05T21:32:33Z","title":"Sharper Rates and Flexible Framework for Nonconvex SGD with Client and Data Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.02275","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:f73a0866a8c865c121ffdf4343e013a625d8579590abc0a06c4b82f7fa77d120","target":"record","created_at":"2026-07-05T04:29:16Z","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":"049c68c78f9b6f85264a1b6b400f22b164091a02184cbc46f72e92783f53d43e","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-06-05T21:32:33Z","title_canon_sha256":"cd64b0521f35d33b586da78729c5d2d50110ea7f364b42bb66b5de1ddbf5c15b"},"schema_version":"1.0","source":{"id":"2206.02275","kind":"arxiv","version":1}},"canonical_sha256":"318b135ed718413df78ba9b06bc1737846e5a5e7b561007f69e31d3baf3e0e24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"318b135ed718413df78ba9b06bc1737846e5a5e7b561007f69e31d3baf3e0e24","first_computed_at":"2026-07-05T04:29:16.016712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:29:16.016712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YEEUr2Zv6lRVwqNtvRtbjLs2b1kEEVf7hz9oln+7i1CTPZzAwsx3qVMJ4UUdkZWpeW5re9vNTywAHMRc9wTTCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:29:16.017122Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.02275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f73a0866a8c865c121ffdf4343e013a625d8579590abc0a06c4b82f7fa77d120","sha256:01bfc1a22990140fefe8854c743059e724e516c6ae16609cf0cb70a391f8e8aa"],"state_sha256":"48c8a250d389a449b311a4788febdd5bc9cae1365cb9cc30b20467f2e132d1ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8mcJ8usAG4D3g1V1hjzcCBEZokMrTU8ZHyo+As8oVYG/IU+lVEKrmO19jetYjmaPMvll6OFkyjKfhsoWeXCfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T13:54:46.942077Z","bundle_sha256":"c2e31529e5e41508f78ddc411fbcdc92adcd4f80171075a832851784c31b0327"}}