{"id":"W4386044647","doi":"10.48550/arxiv.2308.08977","title":"Hitting the High-Dimensional Notes: An ODE for SGD learning dynamics on GLMs and multi-index models","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Applied mathematics; Ordinary differential equation; Stability (learning theory); Equivalence (formal languages); Rate of convergence; Covariance; Computer science; Statistics; Differential equation; Mathematical analysis; Machine learning; Discrete mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001547316,0.0005800746,0.0007566307,0.0008387035,0.0005737681,0.001612251,0.001071404,0.001791016,0.003189378],"category_scores_gemma":[0.008170124,0.0003673547,0.0008666228,0.0004715929,0.002580944,0.002467637,0.002341511,0.001739761,0.0004217086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001496467,"about_ca_system_score_gemma":0.0007999658,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003818492,"about_ca_topic_score_gemma":0.002215654,"domain_scores_codex":[0.999637,0.0001290575,0.00002251508,0.00007166266,0.000102463,0.00003724336],"domain_scores_gemma":[0.9983122,0.0007649252,0.0003090234,0.0001367478,0.0002443528,0.0002326945],"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":[0.00003187356,0.00002935185,0.001432563,0.00008777681,0.00003462922,0.0001954365,0.0001926491,0.3806951,0.003741051,0.6048258,0.001800449,0.006933346],"study_design_scores_gemma":[0.000004108162,0.000009405326,0.000129113,0.000008658299,0.000002822521,0.00002406951,0.00001079114,0.9319636,0.0001450826,0.0672977,0.0003965506,0.000008114534],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07839808,0.0006437442,0.908982,0.002095273,0.0001328063,0.0000452051,0.0001655394,0.0001960727,0.009341152],"genre_scores_gemma":[0.8879297,0.0009714021,0.09225722,0.0006453412,0.0001703595,0.0001920067,0.0002235164,0.0001974832,0.01741295],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003818492,"threshold_uncertainty_score":0.01085764,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3284815676521052,"score_gpt":0.2874754231619534,"score_spread":0.04100614449015183,"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."}}