{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:T46S7VW2ERDA6XXZB4E6WHLRNJ","short_pith_number":"pith:T46S7VW2","canonical_record":{"source":{"id":"2302.00999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-02T10:37:23Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b6204140056494da1d17538931ebc525b1c4dc7e483b4bf16dc2faf10d3fb381","abstract_canon_sha256":"e42cfe7bd063cd2964f7b90415a7944bc278ee90a469a66169f0226f4578c27d"},"schema_version":"1.0"},"canonical_sha256":"9f3d2fd6da24460f5ef90f09eb1d716a41fb5eee444f55211914c2d8dfe0585b","source":{"kind":"arxiv","id":"2302.00999","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.00999","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"2302.00999v2","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.00999","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"T46S7VW2ERDA","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"T46S7VW2ERDA6XXZ","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"T46S7VW2","created_at":"2026-07-05T06:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:T46S7VW2ERDA6XXZB4E6WHLRNJ","target":"record","payload":{"canonical_record":{"source":{"id":"2302.00999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-02T10:37:23Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"b6204140056494da1d17538931ebc525b1c4dc7e483b4bf16dc2faf10d3fb381","abstract_canon_sha256":"e42cfe7bd063cd2964f7b90415a7944bc278ee90a469a66169f0226f4578c27d"},"schema_version":"1.0"},"canonical_sha256":"9f3d2fd6da24460f5ef90f09eb1d716a41fb5eee444f55211914c2d8dfe0585b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:32:05.586664Z","signature_b64":"eMNaAEe+kGQo+xXlaTdde7vM7FhdO5+An/Silod5NWvOU9xXLV43hegkvmD3y3jJG+QQp9nfBScZPgN7xCkaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f3d2fd6da24460f5ef90f09eb1d716a41fb5eee444f55211914c2d8dfe0585b","last_reissued_at":"2026-07-05T06:32:05.586140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:32:05.586140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.00999","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":"2026-07-05T06:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DeIsNzLe8dUUYjvNCLBjNRC1WQzooOaw/YODEq5Jw16QyXg9t9Jyyu88T2dJaUEzOBOT0PemIMeI2IKV7lfzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:44:28.481864Z"},"content_sha256":"83f6294dc0255c983ffa9ae6abd03889283a1044a9a772fffcdc20753d5504c2","schema_version":"1.0","event_id":"sha256:83f6294dc0255c983ffa9ae6abd03889283a1044a9a772fffcdc20753d5504c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:T46S7VW2ERDA6XXZB4E6WHLRNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Abdurakhmon Sadiev, Alexander Gasnikov, Eduard Gorbunov, Gauthier Gidel, Marina Danilova, Pavel Dvurechensky, Peter Richt\\'arik, Samuel Horv\\'ath","submitted_at":"2023-02-02T10:37:23Z","abstract_excerpt":"During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic convergence results are derived under strong assumptions such as the boundedness of the gradient noise variance or of the objective's gradient itself. In this paper, we propose several algorithms with high-probability convergence results under less r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00999","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.00999/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":"2026-07-05T06:32:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkYNKZA0zT+Nkm0Z4/uwmI7gtO9l9b9DIWgGM7OW46hyNEtPuMVIiZuDBBvnOwdiSuhNQfEeXbCiqnJ3KMciAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:44:28.482437Z"},"content_sha256":"1341d57499ea525755dd7d1d8527eb4473381e61aad4053dc8a4b7c99cf57c2f","schema_version":"1.0","event_id":"sha256:1341d57499ea525755dd7d1d8527eb4473381e61aad4053dc8a4b7c99cf57c2f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ/bundle.json","state_url":"https://pith.science/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ/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":"2026-08-11T07:44:28Z","links":{"resolver":"https://pith.science/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ","bundle":"https://pith.science/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ/bundle.json","state":"https://pith.science/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T46S7VW2ERDA6XXZB4E6WHLRNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:T46S7VW2ERDA6XXZB4E6WHLRNJ","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":"e42cfe7bd063cd2964f7b90415a7944bc278ee90a469a66169f0226f4578c27d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-02T10:37:23Z","title_canon_sha256":"b6204140056494da1d17538931ebc525b1c4dc7e483b4bf16dc2faf10d3fb381"},"schema_version":"1.0","source":{"id":"2302.00999","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.00999","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"arxiv_version","alias_value":"2302.00999v2","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.00999","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"pith_short_12","alias_value":"T46S7VW2ERDA","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"T46S7VW2ERDA6XXZ","created_at":"2026-07-05T06:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"T46S7VW2","created_at":"2026-07-05T06:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:1341d57499ea525755dd7d1d8527eb4473381e61aad4053dc8a4b7c99cf57c2f","target":"graph","created_at":"2026-07-05T06:32:05Z","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/2302.00999/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic convergence results are derived under strong assumptions such as the boundedness of the gradient noise variance or of the objective's gradient itself. In this paper, we propose several algorithms with high-probability convergence results under less r","authors_text":"Abdurakhmon Sadiev, Alexander Gasnikov, Eduard Gorbunov, Gauthier Gidel, Marina Danilova, Pavel Dvurechensky, Peter Richt\\'arik, Samuel Horv\\'ath","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-02T10:37:23Z","title":"High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00999","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":"sha256:83f6294dc0255c983ffa9ae6abd03889283a1044a9a772fffcdc20753d5504c2","target":"record","created_at":"2026-07-05T06:32:05Z","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":"e42cfe7bd063cd2964f7b90415a7944bc278ee90a469a66169f0226f4578c27d","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-02-02T10:37:23Z","title_canon_sha256":"b6204140056494da1d17538931ebc525b1c4dc7e483b4bf16dc2faf10d3fb381"},"schema_version":"1.0","source":{"id":"2302.00999","kind":"arxiv","version":2}},"canonical_sha256":"9f3d2fd6da24460f5ef90f09eb1d716a41fb5eee444f55211914c2d8dfe0585b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f3d2fd6da24460f5ef90f09eb1d716a41fb5eee444f55211914c2d8dfe0585b","first_computed_at":"2026-07-05T06:32:05.586140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:32:05.586140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eMNaAEe+kGQo+xXlaTdde7vM7FhdO5+An/Silod5NWvOU9xXLV43hegkvmD3y3jJG+QQp9nfBScZPgN7xCkaCw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:32:05.586664Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.00999","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83f6294dc0255c983ffa9ae6abd03889283a1044a9a772fffcdc20753d5504c2","sha256:1341d57499ea525755dd7d1d8527eb4473381e61aad4053dc8a4b7c99cf57c2f"],"state_sha256":"381009afef0fbfed9686f30481622a22c3ea5e0f431e8d33f5c38f5ad44ab0aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOGF/tNPOXZmfbYJo1djd6UD4tPHNTOqiyKfZVR2hq14fckJVcdnXj7oKhOnmdzGbiutycE6gdMln16CemRnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T07:44:28.486688Z","bundle_sha256":"67ccc76463903ea4e77aa0644dca31d864cc769d4a83af95dc73a3e2fcaa9604"}}