{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KQHABRQ3MP7QDDX2GIU45OOUNF","short_pith_number":"pith:KQHABRQ3","schema_version":"1.0","canonical_sha256":"540e00c61b63ff018efa3229ceb9d46957d99f49b02c2c6ad14ed6477f2fd8d2","source":{"kind":"arxiv","id":"1711.05424","version":2},"attestation_state":"computed","paper":{"title":"The landscape of the spiked tensor model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Gerard Ben Arous, Mihai Nica, Song Mei","submitted_at":"2017-11-15T06:23:43Z","abstract_excerpt":"We consider the problem of estimating a large rank-one tensor ${\\boldsymbol u}^{\\otimes k}\\in({\\mathbb R}^{n})^{\\otimes k}$, $k\\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\\lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably no polynomial-time algorithm is known that achieved this goal unless $\\lambda\\ge C n^{(k-2)/4}$ and even powerful semidefinite programming relaxations appear to fail for $1\\ll \\lambda\\ll n^{(k-2)/4}$.\n  In order to elucidate this behavior, we co"},"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":"1711.05424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-11-15T06:23:43Z","cross_cats_sorted":["math.PR","stat.ML","stat.TH"],"title_canon_sha256":"4e3e541345b4a0c49a8a2c7e8b3515949a5defefe087105eb4c7ddc00f252f60","abstract_canon_sha256":"bfad0779e314a5b487feb7a1e9814e5275dfa189c2239b9ac9e3c9190cc34748"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:07.347635Z","signature_b64":"UayXYAT9gZZ6sYiRcJz7a0m7qpaPb4g7nPfJspRLA/YprC94bFkCB7Y5AAOBr+ALKOmWuePMphzBhbYEMwErAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"540e00c61b63ff018efa3229ceb9d46957d99f49b02c2c6ad14ed6477f2fd8d2","last_reissued_at":"2026-05-18T00:25:07.347093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:07.347093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The landscape of the spiked tensor model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Gerard Ben Arous, Mihai Nica, Song Mei","submitted_at":"2017-11-15T06:23:43Z","abstract_excerpt":"We consider the problem of estimating a large rank-one tensor ${\\boldsymbol u}^{\\otimes k}\\in({\\mathbb R}^{n})^{\\otimes k}$, $k\\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\\lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably no polynomial-time algorithm is known that achieved this goal unless $\\lambda\\ge C n^{(k-2)/4}$ and even powerful semidefinite programming relaxations appear to fail for $1\\ll \\lambda\\ll n^{(k-2)/4}$.\n  In order to elucidate this behavior, we co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05424","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":""},"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":"1711.05424","created_at":"2026-05-18T00:25:07.347186+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.05424v2","created_at":"2026-05-18T00:25:07.347186+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05424","created_at":"2026-05-18T00:25:07.347186+00:00"},{"alias_kind":"pith_short_12","alias_value":"KQHABRQ3MP7Q","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KQHABRQ3MP7QDDX2","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KQHABRQ3","created_at":"2026-05-18T12:31:24.725408+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/KQHABRQ3MP7QDDX2GIU45OOUNF","json":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF.json","graph_json":"https://pith.science/api/pith-number/KQHABRQ3MP7QDDX2GIU45OOUNF/graph.json","events_json":"https://pith.science/api/pith-number/KQHABRQ3MP7QDDX2GIU45OOUNF/events.json","paper":"https://pith.science/paper/KQHABRQ3"},"agent_actions":{"view_html":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF","download_json":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF.json","view_paper":"https://pith.science/paper/KQHABRQ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.05424&json=true","fetch_graph":"https://pith.science/api/pith-number/KQHABRQ3MP7QDDX2GIU45OOUNF/graph.json","fetch_events":"https://pith.science/api/pith-number/KQHABRQ3MP7QDDX2GIU45OOUNF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF/action/storage_attestation","attest_author":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF/action/author_attestation","sign_citation":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF/action/citation_signature","submit_replication":"https://pith.science/pith/KQHABRQ3MP7QDDX2GIU45OOUNF/action/replication_record"}},"created_at":"2026-05-18T00:25:07.347186+00:00","updated_at":"2026-05-18T00:25:07.347186+00:00"}