{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LGTTJXIXA57X4YB2DINFYHD7GK","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":"01afeb2bd633c79eab96276105141a7c4a917fe9077c0397207250b6cf9c8927","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-26T18:47:08Z","title_canon_sha256":"61bee2d30cd5f5f72b46eb5f19bd28c930eab094f8117bf7deace7e163869b98"},"schema_version":"1.0","source":{"id":"2402.16821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.16821","created_at":"2026-07-05T07:49:26Z"},{"alias_kind":"arxiv_version","alias_value":"2402.16821v1","created_at":"2026-07-05T07:49:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.16821","created_at":"2026-07-05T07:49:26Z"},{"alias_kind":"pith_short_12","alias_value":"LGTTJXIXA57X","created_at":"2026-07-05T07:49:26Z"},{"alias_kind":"pith_short_16","alias_value":"LGTTJXIXA57X4YB2","created_at":"2026-07-05T07:49:26Z"},{"alias_kind":"pith_short_8","alias_value":"LGTTJXIX","created_at":"2026-07-05T07:49:26Z"}],"graph_snapshots":[{"event_id":"sha256:21a4138cf708fb08fbcdd14c5d2762e3e64fd2a79a7c387fc3ecca7741eff1d4","target":"graph","created_at":"2026-07-05T07:49:26Z","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/2402.16821/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a numerical analysis and computation of neural network projected schemes for approximating one dimensional Wasserstein gradient flows. We approximate the Lagrangian mapping functions of gradient flows by the class of two-layer neural network functions with ReLU (rectified linear unit) activation functions. The numerical scheme is based on a projected gradient method, namely the Wasserstein natural gradient, where the projection is constructed from the $L^2$ mapping spaces onto the neural network parameterized mapping space. We establish theoretical guarantees for the performance of ","authors_text":"Jiaxi Zhao, Shu Liu, Stanley Osher, Wuchen Li, Xinzhe Zuo","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-26T18:47:08Z","title":"Numerical Analysis on Neural Network Projected Schemes for Approximating One Dimensional Wasserstein Gradient Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.16821","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:c9dd4a40e70123e26e0af276f45fd2b491cc2d9b08ebf9244361d51ecccca728","target":"record","created_at":"2026-07-05T07:49:26Z","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":"01afeb2bd633c79eab96276105141a7c4a917fe9077c0397207250b6cf9c8927","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-02-26T18:47:08Z","title_canon_sha256":"61bee2d30cd5f5f72b46eb5f19bd28c930eab094f8117bf7deace7e163869b98"},"schema_version":"1.0","source":{"id":"2402.16821","kind":"arxiv","version":1}},"canonical_sha256":"59a734dd17077f7e603a1a1a5c1c7f32891b29971df2988997060dd416adf987","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59a734dd17077f7e603a1a1a5c1c7f32891b29971df2988997060dd416adf987","first_computed_at":"2026-07-05T07:49:26.502036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:49:26.502036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XwsvCRUPztvwoJmBta2bYJLBduqZC1lKJ2hn5XkJ763RNA47wykl2yQ4ofrqmPhmFuxzOwj1JFG3Z0PFhR/uAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:49:26.502437Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.16821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9dd4a40e70123e26e0af276f45fd2b491cc2d9b08ebf9244361d51ecccca728","sha256:21a4138cf708fb08fbcdd14c5d2762e3e64fd2a79a7c387fc3ecca7741eff1d4"],"state_sha256":"5187c912aecfd1fad2902c8ae694c596225b469d8bffc07b566ab70713ec6009"}