{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6SJXBEM33NBU5EEDVW3BMAW4GL","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":"79b500f3e8889848ae107cf6896750c791f0c3fb467a350fa6db697153a6c2b6","cross_cats_sorted":["math.AP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-14T20:33:30Z","title_canon_sha256":"6572eb5ca9e9e14a11df59e544b3da839a88e3647da1bdc4288d2d97dc419372"},"schema_version":"1.0","source":{"id":"2501.08425","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08425","created_at":"2026-06-12T01:09:06Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08425v3","created_at":"2026-06-12T01:09:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08425","created_at":"2026-06-12T01:09:06Z"},{"alias_kind":"pith_short_12","alias_value":"6SJXBEM33NBU","created_at":"2026-06-12T01:09:06Z"},{"alias_kind":"pith_short_16","alias_value":"6SJXBEM33NBU5EED","created_at":"2026-06-12T01:09:06Z"},{"alias_kind":"pith_short_8","alias_value":"6SJXBEM3","created_at":"2026-06-12T01:09:06Z"}],"graph_snapshots":[{"event_id":"sha256:0678207cef390bc9a30cdffe838cee383622ab19afc5191789cf3c394cb40c01","target":"graph","created_at":"2026-06-12T01:09:06Z","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/2501.08425/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of E, Li and Tai (2017), the underlying structure of such processes can be understood via parabolic PDEs of Fokker-Planck type, which are at the core of our analysis. Even if Fokker-Planck equations have a long history and a extensive literature, almost nothing is known when the potential is non-convex or when the diffusion matrix is degenerate, and this is th","authors_text":"Davide Barbieri, Matteo Bonforte, Peio Ibarrondo","cross_cats":["math.AP","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-14T20:33:30Z","title":"Is Stochastic Gradient Descent Effective? A PDE Perspective on Machine Learning processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08425","kind":"arxiv","version":3},"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:f38f59462490a47a4f0c9b970cc8d8491a02ec811c599e1c412fe79f65b2593b","target":"record","created_at":"2026-06-12T01:09:06Z","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":"79b500f3e8889848ae107cf6896750c791f0c3fb467a350fa6db697153a6c2b6","cross_cats_sorted":["math.AP","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-14T20:33:30Z","title_canon_sha256":"6572eb5ca9e9e14a11df59e544b3da839a88e3647da1bdc4288d2d97dc419372"},"schema_version":"1.0","source":{"id":"2501.08425","kind":"arxiv","version":3}},"canonical_sha256":"f49370919bdb434e9083adb61602dc32d67192b7cd26b813456a639c1ac60830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f49370919bdb434e9083adb61602dc32d67192b7cd26b813456a639c1ac60830","first_computed_at":"2026-06-12T01:09:06.682498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:06.682498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"phVL8nY8KZZNo0k2HluSISwngwKf/0514/dUFSBY+t6yQPlOBEy6VYQFqEwN+u2PJEW4kWvb1LKau9+q/xUfDg==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:06.683501Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.08425","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f38f59462490a47a4f0c9b970cc8d8491a02ec811c599e1c412fe79f65b2593b","sha256:0678207cef390bc9a30cdffe838cee383622ab19afc5191789cf3c394cb40c01"],"state_sha256":"3e2108e873786a2d6f400eaa9c172301fa1e9f3f6dccbfda62aafbdda3340481"}