{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:V32KLOMWMKMSH6FON3Q3VY7F5N","short_pith_number":"pith:V32KLOMW","schema_version":"1.0","canonical_sha256":"aef4a5b996629923f8ae6ee1bae3e5eb66854709c86df4f651b0a46806534a9a","source":{"kind":"arxiv","id":"2412.06111","version":1},"attestation_state":"computed","paper":{"title":"Randomized algorithms for streaming low-rank approximation in tree tensor network format","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alberto Bucci, Gianfranco Verzella","submitted_at":"2024-12-09T00:11:01Z","abstract_excerpt":"In this work, we present the tree tensor network Nystr\\\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nystr\\\"om approximation for matrices, that is randomized, single-pass, streamable, and cost-effective. Additionally, the structure of the sketching allows for parallel implementation. We provide a deterministic error bound for the algorithm and, in "},"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":"2412.06111","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-12-09T00:11:01Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2d971057c493ce1ff8b6af5896918cf6bb83c2e9d740be4982d3c9045df4cc76","abstract_canon_sha256":"a993a065bcc3de55f0072d50edad2ad66e2b80f47329517622d231a2c9a06404"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:46:15.217067Z","signature_b64":"ViN6YqtuKBzKt7BsiE/EvtavDnThjSXAAIRt5SXFnu8anzGHY3ryfh0B7056/ZFVrk0nRJPCGbxgEmSaSwV6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aef4a5b996629923f8ae6ee1bae3e5eb66854709c86df4f651b0a46806534a9a","last_reissued_at":"2026-07-05T09:46:15.216590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:46:15.216590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Randomized algorithms for streaming low-rank approximation in tree tensor network format","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alberto Bucci, Gianfranco Verzella","submitted_at":"2024-12-09T00:11:01Z","abstract_excerpt":"In this work, we present the tree tensor network Nystr\\\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format, enabling a unified treatment of various existing methods. Our method retains the key features of the generalized Nystr\\\"om approximation for matrices, that is randomized, single-pass, streamable, and cost-effective. Additionally, the structure of the sketching allows for parallel implementation. We provide a deterministic error bound for the algorithm and, in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06111","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/2412.06111/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":"2412.06111","created_at":"2026-07-05T09:46:15.216656+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.06111v1","created_at":"2026-07-05T09:46:15.216656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.06111","created_at":"2026-07-05T09:46:15.216656+00:00"},{"alias_kind":"pith_short_12","alias_value":"V32KLOMWMKMS","created_at":"2026-07-05T09:46:15.216656+00:00"},{"alias_kind":"pith_short_16","alias_value":"V32KLOMWMKMSH6FO","created_at":"2026-07-05T09:46:15.216656+00:00"},{"alias_kind":"pith_short_8","alias_value":"V32KLOMW","created_at":"2026-07-05T09:46:15.216656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N","json":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N.json","graph_json":"https://pith.science/api/pith-number/V32KLOMWMKMSH6FON3Q3VY7F5N/graph.json","events_json":"https://pith.science/api/pith-number/V32KLOMWMKMSH6FON3Q3VY7F5N/events.json","paper":"https://pith.science/paper/V32KLOMW"},"agent_actions":{"view_html":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N","download_json":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N.json","view_paper":"https://pith.science/paper/V32KLOMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.06111&json=true","fetch_graph":"https://pith.science/api/pith-number/V32KLOMWMKMSH6FON3Q3VY7F5N/graph.json","fetch_events":"https://pith.science/api/pith-number/V32KLOMWMKMSH6FON3Q3VY7F5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N/action/storage_attestation","attest_author":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N/action/author_attestation","sign_citation":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N/action/citation_signature","submit_replication":"https://pith.science/pith/V32KLOMWMKMSH6FON3Q3VY7F5N/action/replication_record"}},"created_at":"2026-07-05T09:46:15.216656+00:00","updated_at":"2026-07-05T09:46:15.216656+00:00"}