{"id":"W4286891768","doi":"10.48550/arxiv.2110.15479","title":"The Set of Orthogonal Tensor Trains","year":2021,"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":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Tensor (intrinsic definition); Rank (graph theory); Mathematics; Set (abstract data type); Extension (predicate logic); Quadratic equation; Decomposition; Pure mathematics; Invariants of tensors; Type (biology); Algebra over a field; Applied mathematics; Combinatorics; Computer science; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001645009,0.0001739325,0.0002656867,0.00006109844,0.0001889446,0.00003966011,0.0005118606,0.0001701096,0.0001577165],"category_scores_gemma":[0.00006544735,0.0001560008,0.0002910928,0.0002399075,0.0001698877,0.00003884454,0.0003490256,0.0003775992,0.00001909265],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000539443,"about_ca_system_score_gemma":0.0001294653,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001374944,"about_ca_topic_score_gemma":0.00008529488,"domain_scores_codex":[0.9990145,0.0001053422,0.0002349691,0.0003919121,0.0000777031,0.0001755854],"domain_scores_gemma":[0.9981839,0.0004045857,0.0002772954,0.0008189718,0.0002346905,0.0000805517],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002560725,0.0001472532,0.0006412066,0.0001140511,0.0002128197,0.00005278774,0.0003600793,0.002590694,0.0002633955,0.9932969,0.002040085,0.000255104],"study_design_scores_gemma":[0.001265286,0.00005766472,0.008003906,0.0003053353,0.0007719613,0.00003280822,0.004843247,0.03041653,0.001274921,0.9408324,0.01123194,0.0009640528],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9678448,0.00003715736,0.025531,0.0004297497,0.0001340703,0.0003080879,0.000175212,0.00009658353,0.005443341],"genre_scores_gemma":[0.995585,0.0001280207,0.0009952282,0.00003985374,0.000055556,0.000002141788,0.00005349014,0.00001941114,0.003121273],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05246457,"threshold_uncertainty_score":0.6361526,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1711197924235739,"score_gpt":0.2480399177449049,"score_spread":0.07692012532133097,"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."}}