{"id":"W4379251772","doi":"10.48550/arxiv.2306.00091","title":"A General Framework for Equivariant Neural Networks on Reductive Lie Groups","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Computational Physics and Python Applications","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lie group; Equivariant map; Simple Lie group; Representation of a Lie group; Homogeneous space; Computer science; Pure mathematics; Mathematics; Algebra over a field; Geometry","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001547756,0.0002746014,0.0002568703,0.0001639857,0.0002577174,0.0001811754,0.001433994,0.0002295881,0.00000485386],"category_scores_gemma":[0.00002940793,0.0003250662,0.0002838571,0.0006878416,0.00006274896,0.0001450697,0.001322698,0.0006012194,0.00004808464],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001448061,"about_ca_system_score_gemma":0.0001186653,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004885482,"about_ca_topic_score_gemma":0.00000516872,"domain_scores_codex":[0.9981527,0.00006862806,0.0001785217,0.001158847,0.00009523897,0.0003460174],"domain_scores_gemma":[0.9978754,0.0005467999,0.0002255077,0.001025454,0.0001810396,0.0001458081],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001343876,0.00003799751,0.000009390337,0.000006723251,0.00003569745,0.00001167943,0.00005104483,0.4817281,0.000001419988,0.5170838,0.0004791283,0.0005415753],"study_design_scores_gemma":[0.00009667299,0.00003522792,0.0003922504,0.00002163351,0.00001643587,5.847396e-7,0.000006309572,0.5166562,0.000002742088,0.4824912,0.0001051522,0.0001756544],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01987486,0.00001284065,0.9766256,0.0009821353,0.001288922,0.0005696911,0.0000499842,0.0003199705,0.0002759864],"genre_scores_gemma":[0.9761294,0.00002283259,0.02200634,0.000296293,0.0007656767,0.00001826488,0.00009851182,0.00003199207,0.0006307045],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9562545,"threshold_uncertainty_score":0.9999201,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1116693147691179,"score_gpt":0.2381337001109063,"score_spread":0.1264643853417884,"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."}}