{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LCH5RG4XSDEB2RVZFXAMMI7AJJ","short_pith_number":"pith:LCH5RG4X","canonical_record":{"source":{"id":"2405.16732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-27T00:23:42Z","cross_cats_sorted":["cs.LG","math.OC","math.ST","stat.TH"],"title_canon_sha256":"91b4fa8f553ea178219c2564880e36b59e96826648ded1dce5c3bcc84ebecd31","abstract_canon_sha256":"cee12a0d5f34453e321d56779b2e7ccd767df106b1a5984c4cd90b032c48b8fc"},"schema_version":"1.0"},"canonical_sha256":"588fd89b9790c81d46b92dc0c623e04a60738b0642830d73c40ed3ddac9ed012","source":{"kind":"arxiv","id":"2405.16732","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16732","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16732v1","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16732","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"LCH5RG4XSDEB","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"LCH5RG4XSDEB2RVZ","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"LCH5RG4X","created_at":"2026-07-05T10:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LCH5RG4XSDEB2RVZFXAMMI7AJJ","target":"record","payload":{"canonical_record":{"source":{"id":"2405.16732","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-27T00:23:42Z","cross_cats_sorted":["cs.LG","math.OC","math.ST","stat.TH"],"title_canon_sha256":"91b4fa8f553ea178219c2564880e36b59e96826648ded1dce5c3bcc84ebecd31","abstract_canon_sha256":"cee12a0d5f34453e321d56779b2e7ccd767df106b1a5984c4cd90b032c48b8fc"},"schema_version":"1.0"},"canonical_sha256":"588fd89b9790c81d46b92dc0c623e04a60738b0642830d73c40ed3ddac9ed012","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:31:43.690036Z","signature_b64":"5PYIHdta+JrzsRRLCXnAUrbNZOua0HwBHLeB64mQ8G/MoUGdvKb2JpSDalO/KaMPGjrA2TW+kL1ZsIxTqC3oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"588fd89b9790c81d46b92dc0c623e04a60738b0642830d73c40ed3ddac9ed012","last_reissued_at":"2026-07-05T10:31:43.689326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:31:43.689326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.16732","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":"2026-07-05T10:31:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p5aMbcK1hPZK8Xz09gXiYDJtvtJf974ZOWrK6ilki8e/9QXIivP6Ubhd/17kOeZldk2t/A/4hnQzUrWAXai+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:08:26.156503Z"},"content_sha256":"527aa3bcf796b0455c25309cf97c5b79c1ad07e204db63e43c5e0b1411374bc3","schema_version":"1.0","event_id":"sha256:527aa3bcf796b0455c25309cf97c5b79c1ad07e204db63e43c5e0b1411374bc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LCH5RG4XSDEB2RVZFXAMMI7AJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Collusion of Memory and Nonlinearity in Stochastic Approximation With Constant Stepsize","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Dongyan Huo, Qiaomin Xie, Yixuan Zhang, Yudong Chen","submitted_at":"2024-05-27T00:23:42Z","abstract_excerpt":"In this work, we investigate stochastic approximation (SA) with Markovian data and nonlinear updates under constant stepsize $\\alpha>0$. Existing work has primarily focused on either i.i.d. data or linear update rules. We take a new perspective and carefully examine the simultaneous presence of Markovian dependency of data and nonlinear update rules, delineating how the interplay between these two structures leads to complications that are not captured by prior techniques. By leveraging the smoothness and recurrence properties of the SA updates, we develop a fine-grained analysis of the correl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16732","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/2405.16732/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":"2026-07-05T10:31:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjfLPKBBfxO0muTXSzosRIpxYs9405EjQD680vEcijtWoCKmmCQneTcMWX1rDhQtT00Qq2XpncfJPBWbc3CiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T10:08:26.156889Z"},"content_sha256":"60ff2ec68ff6ea794e6e11bec85cb7b47401cfb404773a2032227d68d3b0abba","schema_version":"1.0","event_id":"sha256:60ff2ec68ff6ea794e6e11bec85cb7b47401cfb404773a2032227d68d3b0abba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ/bundle.json","state_url":"https://pith.science/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ/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":"2026-08-19T10:08:26Z","links":{"resolver":"https://pith.science/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ","bundle":"https://pith.science/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ/bundle.json","state":"https://pith.science/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCH5RG4XSDEB2RVZFXAMMI7AJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LCH5RG4XSDEB2RVZFXAMMI7AJJ","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":"cee12a0d5f34453e321d56779b2e7ccd767df106b1a5984c4cd90b032c48b8fc","cross_cats_sorted":["cs.LG","math.OC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-27T00:23:42Z","title_canon_sha256":"91b4fa8f553ea178219c2564880e36b59e96826648ded1dce5c3bcc84ebecd31"},"schema_version":"1.0","source":{"id":"2405.16732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16732","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16732v1","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16732","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"LCH5RG4XSDEB","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"LCH5RG4XSDEB2RVZ","created_at":"2026-07-05T10:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"LCH5RG4X","created_at":"2026-07-05T10:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:60ff2ec68ff6ea794e6e11bec85cb7b47401cfb404773a2032227d68d3b0abba","target":"graph","created_at":"2026-07-05T10:31:43Z","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/2405.16732/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we investigate stochastic approximation (SA) with Markovian data and nonlinear updates under constant stepsize $\\alpha>0$. Existing work has primarily focused on either i.i.d. data or linear update rules. We take a new perspective and carefully examine the simultaneous presence of Markovian dependency of data and nonlinear update rules, delineating how the interplay between these two structures leads to complications that are not captured by prior techniques. By leveraging the smoothness and recurrence properties of the SA updates, we develop a fine-grained analysis of the correl","authors_text":"Dongyan Huo, Qiaomin Xie, Yixuan Zhang, Yudong Chen","cross_cats":["cs.LG","math.OC","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-27T00:23:42Z","title":"The Collusion of Memory and Nonlinearity in Stochastic Approximation With Constant Stepsize"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16732","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":"sha256:527aa3bcf796b0455c25309cf97c5b79c1ad07e204db63e43c5e0b1411374bc3","target":"record","created_at":"2026-07-05T10:31:43Z","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":"cee12a0d5f34453e321d56779b2e7ccd767df106b1a5984c4cd90b032c48b8fc","cross_cats_sorted":["cs.LG","math.OC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-27T00:23:42Z","title_canon_sha256":"91b4fa8f553ea178219c2564880e36b59e96826648ded1dce5c3bcc84ebecd31"},"schema_version":"1.0","source":{"id":"2405.16732","kind":"arxiv","version":1}},"canonical_sha256":"588fd89b9790c81d46b92dc0c623e04a60738b0642830d73c40ed3ddac9ed012","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"588fd89b9790c81d46b92dc0c623e04a60738b0642830d73c40ed3ddac9ed012","first_computed_at":"2026-07-05T10:31:43.689326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:43.689326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5PYIHdta+JrzsRRLCXnAUrbNZOua0HwBHLeB64mQ8G/MoUGdvKb2JpSDalO/KaMPGjrA2TW+kL1ZsIxTqC3oDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:43.690036Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.16732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:527aa3bcf796b0455c25309cf97c5b79c1ad07e204db63e43c5e0b1411374bc3","sha256:60ff2ec68ff6ea794e6e11bec85cb7b47401cfb404773a2032227d68d3b0abba"],"state_sha256":"4bf496ec9a596e1c8ba129db3064b56ff1620027a37b5eb73549ccda6cea3971"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5TJKovqmXk12g5OqDH3flTmfASi6Zo2RU30ZZB24dHdaFl3A0T4fAO9ng/Cq3yB27CK/Q3HRWD0ilnS1oQ0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T10:08:26.159557Z","bundle_sha256":"c6ef9cdaa0a06024984d2429b62351be23c3fc13dff37de7511147384c45f91a"}}