{"id":"W4414631669","doi":"10.48550/arxiv.2504.15558","title":"Dynamical mean-field analysis of adaptive Langevin diffusions: Replica-symmetric fixed point and empirical Bayes","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Bayesian Methods and Mixture Models","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs; Abdus Salam International Centre for Theoretical Physics; National Science Foundation","keywords":"Langevin dynamics; Limit (mathematics); Langevin equation; Bayesian probability; Posterior probability; Scalar (mathematics); Dynamical systems theory; Trajectory; Kalman filter; Fixed point","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":[0.005303255,0.001151807,0.001467307,0.001899437,0.0007783385,0.001580559,0.002554164,0.002377688,0.002901827],"category_scores_gemma":[0.01928566,0.0008251034,0.001609359,0.0009039195,0.003673298,0.003791607,0.00222491,0.002655018,0.0003715503],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002476823,"about_ca_system_score_gemma":0.001413731,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005099886,"about_ca_topic_score_gemma":0.003066111,"domain_scores_codex":[0.9989999,0.0004912697,0.00003903016,0.0001649073,0.0002259967,0.00007890358],"domain_scores_gemma":[0.9926941,0.005238863,0.0007520872,0.0003639715,0.0006371225,0.0003138911],"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":[0.00001395692,0.00001857277,0.0006593853,0.00006647633,0.00004168811,0.0000726752,0.000113647,0.158517,0.0006295362,0.8356541,0.0005541552,0.003658783],"study_design_scores_gemma":[0.000006439693,0.000007831341,0.0001402019,0.00001852287,0.000006100137,0.0000184424,0.00001348728,0.7381523,0.0001197054,0.2609636,0.0005380555,0.00001523128],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02436401,0.0009365618,0.970224,0.001031414,0.00006765029,0.00003964595,0.00008538368,0.0000929062,0.003158443],"genre_scores_gemma":[0.77881,0.002960854,0.2009817,0.0006663782,0.0003893529,0.0004889876,0.0003781235,0.0003116586,0.01501289],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005303255,"threshold_uncertainty_score":0.02804661,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05557580835663348,"score_gpt":0.3329894941702315,"score_spread":0.277413685813598,"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."}}