{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001163938,0.0008610536,0.0009985946,0.002511517,0.001955428,0.003288011,0.0009187248,0.0009077719,0.005732771],"category_scores_gemma":[0.003041008,0.0004824598,0.00113825,0.001203671,0.002999432,0.003871347,0.002910171,0.001931987,0.0009532079],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009585196,"about_ca_system_score_gemma":0.0008065327,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001398631,"about_ca_topic_score_gemma":0.0006677328,"domain_scores_codex":[0.9980849,0.0003184685,0.0001196507,0.0004963817,0.0006551641,0.0003254229],"domain_scores_gemma":[0.9982224,0.0003533016,0.0003773776,0.0002244388,0.0004566511,0.0003658557],"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":[0.00004552058,0.00002795144,0.001013611,0.00004919723,0.00002179885,0.0001173762,0.0001971268,0.002180454,0.002199275,0.9843827,0.002128323,0.007636749],"study_design_scores_gemma":[0.00002229274,0.00006088365,0.001226231,0.00003368146,0.00002069045,0.0004118818,0.000193329,0.02941614,0.001673449,0.9555344,0.01136647,0.00004056426],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5911767,0.001249531,0.3384878,0.001461958,0.0003971105,0.0001093774,0.002178685,0.0004728143,0.06446599],"genre_scores_gemma":[0.932749,0.0008829939,0.03637001,0.0004632457,0.0005978214,0.0001387327,0.003367279,0.0003062487,0.02512475],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005732771,"threshold_uncertainty_score":0.01917803,"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."}}