{"id":"W3008903234","doi":"10.4230/lipics.ccc.2020.35","title":"Geometric Rank of Tensors and Subrank of Matrix Multiplication","year":2020,"lang":"en","type":"preprint","venue":"UvA-DARE (University of Amsterdam)","topic":"Tensor decomposition and applications","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"York University; National Science Foundation","keywords":"Rank (graph theory); Mathematics; Strassen algorithm; Combinatorics; Matrix multiplication; Matrix (chemical analysis); Upper and lower bounds; Discrete mathematics; Physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001351889,0.0009607757,0.0007674551,0.002929612,0.001220256,0.003442477,0.0008105816,0.0006525599,0.007876989],"category_scores_gemma":[0.007572288,0.0003466874,0.0005108144,0.001661376,0.004276608,0.006376156,0.00237786,0.002411626,0.001674642],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001045555,"about_ca_system_score_gemma":0.0006375092,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006196589,"about_ca_topic_score_gemma":0.0006715076,"domain_scores_codex":[0.9981377,0.0004441892,0.00007874418,0.0003614664,0.0006426021,0.0003351397],"domain_scores_gemma":[0.9924615,0.002904084,0.00125864,0.001191719,0.001228186,0.0009559506],"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":[0.00004600394,0.00001785616,0.0006385167,0.00005465047,0.000007746666,0.00006838454,0.0001735874,0.003668204,0.001711224,0.9804223,0.002504055,0.01068746],"study_design_scores_gemma":[0.000007672819,0.00004476953,0.0007656622,0.00002209398,0.00001021519,0.0002087508,0.0001175975,0.01971112,0.002367878,0.9682539,0.008466387,0.00002400054],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3157308,0.003320208,0.5574425,0.002726756,0.0004509339,0.00007518447,0.001036201,0.0009413913,0.118276],"genre_scores_gemma":[0.9479735,0.001481212,0.0358141,0.0003629154,0.0007852049,0.00007335073,0.0006730961,0.0001893143,0.01264731],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007876989,"threshold_uncertainty_score":0.02635115,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04372526490211509,"score_gpt":0.2836267991078776,"score_spread":0.2399015342057625,"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."}}