{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TUBFD55Y3CAE6Z2FRGKLHXVDEL","short_pith_number":"pith:TUBFD55Y","schema_version":"1.0","canonical_sha256":"9d0251f7b8d8804f67458994b3dea322fe887fe7be2febee21d85caa2c2f53dd","source":{"kind":"arxiv","id":"2405.12039","version":2},"attestation_state":"computed","paper":{"title":"Randomized Gradient Descents on Riemannian Manifolds: Almost Sure Convergence to Global Minima in and beyond Quantum Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.OC","authors_text":"Christian Arenz, Emanuel Malvetti, Gunther Dirr, Thomas Schulte-Herbr\\\"uggen","submitted_at":"2024-05-20T14:06:45Z","abstract_excerpt":"We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient descent methods, where the Riemannian gradient is replaced by a random projection of it, converge to a single local optimum almost surely despite the existence of saddle points. We consider both uniformly distributed and discrete random projections. We also discuss the time required to pass a saddle point. As a major application, we consider ground-state pr"},"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":"2405.12039","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-05-20T14:06:45Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"367ff486b77d4dddd00eb2044db4d056d01b72db8dcc7745ae250f468bf5a618","abstract_canon_sha256":"e95c6466e36fdaba1288dc6df65b937e07972f69efc97dc32c6c0f6c40114e4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:38.746589Z","signature_b64":"AX7l8EknVhYuQMEiYl4urNykDnw7H9cKXOGkzslu+MjEy7mmfjv2uiFYWipf5Rug02b5mBUwtRVPN8gf+qAsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d0251f7b8d8804f67458994b3dea322fe887fe7be2febee21d85caa2c2f53dd","last_reissued_at":"2026-07-05T11:31:38.746080Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:38.746080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Randomized Gradient Descents on Riemannian Manifolds: Almost Sure Convergence to Global Minima in and beyond Quantum Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.OC","authors_text":"Christian Arenz, Emanuel Malvetti, Gunther Dirr, Thomas Schulte-Herbr\\\"uggen","submitted_at":"2024-05-20T14:06:45Z","abstract_excerpt":"We analyze convergence of gradient-descent methods on Riemannian manifolds. In particular, we study randomization of Riemannian gradient algorithms for minimizing smooth cost functions (of Morse-Bott type). We prove that randomized gradient descent methods, where the Riemannian gradient is replaced by a random projection of it, converge to a single local optimum almost surely despite the existence of saddle points. We consider both uniformly distributed and discrete random projections. We also discuss the time required to pass a saddle point. As a major application, we consider ground-state pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.12039","kind":"arxiv","version":2},"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/2405.12039/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":"2405.12039","created_at":"2026-07-05T11:31:38.746141+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.12039v2","created_at":"2026-07-05T11:31:38.746141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.12039","created_at":"2026-07-05T11:31:38.746141+00:00"},{"alias_kind":"pith_short_12","alias_value":"TUBFD55Y3CAE","created_at":"2026-07-05T11:31:38.746141+00:00"},{"alias_kind":"pith_short_16","alias_value":"TUBFD55Y3CAE6Z2F","created_at":"2026-07-05T11:31:38.746141+00:00"},{"alias_kind":"pith_short_8","alias_value":"TUBFD55Y","created_at":"2026-07-05T11:31:38.746141+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.27795","citing_title":"Geometric Analysis of Variational Quantum Eigensolver","ref_index":51,"is_internal_anchor":false},{"citing_arxiv_id":"2603.26039","citing_title":"Achieving double-logarithmic precision dependence in optimization-based quantum unstructured search","ref_index":52,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05627","citing_title":"Loss-aware state space geometry for quantum variational algorithms","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL","json":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL.json","graph_json":"https://pith.science/api/pith-number/TUBFD55Y3CAE6Z2FRGKLHXVDEL/graph.json","events_json":"https://pith.science/api/pith-number/TUBFD55Y3CAE6Z2FRGKLHXVDEL/events.json","paper":"https://pith.science/paper/TUBFD55Y"},"agent_actions":{"view_html":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL","download_json":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL.json","view_paper":"https://pith.science/paper/TUBFD55Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.12039&json=true","fetch_graph":"https://pith.science/api/pith-number/TUBFD55Y3CAE6Z2FRGKLHXVDEL/graph.json","fetch_events":"https://pith.science/api/pith-number/TUBFD55Y3CAE6Z2FRGKLHXVDEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL/action/storage_attestation","attest_author":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL/action/author_attestation","sign_citation":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL/action/citation_signature","submit_replication":"https://pith.science/pith/TUBFD55Y3CAE6Z2FRGKLHXVDEL/action/replication_record"}},"created_at":"2026-07-05T11:31:38.746141+00:00","updated_at":"2026-07-05T11:31:38.746141+00:00"}