{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DNZKOXHR5J3457N4Q736IRFDTQ","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":"f8e93190ec593243210b2f59a6b0fe080a679af81b5bc2dd0eec3e8ee45e2db2","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T14:36:55Z","title_canon_sha256":"bf1cc6900ea1a06c7a7d729583395a5ce39e53ec1b9806d73737d15da30bb4ad"},"schema_version":"1.0","source":{"id":"2602.14789","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.14789","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"2602.14789v2","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.14789","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"DNZKOXHR5J34","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"pith_short_16","alias_value":"DNZKOXHR5J3457N4","created_at":"2026-06-19T16:10:54Z"},{"alias_kind":"pith_short_8","alias_value":"DNZKOXHR","created_at":"2026-06-19T16:10:54Z"}],"graph_snapshots":[{"event_id":"sha256:22c2d1df80d5ac753c8b8cbb913e84e43c94f6931d1e1849cf999cac25abf448","target":"graph","created_at":"2026-06-19T16:10:54Z","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/2602.14789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been associated with favorable features. While prior work often relies on linearization to determine stability, it remains unclear whether linearized dynamics faithfully capture the full nonlinear behavior. Recent work has shown that GD may stably oscillate near a linearly unstable minimum and still converge once the step size decays, indicating that linear analysis ca","authors_text":"Rotem Mulayoff, Sebastian U. Stich","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T14:36:55Z","title":"On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.14789","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:a9c5e0f3717a49e0a94ec52497d06ea1c6ea79e70e9b4c79e0eceef114b96b33","target":"record","created_at":"2026-06-19T16:10:54Z","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":"f8e93190ec593243210b2f59a6b0fe080a679af81b5bc2dd0eec3e8ee45e2db2","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T14:36:55Z","title_canon_sha256":"bf1cc6900ea1a06c7a7d729583395a5ce39e53ec1b9806d73737d15da30bb4ad"},"schema_version":"1.0","source":{"id":"2602.14789","kind":"arxiv","version":2}},"canonical_sha256":"1b72a75cf1ea77cefdbc87f7e444a39c0423792b44afa123d23a3ab259997ac1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b72a75cf1ea77cefdbc87f7e444a39c0423792b44afa123d23a3ab259997ac1","first_computed_at":"2026-06-19T16:10:54.821835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:54.821835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TkXQ4BvxPiiwTbvsJoGLSdyC92S1hD6wScPZkyRF7cpszqk/qwDWxscSyjNoJKGLFKyeoF87enMCLlnU27c+Dw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:54.822195Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.14789","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9c5e0f3717a49e0a94ec52497d06ea1c6ea79e70e9b4c79e0eceef114b96b33","sha256:22c2d1df80d5ac753c8b8cbb913e84e43c94f6931d1e1849cf999cac25abf448"],"state_sha256":"fb96d85d0e2cf91bd3aca94ba673a83c30138eeb35c17946c56b71e8bda6c59f"}