{"id":"W7117079369","doi":"","title":"Towards Sharp Minimax Risk Bounds for Operator Learning","year":2025,"lang":"","type":"article","venue":"ArXiv.org","topic":"Statistical Methods and Inference","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Hausdorff Center for Mathematics; Deutsche Forschungsgemeinschaft","keywords":"Minimax; Lipschitz continuity; Covariance operator; Operator (biology); Spectrum (functional analysis); Upper and lower bounds; Bounded function; Covariance; Measure (data warehouse)","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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch","metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001802354,0.0005441378,0.0009621127,0.0001577376,0.0008654699,0.0003009618,0.0005833594,0.0003965759,0.002029455],"category_scores_gemma":[0.02891748,0.0005111814,0.0003422892,0.0005490214,0.000295712,0.0001575013,0.0003562204,0.0009353553,0.000292542],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001572774,"about_ca_system_score_gemma":0.0005871772,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009520604,"about_ca_topic_score_gemma":0.00001155373,"domain_scores_codex":[0.9962344,0.0005244857,0.001134872,0.0008865926,0.0003076548,0.0009120087],"domain_scores_gemma":[0.9937311,0.004383555,0.000367944,0.0007089981,0.0005407445,0.0002676131],"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":[0.0004303958,0.0008593067,0.3398893,0.002545499,0.0009352326,0.00002359275,0.002650756,0.00001839201,0.002976959,0.3651262,0.01445627,0.270088],"study_design_scores_gemma":[0.006136273,0.002693772,0.219228,0.002358356,0.002762473,0.000008444419,0.003091475,0.04559075,0.02373459,0.3983179,0.2935245,0.002553537],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4961977,0.0009317434,0.4862723,0.0007972349,0.001474315,0.0008620198,0.0002858012,0.0001143428,0.01306454],"genre_scores_gemma":[0.7025024,0.0004823524,0.2819939,0.0006708678,0.0004102563,0.0002388522,0.00001639234,0.00008534524,0.01359963],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2790682,"threshold_uncertainty_score":0.999734,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1010603405838089,"score_gpt":0.399852165307802,"score_spread":0.2987918247239932,"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."}}