{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HRHSVFZVPFVH6OVNW3OSP7RUNZ","short_pith_number":"pith:HRHSVFZV","schema_version":"1.0","canonical_sha256":"3c4f2a9735796a7f3aadb6dd27fe346e73e8a9f6a240160d7546a47b6aeba0e9","source":{"kind":"arxiv","id":"2410.20622","version":1},"attestation_state":"computed","paper":{"title":"Kernel Approximation of Fisher-Rao Gradient Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AP"],"primary_cat":"stat.ML","authors_text":"Alexander Mielke, Jia-Jie Zhu","submitted_at":"2024-10-27T22:52:08Z","abstract_excerpt":"The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous investigation of Fisher-Rao and Wasserstein type gradient flows concerning their gradient structures, flow equations, and their kernel approximations. Specifically, we focus on the Fisher-Rao (also known as Hellinger) geometry and its various kernel-based approximations, developing a principled theoretical framework using tools from PDE gradient flows and o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.20622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-10-27T22:52:08Z","cross_cats_sorted":["cs.LG","math.AP"],"title_canon_sha256":"2fe21f2dea9dd6181a72d6a2a0e001f593b60457e4196fd0f5d9532dac739e6d","abstract_canon_sha256":"0cf542fe97c849815b37d744bb3385330eb8489dd761c71ec5819e4c642a3b07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:27:08.314134Z","signature_b64":"rT++BEbtfsHw6Q+fqEwzr4uKqMoJhtwX0HjsOlWf0YtnPEMhn7npiSHapNDNdkLTaTY6Yb0rfjeocdnShn5oDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c4f2a9735796a7f3aadb6dd27fe346e73e8a9f6a240160d7546a47b6aeba0e9","last_reissued_at":"2026-07-05T09:27:08.313638Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:27:08.313638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kernel Approximation of Fisher-Rao Gradient Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.AP"],"primary_cat":"stat.ML","authors_text":"Alexander Mielke, Jia-Jie Zhu","submitted_at":"2024-10-27T22:52:08Z","abstract_excerpt":"The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous investigation of Fisher-Rao and Wasserstein type gradient flows concerning their gradient structures, flow equations, and their kernel approximations. Specifically, we focus on the Fisher-Rao (also known as Hellinger) geometry and its various kernel-based approximations, developing a principled theoretical framework using tools from PDE gradient flows and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20622","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/2410.20622/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2410.20622","created_at":"2026-07-05T09:27:08.313699+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.20622v1","created_at":"2026-07-05T09:27:08.313699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.20622","created_at":"2026-07-05T09:27:08.313699+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRHSVFZVPFVH","created_at":"2026-07-05T09:27:08.313699+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRHSVFZVPFVH6OVN","created_at":"2026-07-05T09:27:08.313699+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRHSVFZV","created_at":"2026-07-05T09:27:08.313699+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2502.10600","citing_title":"Weighted quantization using MMD: From mean field to mean shift via gradient flows","ref_index":92,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11884","citing_title":"Sobolev Regularized MMD Gradient Flow","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20301","citing_title":"Properties and limitations of geometric tempering for gradient flow dynamics","ref_index":100,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ","json":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ.json","graph_json":"https://pith.science/api/pith-number/HRHSVFZVPFVH6OVNW3OSP7RUNZ/graph.json","events_json":"https://pith.science/api/pith-number/HRHSVFZVPFVH6OVNW3OSP7RUNZ/events.json","paper":"https://pith.science/paper/HRHSVFZV"},"agent_actions":{"view_html":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ","download_json":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ.json","view_paper":"https://pith.science/paper/HRHSVFZV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.20622&json=true","fetch_graph":"https://pith.science/api/pith-number/HRHSVFZVPFVH6OVNW3OSP7RUNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/HRHSVFZVPFVH6OVNW3OSP7RUNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ/action/storage_attestation","attest_author":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ/action/author_attestation","sign_citation":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ/action/citation_signature","submit_replication":"https://pith.science/pith/HRHSVFZVPFVH6OVNW3OSP7RUNZ/action/replication_record"}},"created_at":"2026-07-05T09:27:08.313699+00:00","updated_at":"2026-07-05T09:27:08.313699+00:00"}