{"id":"W6966710554","doi":"10.48550/arxiv.2502.09074","title":"Bilevel gradient methods and the Morse parametric qualification condition","year":2025,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Discovery Air (Canada)","funders":"","keywords":"Bilevel optimization; Piecewise; Morse code; Parametric statistics; Sequence (biology); Differentiable function; Class (philosophy); Regular polygon","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":[0.002050392,0.0009684137,0.00104697,0.0007447831,0.0005204577,0.00195241,0.001170643,0.001785878,0.005729445],"category_scores_gemma":[0.009261877,0.0005913675,0.0009441534,0.0008326243,0.002505235,0.003416094,0.004011187,0.003371573,0.001436685],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008467658,"about_ca_system_score_gemma":0.00120733,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009059772,"about_ca_topic_score_gemma":0.0008081236,"domain_scores_codex":[0.9988734,0.0004703077,0.00005573635,0.000150433,0.000335054,0.0001150056],"domain_scores_gemma":[0.9978815,0.001167976,0.0002223969,0.0002532611,0.0003294065,0.0001454533],"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":[0.00002297352,0.0000285097,0.0003715144,0.0001290697,0.00002587393,0.00007622667,0.0001378657,0.1573052,0.001952734,0.8111628,0.001413503,0.02737383],"study_design_scores_gemma":[0.000009771853,0.00005501951,0.000106145,0.0000450305,0.000006449943,0.00005457703,0.00003070251,0.6584096,0.001173,0.3345245,0.00556745,0.00001766054],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.003048049,0.0001763272,0.9928522,0.0003257958,0.00002107937,0.00001701647,0.00003452244,0.00006778065,0.003457207],"genre_scores_gemma":[0.4280951,0.001356318,0.5561885,0.0007250935,0.0002495637,0.0003729236,0.000304775,0.0004546204,0.01225309],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005729445,"threshold_uncertainty_score":0.01916689,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09370189232750736,"score_gpt":0.2613209673149412,"score_spread":0.1676190749874338,"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."}}