{"id":"W53417064","doi":"10.1007/3-540-46084-5_46","title":"Associative Arithmetic with Boltzmann Machines: The Role of Number Representations","year":2002,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Cognitive and developmental aspects of mathematical skills","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Numerosity adaptation effect; Mental arithmetic; Learnability; Boltzmann machine; Computer science; Associative property; Numerical cognition; Arithmetic; Cognition; Mathematics; Artificial intelligence; Psychology; Artificial neural network; Pure mathematics","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":[0.001009275,0.0006356373,0.0007734122,0.00059025,0.0006570895,0.003722513,0.002160598,0.001409484,0.007660388],"category_scores_gemma":[0.004892282,0.0006400369,0.0007126389,0.001091356,0.00400457,0.01021491,0.001749525,0.002635163,0.001525762],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006300575,"about_ca_system_score_gemma":0.000570509,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004256617,"about_ca_topic_score_gemma":0.000490529,"domain_scores_codex":[0.9994693,0.0002483444,0.00002521272,0.00009295859,0.0001272339,0.00003691268],"domain_scores_gemma":[0.9989554,0.0006453766,0.00006886959,0.000189712,0.00008382383,0.00005681896],"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":[0.000007203774,0.000005426809,0.00004968305,0.00002725139,0.000005409519,0.00001220349,0.00005701777,0.003262561,0.0001913803,0.9855943,0.0009837858,0.009803787],"study_design_scores_gemma":[0.000001451236,0.000002031769,0.0000258064,0.00000482458,0.000001363882,0.00001697834,0.000007105809,0.008318049,0.00008003427,0.9899006,0.001638527,0.000003180224],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03792362,0.01624309,0.7678869,0.004040695,0.001292023,0.00004839783,0.000137173,0.0005091883,0.1719188],"genre_scores_gemma":[0.69955,0.01126772,0.2520436,0.0006527717,0.002121937,0.0001949085,0.0002065984,0.0002634689,0.03369904],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007660388,"threshold_uncertainty_score":0.02562654,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0185554863482013,"score_gpt":0.2795964434373269,"score_spread":0.2610409570891256,"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."}}