{"id":"W4388032305","doi":"10.48550/arxiv.2310.17827","title":"A hierarchy of eigencomputations for polynomial optimization on the sphere","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Tensor decomposition and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Hierarchy; Eigenvalues and eigenvectors; Homogeneous polynomial; Polynomial; Norm (philosophy); Semidefinite programming; Upper and lower bounds; Tensor product; Computation; Combinatorics; Discrete mathematics; Applied mathematics; Mathematical optimization; Pure mathematics; Matrix polynomial; Algorithm; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001427074,0.0001545138,0.0002057262,0.0001196765,0.0001871436,0.00002422921,0.0003963068,0.0001437618,0.00009734484],"category_scores_gemma":[0.00009230671,0.0001438753,0.0002248899,0.00030123,0.0000838433,0.00003147796,0.0001706506,0.0002101577,0.00003192911],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007578903,"about_ca_system_score_gemma":0.0000923731,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002337723,"about_ca_topic_score_gemma":0.00002294184,"domain_scores_codex":[0.9991691,0.00006712679,0.0002136053,0.0003565417,0.00005693403,0.0001367141],"domain_scores_gemma":[0.9980783,0.0008937048,0.0002777335,0.0005270878,0.0001742226,0.00004895731],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00002735939,0.00009054916,0.00002121812,0.00005431434,0.00006245981,0.000001389215,0.0001112281,0.5826559,0.00001184669,0.4110058,0.005917841,0.00004008963],"study_design_scores_gemma":[0.0003476775,0.00004169773,0.0001035726,0.00008278697,0.000143184,4.96792e-7,0.0002759974,0.544564,0.0001239779,0.4537781,0.000356306,0.0001821474],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1019821,0.000003118995,0.8938088,0.0009009647,0.0001792449,0.001097967,0.0003233094,0.0001904103,0.001514126],"genre_scores_gemma":[0.9852401,0.0000218771,0.01209881,0.00006176449,0.00008396564,0.00001726652,0.0001079175,0.00003745684,0.002330834],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.883258,"threshold_uncertainty_score":0.5867065,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2369260626244867,"score_gpt":0.2631305185265006,"score_spread":0.02620445590201387,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}