{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IXINR2RTVIKC5NPOPBP4RQZ24L","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":"717e923430a0439d23858a86411dddc18336c705b3a7eb8986dce84594af99f6","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-12T23:17:09Z","title_canon_sha256":"64c2298e8590d501a3513cec91cea3ebf5a9987ef01c8b70e7bd54e2a90828da"},"schema_version":"1.0","source":{"id":"2506.11357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11357","created_at":"2026-07-05T11:21:02Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11357v1","created_at":"2026-07-05T11:21:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11357","created_at":"2026-07-05T11:21:02Z"},{"alias_kind":"pith_short_12","alias_value":"IXINR2RTVIKC","created_at":"2026-07-05T11:21:02Z"},{"alias_kind":"pith_short_16","alias_value":"IXINR2RTVIKC5NPO","created_at":"2026-07-05T11:21:02Z"},{"alias_kind":"pith_short_8","alias_value":"IXINR2RT","created_at":"2026-07-05T11:21:02Z"}],"graph_snapshots":[{"event_id":"sha256:19ffda997161cbc126247be9afc30f5555eb196ab7458fa3daed1bbe3959e9e3","target":"graph","created_at":"2026-07-05T11:21:02Z","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/2506.11357/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gradient-based optimization methods have shown remarkable empirical success, yet their theoretical generalization properties remain only partially understood. In this paper, we establish a generalization bound for gradient flow that aligns with the classical Rademacher complexity bounds for kernel methods-specifically those based on the RKHS norm and kernel trace-through a data-dependent kernel called the loss path kernel (LPK). Unlike static kernels such as NTK, the LPK captures the entire training trajectory, adapting to both data and optimization dynamics, leading to tighter and more inform","authors_text":"Andi Han, Arya Mazumdar, Taiji Suzuki, Wei Huang, Yilan Chen, Zhichao Wang","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-12T23:17:09Z","title":"Generalization Bound of Gradient Flow through Training Trajectory and Data-dependent Kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11357","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":"sha256:257f5f679392c68a31380e5de7cd12d3c19eb7380876f860de24b06365828772","target":"record","created_at":"2026-07-05T11:21:02Z","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":"717e923430a0439d23858a86411dddc18336c705b3a7eb8986dce84594af99f6","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-06-12T23:17:09Z","title_canon_sha256":"64c2298e8590d501a3513cec91cea3ebf5a9987ef01c8b70e7bd54e2a90828da"},"schema_version":"1.0","source":{"id":"2506.11357","kind":"arxiv","version":1}},"canonical_sha256":"45d0d8ea33aa142eb5ee785fc8c33ae2c5d071485839a11b04cd5ea69ef7006b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45d0d8ea33aa142eb5ee785fc8c33ae2c5d071485839a11b04cd5ea69ef7006b","first_computed_at":"2026-07-05T11:21:02.933962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:21:02.933962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cBYYD2q0qKYvBF1CzAnXqHqozt3/IfbhV6sNRE4iRNtJmGUOffFuBhb5R/FEM7M1LrzRa/fn89VEggdNu52bCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:21:02.934302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:257f5f679392c68a31380e5de7cd12d3c19eb7380876f860de24b06365828772","sha256:19ffda997161cbc126247be9afc30f5555eb196ab7458fa3daed1bbe3959e9e3"],"state_sha256":"67bad7eeeda959a9cadd224d895fe838ad940ec86770dcaaae1723eab30d50f6"}