{"id":"W2970250826","doi":"","title":"Piecewise Strong Convexity of Neural Networks","year":2019,"lang":"en","type":"article","venue":"Neural Information Processing Systems","topic":"Stochastic Gradient Optimization Techniques","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Maxima and minima; Piecewise; Convexity; Artificial neural network; Mathematics; Differentiable function; Stochastic gradient descent; Convex function; Applied mathematics; Norm (philosophy); Open set; Regularization (linguistics); Mathematical optimization; Regular polygon; Algorithm; Computer science; Mathematical analysis; Discrete mathematics; Artificial intelligence; Geometry","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":[0.0002612165,0.0001444039,0.0002246967,0.0001861827,0.00008069936,0.0003580443,0.0005624454,0.00008267094,0.000006170826],"category_scores_gemma":[0.00003733877,0.0001298552,0.00004551287,0.0004878411,0.00003987433,0.00435501,0.0001103454,0.0001380184,0.00001519975],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004040214,"about_ca_system_score_gemma":0.00004336196,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002141172,"about_ca_topic_score_gemma":1.697679e-7,"domain_scores_codex":[0.9985529,0.00004263699,0.0006501456,0.0001509235,0.0003748732,0.0002284912],"domain_scores_gemma":[0.9985363,0.00004408813,0.0006242095,0.0003526253,0.0003781165,0.00006461831],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00001874127,0.0000331259,0.0034611,0.0006845559,0.00001321156,6.485996e-7,0.001829195,0.8838913,0.00007954102,0.04833514,0.0005792625,0.0610742],"study_design_scores_gemma":[0.0002342398,0.00007322687,0.0003140458,0.00007589637,0.000003000716,0.00001954891,0.00009262007,0.9987198,0.0001488011,0.00004744125,0.0001439432,0.0001274964],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01461627,0.0001135362,0.9815039,0.00008003061,0.0009248306,0.0004866033,0.000002349854,0.0004238013,0.001848692],"genre_scores_gemma":[0.996072,0.00000133299,0.003666252,0.0001288059,0.00003055703,0.0000259374,0.00001390137,0.000006175305,0.00005504808],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9814557,"threshold_uncertainty_score":0.5295339,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01416853856891275,"score_gpt":0.2348622963457124,"score_spread":0.2206937577767997,"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."}}