{"id":"W2596625124","doi":"","title":"Nearly-tight VC-dimension bounds for piecewise linear neural networks","year":2017,"lang":"en","type":"article","venue":"arXiv (Cornell University)","topic":"Stochastic Gradient Optimization Techniques","field":"Computer Science","cited_by":108,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of British Columbia","funders":"","keywords":"Dimension (graph theory); Upper and lower bounds; Piecewise linear function; Mathematics; Combinatorics; Omega; Piecewise; VC dimension; Function (biology); Range (aeronautics); Artificial neural network; Discrete mathematics; Mathematical analysis; Physics; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004998351,0.003561106,0.002717022,0.003102455,0.001498986,0.004623688,0.003416214,0.00271658,0.00858715],"category_scores_gemma":[0.04550204,0.001443534,0.001805031,0.002969266,0.003847652,0.01014654,0.007208521,0.01062614,0.001777709],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003998405,"about_ca_system_score_gemma":0.001516146,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002652996,"about_ca_topic_score_gemma":0.002805754,"domain_scores_codex":[0.9960194,0.001205019,0.0001959215,0.0007822248,0.001124451,0.000673062],"domain_scores_gemma":[0.9689126,0.02334552,0.001325374,0.002787849,0.002481413,0.001147264],"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":[0.0004155225,0.0002047439,0.003092345,0.0007786527,0.000253623,0.0002669808,0.0004047153,0.4190646,0.0069906,0.4649099,0.0176756,0.08594283],"study_design_scores_gemma":[0.00001689231,0.00005717288,0.0006326798,0.000127207,0.00003878359,0.0001025167,0.0000364868,0.7330203,0.001927465,0.2604842,0.00351181,0.00004448112],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03964284,0.01128024,0.9161366,0.004517388,0.0004910865,0.0001079294,0.001116063,0.001444441,0.0252634],"genre_scores_gemma":[0.8035972,0.01011004,0.1631265,0.002955248,0.001796148,0.0009603001,0.002134087,0.001319016,0.01400141],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00858715,"threshold_uncertainty_score":0.02901053,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06326245405350339,"score_gpt":0.2035452813463818,"score_spread":0.1402828272928784,"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."}}