{"id":"W3174935984","doi":"","title":"Size and Depth Separation in Approximating Natural Functions with Neural Networks","year":2021,"lang":"en","type":"article","venue":"Conference on Learning Theory","topic":"Machine Learning and Algorithms","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Lipschitz continuity; Bounded function; Mathematics; Function (biology); Polynomial; Artificial neural network; Constant (computer programming); Computational complexity theory; Discrete mathematics; Algorithm; Computer science; Pure mathematics; Artificial intelligence; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0004989504,0.000136684,0.0001515238,0.00005453868,0.0002222714,0.0002627035,0.0001668095,0.00004868591,0.00002571237],"category_scores_gemma":[0.0003897195,0.0001138237,0.00002196557,0.0003103898,0.00005263436,0.0002325097,0.0001020229,0.0008013946,0.000006990187],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000168586,"about_ca_system_score_gemma":0.00005531553,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007296311,"about_ca_topic_score_gemma":0.00002047951,"domain_scores_codex":[0.9986739,0.0004232595,0.0001462752,0.0003846579,0.0001398876,0.0002319785],"domain_scores_gemma":[0.9990638,0.0005121085,0.00008802529,0.0002097114,0.00007192884,0.00005445827],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00007786448,0.00007214249,0.01439118,0.00002524894,0.00002440907,0.0001052626,0.002625241,0.2248852,0.0004379823,0.2230602,0.00001760054,0.5342777],"study_design_scores_gemma":[0.0003216217,0.0001172219,0.01482996,0.00006627056,0.00000369704,0.00005040039,0.0003600048,0.9822786,0.00002672965,0.001684407,0.0001026151,0.0001584535],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2083793,0.0002236874,0.7813597,0.0007269239,0.0002419886,0.00008929834,1.650335e-7,0.0002356432,0.008743345],"genre_scores_gemma":[0.9895741,0.000008715325,0.007648611,0.0001745315,0.00005855224,0.0000106271,0.000005811704,0.000009315093,0.002509732],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7811949,"threshold_uncertainty_score":0.4641596,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01089248834608676,"score_gpt":0.2541372997461577,"score_spread":0.243244811400071,"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."}}