{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:5453QCWQHKIXRY7GHSKL37FAPJ","short_pith_number":"pith:5453QCWQ","schema_version":"1.0","canonical_sha256":"ef3bb80ad03a9178e3e63c94bdfca07a6070d06d99de9115f8335225c6299470","source":{"kind":"arxiv","id":"2207.02851","version":1},"attestation_state":"computed","paper":{"title":"Tensor networks in machine learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI","cs.LG"],"primary_cat":"quant-ph","authors_text":"Ivan Oseledets, Jacob Biamonte, Richik Sengupta, Soumik Adhikary","submitted_at":"2022-07-06T18:00:00Z","abstract_excerpt":"A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear maps. This is reminiscent to how a Boolean function might be decomposed into a gate array: this represents a special case of tensor decomposition, in which the tensor entries are replaced by 0, 1 and the factorisation becomes exact. The collection of associated techniques are called, tensor network methods: the subject developed independently in several disti"},"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":"2207.02851","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-07-06T18:00:00Z","cross_cats_sorted":["cond-mat.dis-nn","cs.AI","cs.LG"],"title_canon_sha256":"fad731547445908532460d1693dccd46cef6291e6388a6823194bcf71a8c662f","abstract_canon_sha256":"311dac89c34c762dc1041ccbd5f896c432d7f1bfe4e389399dbecd3b8f35cf12"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:16.601905Z","signature_b64":"eyElT9AcWL06AGKLMr9wfxKm4/CIgJz8rJn1QMzByKbNkbZXJeY91iV3DSas9X2tHX+O3VBFOn7IMYXQwGh+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef3bb80ad03a9178e3e63c94bdfca07a6070d06d99de9115f8335225c6299470","last_reissued_at":"2026-07-05T04:38:16.601491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:16.601491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor networks in machine learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI","cs.LG"],"primary_cat":"quant-ph","authors_text":"Ivan Oseledets, Jacob Biamonte, Richik Sengupta, Soumik Adhikary","submitted_at":"2022-07-06T18:00:00Z","abstract_excerpt":"A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear maps. This is reminiscent to how a Boolean function might be decomposed into a gate array: this represents a special case of tensor decomposition, in which the tensor entries are replaced by 0, 1 and the factorisation becomes exact. The collection of associated techniques are called, tensor network methods: the subject developed independently in several disti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02851","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/2207.02851/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":"2207.02851","created_at":"2026-07-05T04:38:16.601550+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.02851v1","created_at":"2026-07-05T04:38:16.601550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.02851","created_at":"2026-07-05T04:38:16.601550+00:00"},{"alias_kind":"pith_short_12","alias_value":"5453QCWQHKIX","created_at":"2026-07-05T04:38:16.601550+00:00"},{"alias_kind":"pith_short_16","alias_value":"5453QCWQHKIXRY7G","created_at":"2026-07-05T04:38:16.601550+00:00"},{"alias_kind":"pith_short_8","alias_value":"5453QCWQ","created_at":"2026-07-05T04:38:16.601550+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2503.20683","citing_title":"New perspectives on quantum kernels through the lens of entangled tensor kernels","ref_index":47,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ","json":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ.json","graph_json":"https://pith.science/api/pith-number/5453QCWQHKIXRY7GHSKL37FAPJ/graph.json","events_json":"https://pith.science/api/pith-number/5453QCWQHKIXRY7GHSKL37FAPJ/events.json","paper":"https://pith.science/paper/5453QCWQ"},"agent_actions":{"view_html":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ","download_json":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ.json","view_paper":"https://pith.science/paper/5453QCWQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.02851&json=true","fetch_graph":"https://pith.science/api/pith-number/5453QCWQHKIXRY7GHSKL37FAPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/5453QCWQHKIXRY7GHSKL37FAPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ/action/storage_attestation","attest_author":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ/action/author_attestation","sign_citation":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ/action/citation_signature","submit_replication":"https://pith.science/pith/5453QCWQHKIXRY7GHSKL37FAPJ/action/replication_record"}},"created_at":"2026-07-05T04:38:16.601550+00:00","updated_at":"2026-07-05T04:38:16.601550+00:00"}