{"ir_datasets": ["FiQA-2018", "ArguAna", "SCIDOCS"], "sts_datasets": ["STSBenchmark", "SICK-R", "STS22.v2"], "all_datasets": ["FiQA-2018", "ArguAna", "SCIDOCS", "STSBenchmark", "SICK-R", "STS22.v2"], "ir_metrics": ["nDCG@10", "MRR@10", "Recall@100"], "sts_metrics": ["Spearman (ρ × 100)", "Pearson (r × 100)"], "geom_options": ["All 5 Geometry Metrics", "Centroid Norm ||μ||₂", "Average Cosine", "MEV (Top-1)", "NID (Spectral Entropy)", "IsoScore"], "param_options": ["Variance Partition & Knee Parameters", "Tempering Schedules (γ_SNR, ε*, γ*)"], "all_display_cols": ["EmbGemma", "Qwen3-Emb", "Gemma3-Mean", "Gemma3-Last", "Qwen3.5-Mean", "Qwen3.5-Last", "Dedicated Mean", "Base-Mean", "Base-Last"], "model_cols": ["EmbGemma", "Qwen3-Emb", "Gemma3-Mean", "Gemma3-Last", "Qwen3.5-Mean", "Qwen3.5-Last"], "cat_cols": ["Dedicated Mean", "Base-Mean", "Base-Last"], "full_main_methods": ["Baseline", "Standardization", "R1", "R2", "Soft-ZCA", "COAST (Ours)", "ABTT (D=1)", "ABTT (D=2)", "ABTT (D=3)"], "full_ablation_methods": ["Unreg. ZCA (Σ, γ=1, ε=1e-6)", "Centered + ε* (Σ, γ=1, ε*)", "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "w/o Orth. Proj. (Σ, γ_crowd, ε*)", "Orth. Soft-ZCA (Σ_⊥, γ=1, 1e-4)", "w/o Crowd. Exp. (Σ_⊥, γ=1, ε*)", "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)"], "comp_main_methods": ["Prefix (MRL)", "PCA-k", "Whitening-k", "SpecTemp", "COAST (Ours)"], "comp_ablation_methods": ["Orth. PCA (Σ_⊥, γ=0, ε=0)", "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "w/o Orth. Proj. (Σ, γ*, ε*)"], "tables": {"task_full::Retrieval (IR)::nDCG@10": [{"Dataset": "FiQA-2018", "k": "d", "Method": "Baseline", "EmbGemma": "0.4739", "Qwen3-Emb": "0.4737", "Gemma3-Mean": "0.0589", "Gemma3-Last": "0.0246", "Qwen3.5-Mean": "0.0419", "Qwen3.5-Last": "0.0026", "Dedicated Mean": "0.4738", "Base-Mean": "0.0504", "Base-Last": "0.0136"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Standardization", "EmbGemma": "0.4704", "Qwen3-Emb": "0.4656", "Gemma3-Mean": "0.0681", "Gemma3-Last": "0.0187", "Qwen3.5-Mean": "0.0385", "Qwen3.5-Last": "0.0019", "Dedicated Mean": "0.4680", "Base-Mean": "0.0533", "Base-Last": "0.0103"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "R1", "EmbGemma": "0.4731", "Qwen3-Emb": "0.4725", "Gemma3-Mean": "0.0564", "Gemma3-Last": "0.0225", "Qwen3.5-Mean": "0.0420", "Qwen3.5-Last": "0.0025", "Dedicated Mean": "0.4728", "Base-Mean": "0.0492", "Base-Last": "0.0125"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "R2", "EmbGemma": "0.4765", "Qwen3-Emb": "0.4730", "Gemma3-Mean": "0.0572", "Gemma3-Last": "0.0223", "Qwen3.5-Mean": "0.0433", "Qwen3.5-Last": "0.0028", "Dedicated Mean": "0.4748", "Base-Mean": "0.0502", "Base-Last": "0.0126"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Soft-ZCA", "EmbGemma": "0.4056", "Qwen3-Emb": "0.4151", "Gemma3-Mean": "0.0968", "Gemma3-Last": "0.0389", "Qwen3.5-Mean": "0.0615", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4103", "Base-Mean": "0.0791", "Base-Last": "0.0215"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "COAST (Ours)", "EmbGemma": "0.4779", "Qwen3-Emb": "0.4718", "Gemma3-Mean": "0.1011", "Gemma3-Last": "0.0392", "Qwen3.5-Mean": "0.0631", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4748", "Base-Mean": "0.0821", "Base-Last": "0.0217"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "ABTT (D=1)", "EmbGemma": "0.4736", "Qwen3-Emb": "0.4769", "Gemma3-Mean": "0.0568", "Gemma3-Last": "0.0222", "Qwen3.5-Mean": "0.0378", "Qwen3.5-Last": "0.0026", "Dedicated Mean": "0.4752", "Base-Mean": "0.0473", "Base-Last": "0.0124"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "ABTT (D=2)", "EmbGemma": "0.4641", "Qwen3-Emb": "0.4765", "Gemma3-Mean": "0.0555", "Gemma3-Last": "0.0272", "Qwen3.5-Mean": "0.0422", "Qwen3.5-Last": "0.0036", "Dedicated Mean": "0.4703", "Base-Mean": "0.0489", "Base-Last": "0.0154"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "ABTT (D=3)", "EmbGemma": "0.4625", "Qwen3-Emb": "0.4676", "Gemma3-Mean": "0.0689", "Gemma3-Last": "0.0254", "Qwen3.5-Mean": "0.0446", "Qwen3.5-Last": "0.0036", "Dedicated Mean": "0.4651", "Base-Mean": "0.0567", "Base-Last": "0.0145"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Unreg. ZCA (Σ, γ=1, ε=1e-6)", "EmbGemma": "0.3773", "Qwen3-Emb": "0.4073", "Gemma3-Mean": "0.0926", "Gemma3-Last": "0.0303", "Qwen3.5-Mean": "0.0549", "Qwen3.5-Last": "0.0039", "Dedicated Mean": "0.3923", "Base-Mean": "0.0737", "Base-Last": "0.0171"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Centered + ε* (Σ, γ=1, ε*)", "EmbGemma": "0.4556", "Qwen3-Emb": "0.4533", "Gemma3-Mean": "0.1011", "Gemma3-Last": "0.0392", "Qwen3.5-Mean": "0.0617", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4544", "Base-Mean": "0.0814", "Base-Last": "0.0217"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "EmbGemma": "0.4741", "Qwen3-Emb": "0.4717", "Gemma3-Mean": "0.0968", "Gemma3-Last": "0.0389", "Qwen3.5-Mean": "0.0615", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4729", "Base-Mean": "0.0791", "Base-Last": "0.0215"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "w/o Orth. Proj. (Σ, γ_crowd, ε*)", "EmbGemma": "0.4737", "Qwen3-Emb": "0.4725", "Gemma3-Mean": "0.1011", "Gemma3-Last": "0.0392", "Qwen3.5-Mean": "0.0617", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4731", "Base-Mean": "0.0814", "Base-Last": "0.0217"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Orth. Soft-ZCA (Σ_⊥, γ=1, 1e-4)", "EmbGemma": "0.4058", "Qwen3-Emb": "0.4150", "Gemma3-Mean": "0.0964", "Gemma3-Last": "0.0389", "Qwen3.5-Mean": "0.0624", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4104", "Base-Mean": "0.0794", "Base-Last": "0.0215"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "w/o Crowd. Exp. (Σ_⊥, γ=1, ε*)", "EmbGemma": "0.4548", "Qwen3-Emb": "0.4552", "Gemma3-Mean": "0.1011", "Gemma3-Last": "0.0392", "Qwen3.5-Mean": "0.0631", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4550", "Base-Mean": "0.0821", "Base-Last": "0.0217"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "EmbGemma": "0.4497", "Qwen3-Emb": "0.4584", "Gemma3-Mean": "0.0890", "Gemma3-Last": "0.0350", "Qwen3.5-Mean": "0.0613", "Qwen3.5-Last": "0.0039", "Dedicated Mean": "0.4541", "Base-Mean": "0.0752", "Base-Last": "0.0194"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)", "EmbGemma": "0.4769", "Qwen3-Emb": "0.4718", "Gemma3-Mean": "0.0964", "Gemma3-Last": "0.0389", "Qwen3.5-Mean": "0.0624", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.4744", "Base-Mean": "0.0794", "Base-Last": "0.0215"}, {"Dataset": "ArguAna", "k": "d", "Method": "Baseline", "EmbGemma": "0.4702", "Qwen3-Emb": "0.4930", "Gemma3-Mean": "0.2938", "Gemma3-Last": "0.1124", "Qwen3.5-Mean": "0.3162", "Qwen3.5-Last": "0.1064", "Dedicated Mean": "0.4816", "Base-Mean": "0.3050", "Base-Last": "0.1094"}, {"Dataset": "ArguAna", "k": "d", "Method": "Standardization", "EmbGemma": "0.4754", "Qwen3-Emb": "0.4796", "Gemma3-Mean": "0.3172", "Gemma3-Last": "0.1299", "Qwen3.5-Mean": "0.3077", "Qwen3.5-Last": "0.1125", "Dedicated Mean": "0.4775", "Base-Mean": "0.3124", "Base-Last": "0.1212"}, {"Dataset": "ArguAna", "k": "d", "Method": "R1", "EmbGemma": "0.4760", "Qwen3-Emb": "0.4829", "Gemma3-Mean": "0.2988", "Gemma3-Last": "0.1108", "Qwen3.5-Mean": "0.2954", "Qwen3.5-Last": "0.1078", "Dedicated Mean": "0.4794", "Base-Mean": "0.2971", "Base-Last": "0.1093"}, {"Dataset": "ArguAna", "k": "d", "Method": "R2", "EmbGemma": "0.4697", "Qwen3-Emb": "0.4852", "Gemma3-Mean": "0.2985", "Gemma3-Last": "0.1121", "Qwen3.5-Mean": "0.2952", "Qwen3.5-Last": "0.1080", "Dedicated Mean": "0.4774", "Base-Mean": "0.2969", "Base-Last": "0.1100"}, {"Dataset": "ArguAna", "k": "d", "Method": "Soft-ZCA", "EmbGemma": "0.4287", "Qwen3-Emb": "0.4447", "Gemma3-Mean": "0.3599", "Gemma3-Last": "0.1584", "Qwen3.5-Mean": "0.3622", "Qwen3.5-Last": "0.1485", "Dedicated Mean": "0.4367", "Base-Mean": "0.3610", "Base-Last": "0.1534"}, {"Dataset": "ArguAna", "k": "d", "Method": "COAST (Ours)", "EmbGemma": "0.4700", "Qwen3-Emb": "0.4844", "Gemma3-Mean": "0.3528", "Gemma3-Last": "0.1596", "Qwen3.5-Mean": "0.3580", "Qwen3.5-Last": "0.1489", "Dedicated Mean": "0.4772", "Base-Mean": "0.3554", "Base-Last": "0.1543"}, {"Dataset": "ArguAna", "k": "d", "Method": "ABTT (D=1)", "EmbGemma": "0.4764", "Qwen3-Emb": "0.4825", "Gemma3-Mean": "0.3056", "Gemma3-Last": "0.1286", "Qwen3.5-Mean": "0.2986", "Qwen3.5-Last": "0.1109", "Dedicated Mean": "0.4795", "Base-Mean": "0.3021", "Base-Last": "0.1198"}, {"Dataset": "ArguAna", "k": "d", "Method": "ABTT (D=2)", "EmbGemma": "0.4767", "Qwen3-Emb": "0.4805", "Gemma3-Mean": "0.3108", "Gemma3-Last": "0.1338", "Qwen3.5-Mean": "0.3012", "Qwen3.5-Last": "0.1169", "Dedicated Mean": "0.4786", "Base-Mean": "0.3060", "Base-Last": "0.1253"}, {"Dataset": "ArguAna", "k": "d", "Method": "ABTT (D=3)", "EmbGemma": "0.4686", "Qwen3-Emb": "0.4792", "Gemma3-Mean": "0.3104", "Gemma3-Last": "0.1433", "Qwen3.5-Mean": "0.3157", "Qwen3.5-Last": "0.1301", "Dedicated Mean": "0.4739", "Base-Mean": "0.3130", "Base-Last": "0.1367"}, {"Dataset": "ArguAna", "k": "d", "Method": "Unreg. ZCA (Σ, γ=1, ε=1e-6)", "EmbGemma": "0.4014", "Qwen3-Emb": "0.4249", "Gemma3-Mean": "0.3362", "Gemma3-Last": "0.1442", "Qwen3.5-Mean": "0.3371", "Qwen3.5-Last": "0.1331", "Dedicated Mean": "0.4131", "Base-Mean": "0.3367", "Base-Last": "0.1387"}, {"Dataset": "ArguAna", "k": "d", "Method": "Centered + ε* (Σ, γ=1, ε*)", "EmbGemma": "0.4606", "Qwen3-Emb": "0.4756", "Gemma3-Mean": "0.3527", "Gemma3-Last": "0.1592", "Qwen3.5-Mean": "0.3587", "Qwen3.5-Last": "0.1485", "Dedicated Mean": "0.4681", "Base-Mean": "0.3557", "Base-Last": "0.1539"}, {"Dataset": "ArguAna", "k": "d", "Method": "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "EmbGemma": "0.4756", "Qwen3-Emb": "0.4832", "Gemma3-Mean": "0.3599", "Gemma3-Last": "0.1584", "Qwen3.5-Mean": "0.3622", "Qwen3.5-Last": "0.1485", "Dedicated Mean": "0.4794", "Base-Mean": "0.3610", "Base-Last": "0.1534"}, {"Dataset": "ArguAna", "k": "d", "Method": "w/o Orth. Proj. (Σ, γ_crowd, ε*)", "EmbGemma": "0.4754", "Qwen3-Emb": "0.4826", "Gemma3-Mean": "0.3527", "Gemma3-Last": "0.1592", "Qwen3.5-Mean": "0.3587", "Qwen3.5-Last": "0.1485", "Dedicated Mean": "0.4790", "Base-Mean": "0.3557", "Base-Last": "0.1539"}, {"Dataset": "ArguAna", "k": "d", "Method": "Orth. Soft-ZCA (Σ_⊥, γ=1, 1e-4)", "EmbGemma": "0.4336", "Qwen3-Emb": "0.4452", "Gemma3-Mean": "0.3595", "Gemma3-Last": "0.1583", "Qwen3.5-Mean": "0.3613", "Qwen3.5-Last": "0.1487", "Dedicated Mean": "0.4394", "Base-Mean": "0.3604", "Base-Last": "0.1535"}, {"Dataset": "ArguAna", "k": "d", "Method": "w/o Crowd. Exp. (Σ_⊥, γ=1, ε*)", "EmbGemma": "0.4638", "Qwen3-Emb": "0.4786", "Gemma3-Mean": "0.3528", "Gemma3-Last": "0.1596", "Qwen3.5-Mean": "0.3580", "Qwen3.5-Last": "0.1489", "Dedicated Mean": "0.4712", "Base-Mean": "0.3554", "Base-Last": "0.1543"}, {"Dataset": "ArguAna", "k": "d", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "EmbGemma": "0.4606", "Qwen3-Emb": "0.4713", "Gemma3-Mean": "0.3435", "Gemma3-Last": "0.1492", "Qwen3.5-Mean": "0.3462", "Qwen3.5-Last": "0.1346", "Dedicated Mean": "0.4660", "Base-Mean": "0.3449", "Base-Last": "0.1419"}, {"Dataset": "ArguAna", "k": "d", "Method": "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)", "EmbGemma": "0.4707", "Qwen3-Emb": "0.4842", "Gemma3-Mean": "0.3595", "Gemma3-Last": "0.1583", "Qwen3.5-Mean": "0.3613", "Qwen3.5-Last": "0.1487", "Dedicated Mean": "0.4775", "Base-Mean": "0.3604", "Base-Last": "0.1535"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "Baseline", "EmbGemma": "0.1948", "Qwen3-Emb": "0.2439", "Gemma3-Mean": "0.0302", "Gemma3-Last": "0.0057", "Qwen3.5-Mean": "0.0268", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.2194", "Base-Mean": "0.0285", "Base-Last": "0.0050"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "Standardization", "EmbGemma": "0.1940", "Qwen3-Emb": "0.2402", "Gemma3-Mean": "0.0420", "Gemma3-Last": "0.0062", "Qwen3.5-Mean": "0.0193", "Qwen3.5-Last": "0.0049", "Dedicated Mean": "0.2171", "Base-Mean": "0.0307", "Base-Last": "0.0055"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "R1", "EmbGemma": "0.1992", "Qwen3-Emb": "0.2403", "Gemma3-Mean": "0.0222", "Gemma3-Last": "0.0052", "Qwen3.5-Mean": "0.0216", "Qwen3.5-Last": "0.0048", "Dedicated Mean": "0.2198", "Base-Mean": "0.0219", "Base-Last": "0.0050"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "R2", "EmbGemma": "0.1966", "Qwen3-Emb": "0.2405", "Gemma3-Mean": "0.0244", "Gemma3-Last": "0.0055", "Qwen3.5-Mean": "0.0229", "Qwen3.5-Last": "0.0048", "Dedicated Mean": "0.2185", "Base-Mean": "0.0237", "Base-Last": "0.0051"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "Soft-ZCA", "EmbGemma": "0.1686", "Qwen3-Emb": "0.2161", "Gemma3-Mean": "0.0679", "Gemma3-Last": "0.0106", "Qwen3.5-Mean": "0.0536", "Qwen3.5-Last": "0.0080", "Dedicated Mean": "0.1924", "Base-Mean": "0.0607", "Base-Last": "0.0093"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "COAST (Ours)", "EmbGemma": "0.1985", "Qwen3-Emb": "0.2396", "Gemma3-Mean": "0.0744", "Gemma3-Last": "0.0106", "Qwen3.5-Mean": "0.0557", "Qwen3.5-Last": "0.0081", "Dedicated Mean": "0.2190", "Base-Mean": "0.0651", "Base-Last": "0.0093"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "ABTT (D=1)", "EmbGemma": "0.1994", "Qwen3-Emb": "0.2406", "Gemma3-Mean": "0.0226", "Gemma3-Last": "0.0053", "Qwen3.5-Mean": "0.0197", "Qwen3.5-Last": "0.0042", "Dedicated Mean": "0.2200", "Base-Mean": "0.0212", "Base-Last": "0.0048"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "ABTT (D=2)", "EmbGemma": "0.2012", "Qwen3-Emb": "0.2405", "Gemma3-Mean": "0.0214", "Gemma3-Last": "0.0057", "Qwen3.5-Mean": "0.0189", "Qwen3.5-Last": "0.0044", "Dedicated Mean": "0.2208", "Base-Mean": "0.0201", "Base-Last": "0.0051"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "ABTT (D=3)", "EmbGemma": "0.1996", "Qwen3-Emb": "0.2380", "Gemma3-Mean": "0.0226", "Gemma3-Last": "0.0068", "Qwen3.5-Mean": "0.0172", "Qwen3.5-Last": "0.0055", "Dedicated Mean": "0.2188", "Base-Mean": "0.0199", "Base-Last": "0.0061"}, {"Dataset": "SCIDOCS", "k": "d", "Method": "Unreg. 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(Σ, γ*, ε*)", "EmbGemma": "0.4215 (88.9%)", "Qwen3-Emb": "0.4496 (94.9%)", "Gemma3-Mean": "0.0512 (87.0%)", "Gemma3-Last": "0.0189 (77.0%)", "Qwen3.5-Mean": "0.0355 (84.7%)", "Qwen3.5-Last": "0.0050 (193.9%)", "Dedicated Mean": "0.4355 (91.9%)", "Base-Mean": "0.0433 (85.8%)", "Base-Last": "0.0120 (135.4%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.2957 (62.4%)", "Qwen3-Emb": "0.3692 (77.9%)", "Gemma3-Mean": "0.0250 (42.4%)", "Gemma3-Last": "0.0093 (37.9%)", "Qwen3.5-Mean": "0.0113 (26.9%)", "Qwen3.5-Last": "0.0027 (106.0%)", "Dedicated Mean": "0.3325 (70.2%)", "Base-Mean": "0.0181 (34.7%)", "Base-Last": "0.0060 (72.0%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "PCA-k", "EmbGemma": "0.3134 (66.1%)", "Qwen3-Emb": "0.3978 (84.0%)", "Gemma3-Mean": "0.0204 (34.7%)", "Gemma3-Last": "0.0161 (65.3%)", "Qwen3.5-Mean": "0.0244 (58.2%)", "Qwen3.5-Last": "0.0018 (69.5%)", "Dedicated Mean": "0.3556 (75.1%)", "Base-Mean": "0.0224 (46.4%)", "Base-Last": "0.0089 (67.4%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.3277 (69.1%)", "Qwen3-Emb": "0.3831 (80.9%)", "Gemma3-Mean": "0.0313 (53.2%)", "Gemma3-Last": "0.0128 (52.0%)", "Qwen3.5-Mean": "0.0289 (69.1%)", "Qwen3.5-Last": "0.0020 (78.4%)", "Dedicated Mean": "0.3554 (75.0%)", "Base-Mean": "0.0301 (61.2%)", "Base-Last": "0.0074 (65.2%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.3285 (69.3%)", "Qwen3-Emb": "0.3890 (82.1%)", "Gemma3-Mean": "0.0287 (48.8%)", "Gemma3-Last": "0.0162 (65.7%)", "Qwen3.5-Mean": "0.0284 (67.8%)", "Qwen3.5-Last": "0.0015 (60.1%)", "Dedicated Mean": "0.3588 (75.7%)", "Base-Mean": "0.0285 (58.3%)", "Base-Last": "0.0089 (62.9%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.3397 (71.7%)", "Qwen3-Emb": "0.4011 (84.7%)", "Gemma3-Mean": "0.0326 (55.4%)", "Gemma3-Last": "0.0138 (56.1%)", "Qwen3.5-Mean": "0.0308 (73.5%)", "Qwen3.5-Last": "0.0019 (75.0%)", "Dedicated Mean": "0.3704 (78.2%)", "Base-Mean": "0.0317 (64.4%)", "Base-Last": "0.0078 (65.6%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.3362 (71.0%)", "Qwen3-Emb": "0.4048 (85.5%)", "Gemma3-Mean": "0.0305 (51.8%)", "Gemma3-Last": "0.0145 (59.1%)", "Qwen3.5-Mean": "0.0301 (71.9%)", "Qwen3.5-Last": "0.0018 (71.5%)", "Dedicated Mean": "0.3705 (78.2%)", "Base-Mean": "0.0303 (61.9%)", "Base-Last": "0.0082 (65.3%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.3392 (71.6%)", "Qwen3-Emb": "0.3969 (83.8%)", "Gemma3-Mean": "0.0326 (55.4%)", "Gemma3-Last": "0.0138 (56.1%)", "Qwen3.5-Mean": "0.0308 (73.5%)", "Qwen3.5-Last": "0.0019 (75.0%)", "Dedicated Mean": "0.3680 (77.7%)", "Base-Mean": "0.0317 (64.4%)", "Base-Last": "0.0078 (65.6%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.3376 (71.2%)", "Qwen3-Emb": "0.4034 (85.2%)", "Gemma3-Mean": "0.0322 (54.8%)", "Gemma3-Last": "0.0136 (55.3%)", "Qwen3.5-Mean": "0.0311 (74.2%)", "Qwen3.5-Last": "0.0018 (69.2%)", "Dedicated Mean": "0.3705 (78.2%)", "Base-Mean": "0.0316 (64.5%)", "Base-Last": "0.0077 (62.2%)"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.3250 (68.6%)", "Qwen3-Emb": "0.3953 (83.4%)", "Gemma3-Mean": "0.0316 (53.7%)", "Gemma3-Last": "0.0128 (52.0%)", "Qwen3.5-Mean": "0.0289 (69.1%)", "Qwen3.5-Last": "0.0020 (78.4%)", "Dedicated Mean": "0.3601 (76.0%)", "Base-Mean": "0.0302 (61.4%)", "Base-Last": "0.0074 (65.2%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.4688 (99.7%)", "Qwen3-Emb": "0.4940 (100.2%)", "Gemma3-Mean": "0.2748 (93.6%)", "Gemma3-Last": "0.1157 (102.9%)", "Qwen3.5-Mean": "0.3008 (95.1%)", "Qwen3.5-Last": "0.1045 (98.2%)", "Dedicated Mean": "0.4814 (100.0%)", "Base-Mean": "0.2878 (94.3%)", "Base-Last": "0.1101 (100.6%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "PCA-k", "EmbGemma": "0.4762 (101.3%)", "Qwen3-Emb": "0.4823 (97.8%)", "Gemma3-Mean": "0.2976 (101.3%)", "Gemma3-Last": "0.1100 (97.9%)", "Qwen3.5-Mean": "0.2954 (93.4%)", "Qwen3.5-Last": "0.1069 (100.4%)", "Dedicated Mean": "0.4793 (99.6%)", "Base-Mean": "0.2965 (97.4%)", "Base-Last": "0.1084 (99.1%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.4296 (91.4%)", "Qwen3-Emb": "0.4435 (90.0%)", "Gemma3-Mean": "0.3558 (121.1%)", "Gemma3-Last": "0.1610 (143.2%)", "Qwen3.5-Mean": "0.3568 (112.8%)", "Qwen3.5-Last": "0.1482 (139.3%)", "Dedicated Mean": "0.4365 (90.7%)", "Base-Mean": "0.3563 (117.0%)", "Base-Last": "0.1546 (141.2%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.4749 (101.0%)", "Qwen3-Emb": "0.4826 (97.9%)", "Gemma3-Mean": "0.3009 (102.4%)", "Gemma3-Last": "0.1122 (99.8%)", "Qwen3.5-Mean": "0.2988 (94.5%)", "Qwen3.5-Last": "0.1093 (102.7%)", "Dedicated Mean": "0.4788 (99.5%)", "Base-Mean": "0.2999 (98.5%)", "Base-Last": "0.1107 (101.3%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.4709 (100.2%)", "Qwen3-Emb": "0.4848 (98.3%)", "Gemma3-Mean": "0.3569 (121.5%)", "Gemma3-Last": "0.1611 (143.4%)", "Qwen3.5-Mean": "0.3588 (113.5%)", "Qwen3.5-Last": "0.1503 (141.3%)", "Dedicated Mean": "0.4778 (99.3%)", "Base-Mean": "0.3579 (117.5%)", "Base-Last": "0.1557 (142.3%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.4690 (99.7%)", "Qwen3-Emb": "0.4848 (98.3%)", "Gemma3-Mean": "0.3488 (118.7%)", "Gemma3-Last": "0.1502 (133.6%)", "Qwen3.5-Mean": "0.3521 (111.3%)", "Qwen3.5-Last": "0.1359 (127.7%)", "Dedicated Mean": "0.4769 (99.0%)", "Base-Mean": "0.3505 (115.0%)", "Base-Last": "0.1431 (130.6%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.4717 (100.3%)", "Qwen3-Emb": "0.4848 (98.3%)", "Gemma3-Mean": "0.3554 (121.0%)", "Gemma3-Last": "0.1608 (143.0%)", "Qwen3.5-Mean": "0.3553 (112.4%)", "Qwen3.5-Last": "0.1479 (139.0%)", "Dedicated Mean": "0.4783 (99.3%)", "Base-Mean": "0.3553 (116.7%)", "Base-Last": "0.1543 (141.0%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.4710 (100.2%)", "Qwen3-Emb": "0.4850 (98.4%)", "Gemma3-Mean": "0.3599 (122.5%)", "Gemma3-Last": "0.1638 (145.7%)", "Qwen3.5-Mean": "0.3639 (115.1%)", "Qwen3.5-Last": "0.1507 (141.6%)", "Dedicated Mean": "0.4780 (99.3%)", "Base-Mean": "0.3619 (118.8%)", "Base-Last": "0.1573 (143.7%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Orth. Proj. 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(Σ, γ*, ε*)", "EmbGemma": "0.4603 (97.9%)", "Qwen3-Emb": "0.4744 (96.2%)", "Gemma3-Mean": "0.3369 (114.7%)", "Gemma3-Last": "0.1531 (136.2%)", "Qwen3.5-Mean": "0.3418 (108.1%)", "Qwen3.5-Last": "0.1369 (128.7%)", "Dedicated Mean": "0.4673 (97.1%)", "Base-Mean": "0.3393 (111.4%)", "Base-Last": "0.1450 (132.4%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.3871 (82.3%)", "Qwen3-Emb": "0.4413 (89.5%)", "Gemma3-Mean": "0.2285 (77.8%)", "Gemma3-Last": "0.0858 (76.3%)", "Qwen3.5-Mean": "0.1932 (61.1%)", "Qwen3.5-Last": "0.0692 (65.0%)", "Dedicated Mean": "0.4142 (85.9%)", "Base-Mean": "0.2109 (69.5%)", "Base-Last": "0.0775 (70.6%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "0.4353 (92.6%)", "Qwen3-Emb": "0.4476 (90.8%)", "Gemma3-Mean": "0.2396 (81.6%)", "Gemma3-Last": "0.0776 (69.1%)", "Qwen3.5-Mean": "0.2596 (82.1%)", "Qwen3.5-Last": "0.0832 (78.2%)", "Dedicated Mean": "0.4415 (91.7%)", "Base-Mean": "0.2496 (81.8%)", "Base-Last": "0.0804 (73.6%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.4071 (86.6%)", "Qwen3-Emb": "0.4377 (88.8%)", "Gemma3-Mean": "0.2882 (98.1%)", "Gemma3-Last": "0.1210 (107.6%)", "Qwen3.5-Mean": "0.3010 (95.2%)", "Qwen3.5-Last": "0.1048 (98.5%)", "Dedicated Mean": "0.4224 (87.7%)", "Base-Mean": "0.2946 (96.7%)", "Base-Last": "0.1129 (103.1%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.4140 (88.0%)", "Qwen3-Emb": "0.4468 (90.6%)", "Gemma3-Mean": "0.2728 (92.9%)", "Gemma3-Last": "0.0940 (83.6%)", "Qwen3.5-Mean": "0.2903 (91.8%)", "Qwen3.5-Last": "0.0931 (87.5%)", "Dedicated Mean": "0.4304 (89.3%)", "Base-Mean": "0.2815 (92.3%)", "Base-Last": "0.0935 (85.5%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.4273 (90.9%)", "Qwen3-Emb": "0.4541 (92.1%)", "Gemma3-Mean": "0.2886 (98.2%)", "Gemma3-Last": "0.1222 (108.8%)", "Qwen3.5-Mean": "0.2999 (94.8%)", "Qwen3.5-Last": "0.1050 (98.6%)", "Dedicated Mean": "0.4407 (91.5%)", "Base-Mean": "0.2943 (96.5%)", "Base-Last": "0.1136 (103.7%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.4195 (89.2%)", "Qwen3-Emb": "0.4485 (91.0%)", "Gemma3-Mean": "0.2884 (98.2%)", "Gemma3-Last": "0.1212 (107.8%)", "Qwen3.5-Mean": "0.3008 (95.1%)", "Qwen3.5-Last": "0.1048 (98.5%)", "Dedicated Mean": "0.4340 (90.1%)", "Base-Mean": "0.2946 (96.7%)", "Base-Last": "0.1130 (103.2%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.1885 (96.8%)", "Qwen3-Emb": "0.2398 (98.3%)", "Gemma3-Mean": "0.0256 (85.0%)", "Gemma3-Last": "0.0048 (84.2%)", "Qwen3.5-Mean": "0.0215 (80.4%)", "Qwen3.5-Last": "0.0042 (98.5%)", "Dedicated Mean": "0.2142 (97.5%)", "Base-Mean": "0.0236 (82.7%)", "Base-Last": "0.0045 (91.4%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "0.1987 (102.0%)", "Qwen3-Emb": "0.2399 (98.3%)", "Gemma3-Mean": "0.0195 (64.6%)", "Gemma3-Last": "0.0053 (92.8%)", "Qwen3.5-Mean": "0.0201 (75.1%)", "Qwen3.5-Last": "0.0043 (100.7%)", "Dedicated Mean": "0.2193 (100.2%)", "Base-Mean": "0.0198 (69.9%)", "Base-Last": "0.0048 (96.7%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.1784 (91.6%)", "Qwen3-Emb": "0.2147 (88.0%)", "Gemma3-Mean": "0.0634 (210.3%)", "Gemma3-Last": "0.0089 (154.6%)", "Qwen3.5-Mean": "0.0487 (181.9%)", "Qwen3.5-Last": "0.0085 (201.0%)", "Dedicated Mean": "0.1966 (89.8%)", "Base-Mean": "0.0561 (196.1%)", "Base-Last": "0.0087 (177.8%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.1999 (102.6%)", "Qwen3-Emb": "0.2410 (98.8%)", "Gemma3-Mean": "0.0202 (67.0%)", "Gemma3-Last": "0.0055 (95.5%)", "Qwen3.5-Mean": "0.0206 (76.9%)", "Qwen3.5-Last": "0.0046 (108.4%)", "Dedicated Mean": "0.2204 (100.7%)", "Base-Mean": "0.0204 (72.0%)", "Base-Last": "0.0050 (101.9%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.1994 (102.4%)", "Qwen3-Emb": "0.2401 (98.4%)", "Gemma3-Mean": "0.0634 (210.3%)", "Gemma3-Last": "0.0087 (151.3%)", "Qwen3.5-Mean": "0.0478 (178.5%)", "Qwen3.5-Last": "0.0084 (196.9%)", "Dedicated Mean": "0.2198 (100.4%)", "Base-Mean": "0.0556 (194.4%)", "Base-Last": "0.0085 (174.1%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.2017 (103.6%)", "Qwen3-Emb": "0.2406 (98.7%)", "Gemma3-Mean": "0.0634 (210.0%)", "Gemma3-Last": "0.0083 (145.5%)", "Qwen3.5-Mean": "0.0470 (175.7%)", "Qwen3.5-Last": "0.0081 (190.5%)", "Dedicated Mean": "0.2212 (101.1%)", "Base-Mean": "0.0552 (192.9%)", "Base-Last": "0.0082 (168.0%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "0.1793 (92.0%)", "Qwen3-Emb": "0.2310 (94.7%)", "Gemma3-Mean": "0.0379 (125.7%)", "Gemma3-Last": "0.0061 (105.6%)", "Qwen3.5-Mean": "0.0165 (61.5%)", "Qwen3.5-Last": "0.0033 (78.3%)", "Dedicated Mean": "0.2051 (93.4%)", "Base-Mean": "0.0272 (93.6%)", "Base-Last": "0.0047 (92.0%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "0.1873 (96.2%)", "Qwen3-Emb": "0.2347 (96.2%)", "Gemma3-Mean": "0.0179 (59.2%)", "Gemma3-Last": "0.0052 (89.9%)", "Qwen3.5-Mean": "0.0189 (70.4%)", "Qwen3.5-Last": "0.0040 (94.7%)", "Dedicated Mean": "0.2110 (96.2%)", "Base-Mean": "0.0184 (64.8%)", "Base-Last": "0.0046 (92.3%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "0.1807 (92.8%)", "Qwen3-Emb": "0.2210 (90.6%)", "Gemma3-Mean": "0.0499 (165.4%)", "Gemma3-Last": "0.0095 (166.1%)", "Qwen3.5-Mean": "0.0389 (145.5%)", "Qwen3.5-Last": "0.0071 (166.3%)", "Dedicated Mean": "0.2009 (91.7%)", "Base-Mean": "0.0444 (155.5%)", "Base-Last": "0.0083 (166.2%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "0.1930 (99.1%)", "Qwen3-Emb": "0.2358 (96.7%)", "Gemma3-Mean": "0.0188 (62.2%)", "Gemma3-Last": "0.0052 (91.4%)", "Qwen3.5-Mean": "0.0194 (72.6%)", "Qwen3.5-Last": "0.0045 (105.7%)", "Dedicated Mean": "0.2144 (97.9%)", "Base-Mean": "0.0191 (67.4%)", "Base-Last": "0.0049 (98.6%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "0.1915 (98.3%)", "Qwen3-Emb": "0.2369 (97.1%)", "Gemma3-Mean": "0.0498 (165.0%)", "Gemma3-Last": "0.0093 (161.7%)", "Qwen3.5-Mean": "0.0389 (145.5%)", "Qwen3.5-Last": "0.0071 (167.2%)", "Dedicated Mean": "0.2142 (97.7%)", "Base-Mean": "0.0444 (155.2%)", "Base-Last": "0.0082 (164.5%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.1913 (98.2%)", "Qwen3-Emb": "0.2359 (96.7%)", "Gemma3-Mean": "0.0499 (165.4%)", "Gemma3-Last": "0.0095 (166.0%)", "Qwen3.5-Mean": "0.0384 (143.6%)", "Qwen3.5-Last": "0.0071 (166.5%)", "Dedicated Mean": "0.2136 (97.5%)", "Base-Mean": "0.0441 (154.5%)", "Base-Last": "0.0083 (166.2%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "0.1525 (78.3%)", "Qwen3-Emb": "0.2139 (87.7%)", "Gemma3-Mean": "0.0332 (110.1%)", "Gemma3-Last": "0.0060 (104.4%)", "Qwen3.5-Mean": "0.0163 (60.8%)", "Qwen3.5-Last": "0.0046 (107.5%)", "Dedicated Mean": "0.1832 (83.0%)", "Base-Mean": "0.0248 (85.5%)", "Base-Last": "0.0053 (106.0%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "PCA-k", "EmbGemma": "0.1649 (84.7%)", "Qwen3-Emb": "0.2228 (91.3%)", "Gemma3-Mean": "0.0153 (50.6%)", "Gemma3-Last": "0.0052 (90.4%)", "Qwen3.5-Mean": "0.0166 (62.0%)", "Qwen3.5-Last": "0.0033 (76.8%)", "Dedicated Mean": "0.1938 (88.0%)", "Base-Mean": "0.0159 (56.3%)", "Base-Last": "0.0043 (83.6%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Whitening-k", "EmbGemma": "0.1638 (84.1%)", "Qwen3-Emb": "0.2154 (88.3%)", "Gemma3-Mean": "0.0302 (100.1%)", "Gemma3-Last": "0.0074 (129.7%)", "Qwen3.5-Mean": "0.0268 (100.0%)", "Qwen3.5-Last": "0.0059 (139.8%)", "Dedicated Mean": "0.1896 (86.2%)", "Base-Mean": "0.0285 (100.1%)", "Base-Last": "0.0066 (134.8%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "SpecTemp", "EmbGemma": "0.1727 (88.7%)", "Qwen3-Emb": "0.2240 (91.8%)", "Gemma3-Mean": "0.0168 (55.8%)", "Gemma3-Last": "0.0052 (91.5%)", "Qwen3.5-Mean": "0.0163 (60.7%)", "Qwen3.5-Last": "0.0038 (89.5%)", "Dedicated Mean": "0.1983 (90.3%)", "Base-Mean": "0.0165 (58.3%)", "Base-Last": "0.0045 (90.5%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "0.1723 (88.5%)", "Qwen3-Emb": "0.2249 (92.2%)", "Gemma3-Mean": "0.0310 (102.7%)", "Gemma3-Last": "0.0075 (131.1%)", "Qwen3.5-Mean": "0.0263 (98.3%)", "Qwen3.5-Last": "0.0058 (136.1%)", "Dedicated Mean": "0.1986 (90.3%)", "Base-Mean": "0.0287 (100.5%)", "Base-Last": "0.0066 (133.6%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. 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Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "71.7%", "Qwen3-Emb": "84.7%", "Gemma3-Mean": "50.1%", "Gemma3-Last": "64.8%", "Qwen3.5-Mean": "70.5%", "Qwen3.5-Last": "67.9%", "Dedicated Mean": "78.2%", "Base-Mean": "60.3%", "Base-Last": "66.3%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "68.5%", "Qwen3-Emb": "85.5%", "Gemma3-Mean": "55.4%", "Gemma3-Last": "56.1%", "Qwen3.5-Mean": "73.5%", "Qwen3.5-Last": "75.0%", "Dedicated Mean": "77.0%", "Base-Mean": "64.4%", "Base-Last": "65.6%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "71.0%", "Qwen3-Emb": "85.5%", "Gemma3-Mean": "51.8%", "Gemma3-Last": "59.1%", "Qwen3.5-Mean": "71.9%", "Qwen3.5-Last": "71.5%", "Dedicated Mean": "78.2%", "Base-Mean": "61.9%", "Base-Last": "65.3%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "71.6%", "Qwen3-Emb": "83.8%", "Gemma3-Mean": "55.4%", "Gemma3-Last": "56.1%", "Qwen3.5-Mean": "73.5%", "Qwen3.5-Last": "75.0%", "Dedicated Mean": "77.7%", "Base-Mean": "64.4%", "Base-Last": "65.6%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "71.2%", "Qwen3-Emb": "85.2%", "Gemma3-Mean": "54.8%", "Gemma3-Last": "55.3%", "Qwen3.5-Mean": "74.2%", "Qwen3.5-Last": "69.2%", "Dedicated Mean": "78.2%", "Base-Mean": "64.5%", "Base-Last": "62.2%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "68.6%", "Qwen3-Emb": "83.4%", "Gemma3-Mean": "53.7%", "Gemma3-Last": "52.0%", "Qwen3.5-Mean": "69.1%", "Qwen3.5-Last": "78.4%", "Dedicated Mean": "76.0%", "Base-Mean": "61.4%", "Base-Last": "65.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "99.7%", "Qwen3-Emb": "100.2%", "Gemma3-Mean": "93.6%", "Gemma3-Last": "102.9%", "Qwen3.5-Mean": "95.1%", "Qwen3.5-Last": "98.2%", "Dedicated Mean": "100.0%", "Base-Mean": "94.3%", "Base-Last": "100.6%"}, {"Dataset": "ArguAna", "k": "512", "Method": "PCA-k", "EmbGemma": "101.3%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "101.3%", "Gemma3-Last": "97.9%", "Qwen3.5-Mean": "93.4%", "Qwen3.5-Last": "100.4%", "Dedicated Mean": "99.6%", "Base-Mean": "97.4%", "Base-Last": "99.1%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Whitening-k", "EmbGemma": "91.4%", "Qwen3-Emb": "90.0%", "Gemma3-Mean": "121.1%", "Gemma3-Last": "143.2%", "Qwen3.5-Mean": "112.8%", "Qwen3.5-Last": "139.3%", "Dedicated Mean": "90.7%", "Base-Mean": "117.0%", "Base-Last": "141.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "SpecTemp", "EmbGemma": "101.0%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "102.4%", "Gemma3-Last": "99.8%", "Qwen3.5-Mean": "94.5%", "Qwen3.5-Last": "102.7%", "Dedicated Mean": "99.5%", "Base-Mean": "98.5%", "Base-Last": "101.3%"}, {"Dataset": "ArguAna", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "100.2%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "121.5%", "Gemma3-Last": "143.4%", "Qwen3.5-Mean": "113.5%", "Qwen3.5-Last": "141.3%", "Dedicated Mean": "99.3%", "Base-Mean": "117.5%", "Base-Last": "142.3%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.0%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "101.3%", "Gemma3-Last": "98.2%", "Qwen3.5-Mean": "93.6%", "Qwen3.5-Last": "100.5%", "Dedicated Mean": "99.2%", "Base-Mean": "97.5%", "Base-Last": "99.4%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.2%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "102.2%", "Gemma3-Last": "100.4%", "Qwen3.5-Mean": "94.9%", "Qwen3.5-Last": "102.4%", "Dedicated Mean": "99.3%", "Base-Mean": "98.5%", "Base-Last": "101.4%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "102.4%", "Gemma3-Last": "100.2%", "Qwen3.5-Mean": "94.8%", "Qwen3.5-Last": "102.2%", "Dedicated Mean": "99.3%", "Base-Mean": "98.6%", "Base-Last": "101.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.2%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "121.5%", "Gemma3-Last": "143.4%", "Qwen3.5-Mean": "113.5%", "Qwen3.5-Last": "141.2%", "Dedicated Mean": "99.2%", "Base-Mean": "117.5%", "Base-Last": "142.3%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.7%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "118.7%", "Gemma3-Last": "133.6%", "Qwen3.5-Mean": "111.3%", "Qwen3.5-Last": "127.7%", "Dedicated Mean": "99.0%", "Base-Mean": "115.0%", "Base-Last": "130.6%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.3%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "121.0%", "Gemma3-Last": "143.0%", "Qwen3.5-Mean": "112.4%", "Qwen3.5-Last": "139.0%", "Dedicated Mean": "99.3%", "Base-Mean": "116.7%", "Base-Last": "141.0%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.2%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "122.5%", "Gemma3-Last": "145.7%", "Qwen3.5-Mean": "115.1%", "Qwen3.5-Last": "141.6%", "Dedicated Mean": "99.3%", "Base-Mean": "118.8%", "Base-Last": "143.7%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "101.1%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "121.3%", "Gemma3-Last": "144.6%", "Qwen3.5-Mean": "113.3%", "Qwen3.5-Last": "140.7%", "Dedicated Mean": "99.5%", "Base-Mean": "117.3%", "Base-Last": "142.6%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "97.9%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "90.3%", "Gemma3-Last": "107.8%", "Qwen3.5-Mean": "88.8%", "Qwen3.5-Last": "90.9%", "Dedicated Mean": "98.1%", "Base-Mean": "89.6%", "Base-Last": "99.3%"}, {"Dataset": "ArguAna", "k": "256", "Method": "PCA-k", "EmbGemma": "100.7%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "99.0%", "Gemma3-Last": "95.8%", "Qwen3.5-Mean": "92.9%", "Qwen3.5-Last": "98.5%", "Dedicated Mean": "99.2%", "Base-Mean": "96.0%", "Base-Last": "97.1%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Whitening-k", "EmbGemma": "94.6%", "Qwen3-Emb": "93.9%", "Gemma3-Mean": "123.4%", "Gemma3-Last": "149.2%", "Qwen3.5-Mean": "113.8%", "Qwen3.5-Last": "138.2%", "Dedicated Mean": "94.2%", "Base-Mean": "118.6%", "Base-Last": "143.7%"}, {"Dataset": "ArguAna", "k": "256", "Method": "SpecTemp", "EmbGemma": "100.3%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "102.8%", "Gemma3-Last": "100.6%", "Qwen3.5-Mean": "95.1%", "Qwen3.5-Last": "103.1%", "Dedicated Mean": "99.1%", "Base-Mean": "99.0%", "Base-Last": "101.8%"}, {"Dataset": "ArguAna", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "99.6%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "123.5%", "Gemma3-Last": "148.0%", "Qwen3.5-Mean": "114.0%", "Qwen3.5-Last": "137.9%", "Dedicated Mean": "98.8%", "Base-Mean": "118.7%", "Base-Last": "143.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.6%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "99.2%", "Gemma3-Last": "96.6%", "Qwen3.5-Mean": "93.0%", "Qwen3.5-Last": "99.4%", "Dedicated Mean": "98.8%", "Base-Mean": "96.1%", "Base-Last": "98.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.7%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "102.7%", "Gemma3-Last": "101.5%", "Qwen3.5-Mean": "95.5%", "Qwen3.5-Last": "101.8%", "Dedicated Mean": "99.0%", "Base-Mean": "99.1%", "Base-Last": "101.7%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "102.6%", "Gemma3-Last": "101.3%", "Qwen3.5-Mean": "95.6%", "Qwen3.5-Last": "101.8%", "Dedicated Mean": "98.8%", "Base-Mean": "99.1%", "Base-Last": "101.6%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.5%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "123.5%", "Gemma3-Last": "148.0%", "Qwen3.5-Mean": "114.0%", "Qwen3.5-Last": "137.9%", "Dedicated Mean": "98.8%", "Base-Mean": "118.7%", "Base-Last": "143.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.5%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "117.9%", "Gemma3-Last": "132.2%", "Qwen3.5-Mean": "110.6%", "Qwen3.5-Last": "125.9%", "Dedicated Mean": "98.8%", "Base-Mean": "114.3%", "Base-Last": "129.1%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.7%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "123.5%", "Gemma3-Last": "148.5%", "Qwen3.5-Mean": "114.0%", "Qwen3.5-Last": "137.5%", "Dedicated Mean": "99.0%", "Base-Mean": "118.7%", "Base-Last": "143.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.6%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "123.5%", "Gemma3-Last": "147.3%", "Qwen3.5-Mean": "113.9%", "Qwen3.5-Last": "137.7%", "Dedicated Mean": "98.8%", "Base-Mean": "118.7%", "Base-Last": "142.5%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.6%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "123.4%", "Gemma3-Last": "149.0%", "Qwen3.5-Mean": "113.9%", "Qwen3.5-Last": "138.4%", "Dedicated Mean": "99.2%", "Base-Mean": "118.7%", "Base-Last": "143.7%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "91.5%", "Qwen3-Emb": "96.0%", "Gemma3-Mean": "91.4%", "Gemma3-Last": "95.3%", "Qwen3.5-Mean": "84.5%", "Qwen3.5-Last": "83.1%", "Dedicated Mean": "93.8%", "Base-Mean": "88.0%", "Base-Last": "89.2%"}, {"Dataset": "ArguAna", "k": "128", "Method": "PCA-k", "EmbGemma": "98.7%", "Qwen3-Emb": "95.9%", "Gemma3-Mean": "92.1%", "Gemma3-Last": "87.5%", "Qwen3.5-Mean": "89.0%", "Qwen3.5-Last": "92.0%", "Dedicated Mean": "97.3%", "Base-Mean": "90.5%", "Base-Last": "89.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Whitening-k", "EmbGemma": "94.5%", "Qwen3-Emb": "93.4%", "Gemma3-Mean": "114.7%", "Gemma3-Last": "136.2%", "Qwen3.5-Mean": "108.1%", "Qwen3.5-Last": "128.7%", "Dedicated Mean": "94.0%", "Base-Mean": "111.4%", "Base-Last": "132.5%"}, {"Dataset": "ArguAna", "k": "128", "Method": "SpecTemp", "EmbGemma": "97.7%", "Qwen3-Emb": "96.2%", "Gemma3-Mean": "101.9%", "Gemma3-Last": "99.0%", "Qwen3.5-Mean": "95.2%", "Qwen3.5-Last": "98.6%", "Dedicated Mean": "96.9%", "Base-Mean": "98.6%", "Base-Last": "98.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "96.9%", "Qwen3-Emb": "96.6%", "Gemma3-Mean": "114.9%", "Gemma3-Last": "137.8%", "Qwen3.5-Mean": "108.6%", "Qwen3.5-Last": "127.8%", "Dedicated Mean": "96.7%", "Base-Mean": "111.7%", "Base-Last": "132.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "96.6%", "Qwen3-Emb": "96.2%", "Gemma3-Mean": "91.7%", "Gemma3-Last": "86.9%", "Qwen3.5-Mean": "89.6%", "Qwen3.5-Last": "92.3%", "Dedicated Mean": "96.4%", "Base-Mean": "90.6%", "Base-Last": "89.6%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "97.1%", "Qwen3-Emb": "96.4%", "Gemma3-Mean": "101.8%", "Gemma3-Last": "100.4%", "Qwen3.5-Mean": "95.0%", "Qwen3.5-Last": "96.0%", "Dedicated Mean": "96.8%", "Base-Mean": "98.4%", "Base-Last": "98.2%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "96.9%", "Qwen3-Emb": "96.6%", "Gemma3-Mean": "101.7%", "Gemma3-Last": "100.3%", "Qwen3.5-Mean": "94.9%", "Qwen3.5-Last": "96.0%", "Dedicated Mean": "96.7%", "Base-Mean": "98.3%", "Base-Last": "98.2%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "96.8%", "Qwen3-Emb": "96.3%", "Gemma3-Mean": "114.9%", "Gemma3-Last": "137.8%", "Qwen3.5-Mean": "108.6%", "Qwen3.5-Last": "127.8%", "Dedicated Mean": "96.6%", "Base-Mean": "111.8%", "Base-Last": "132.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "97.1%", "Qwen3-Emb": "96.1%", "Gemma3-Mean": "110.5%", "Gemma3-Last": "119.6%", "Qwen3.5-Mean": "104.3%", "Qwen3.5-Last": "113.6%", "Dedicated Mean": "96.6%", "Base-Mean": "107.4%", "Base-Last": "116.6%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "97.1%", "Qwen3-Emb": "96.4%", "Gemma3-Mean": "114.8%", "Gemma3-Last": "137.9%", "Qwen3.5-Mean": "108.6%", "Qwen3.5-Last": "128.0%", "Dedicated Mean": "96.8%", "Base-Mean": "111.7%", "Base-Last": "132.9%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "96.9%", "Qwen3-Emb": "96.6%", "Gemma3-Mean": "115.0%", "Gemma3-Last": "135.0%", "Qwen3.5-Mean": "108.4%", "Qwen3.5-Last": "126.0%", "Dedicated Mean": "96.7%", "Base-Mean": "111.7%", "Base-Last": "130.5%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "97.9%", "Qwen3-Emb": "96.2%", "Gemma3-Mean": "114.7%", "Gemma3-Last": "136.2%", "Qwen3.5-Mean": "108.1%", "Qwen3.5-Last": "128.7%", "Dedicated Mean": "97.1%", "Base-Mean": "111.4%", "Base-Last": "132.4%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "82.3%", "Qwen3-Emb": "89.5%", "Gemma3-Mean": "77.8%", "Gemma3-Last": "76.3%", "Qwen3.5-Mean": "61.1%", "Qwen3.5-Last": "65.0%", "Dedicated Mean": "85.9%", "Base-Mean": "69.5%", "Base-Last": "70.6%"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "92.6%", "Qwen3-Emb": "90.8%", "Gemma3-Mean": "81.6%", "Gemma3-Last": "69.1%", "Qwen3.5-Mean": "82.1%", "Qwen3.5-Last": "78.2%", "Dedicated Mean": "91.7%", "Base-Mean": "81.8%", "Base-Last": "73.6%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "86.6%", "Qwen3-Emb": "88.8%", "Gemma3-Mean": "98.1%", "Gemma3-Last": "107.6%", "Qwen3.5-Mean": "95.2%", "Qwen3.5-Last": "98.5%", "Dedicated Mean": "87.7%", "Base-Mean": "96.7%", "Base-Last": "103.1%"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "88.0%", "Qwen3-Emb": "90.6%", "Gemma3-Mean": "92.9%", "Gemma3-Last": "83.6%", "Qwen3.5-Mean": "91.8%", "Qwen3.5-Last": "87.5%", "Dedicated Mean": "89.3%", "Base-Mean": "92.3%", "Base-Last": "85.5%"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "90.9%", "Qwen3-Emb": "92.1%", "Gemma3-Mean": "98.2%", "Gemma3-Last": "108.8%", "Qwen3.5-Mean": "94.8%", "Qwen3.5-Last": "98.6%", "Dedicated Mean": "91.5%", "Base-Mean": "96.5%", "Base-Last": "103.7%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "91.0%", "Qwen3-Emb": "92.0%", "Gemma3-Mean": "81.7%", "Gemma3-Last": "70.9%", "Qwen3.5-Mean": "82.3%", "Qwen3.5-Last": "79.6%", "Dedicated Mean": "91.5%", "Base-Mean": "82.0%", "Base-Last": "75.2%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "90.8%", "Qwen3-Emb": "91.9%", "Gemma3-Mean": "93.0%", "Gemma3-Last": "86.1%", "Qwen3.5-Mean": "91.5%", "Qwen3.5-Last": "84.8%", "Dedicated Mean": "91.3%", "Base-Mean": "92.2%", "Base-Last": "85.5%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "90.9%", "Qwen3-Emb": "92.0%", "Gemma3-Mean": "92.5%", "Gemma3-Last": "97.9%", "Qwen3.5-Mean": "92.2%", "Qwen3.5-Last": "92.0%", "Dedicated Mean": "91.5%", "Base-Mean": "92.3%", "Base-Last": "95.0%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "90.8%", "Qwen3-Emb": "91.9%", "Gemma3-Mean": "98.2%", "Gemma3-Last": "108.8%", "Qwen3.5-Mean": "94.9%", "Qwen3.5-Last": "98.6%", "Dedicated Mean": "91.3%", "Base-Mean": "96.6%", "Base-Last": "103.7%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "91.0%", "Qwen3-Emb": "92.0%", "Gemma3-Mean": "98.1%", "Gemma3-Last": "109.1%", "Qwen3.5-Mean": "94.8%", "Qwen3.5-Last": "98.5%", "Dedicated Mean": "91.5%", "Base-Mean": "96.4%", "Base-Last": "103.8%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "89.2%", "Qwen3-Emb": "91.0%", "Gemma3-Mean": "98.2%", "Gemma3-Last": "107.8%", "Qwen3.5-Mean": "95.1%", "Qwen3.5-Last": "98.5%", "Dedicated Mean": "90.1%", "Base-Mean": "96.7%", "Base-Last": "103.2%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "96.8%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "85.0%", "Gemma3-Last": "84.2%", "Qwen3.5-Mean": "80.4%", "Qwen3.5-Last": "98.5%", "Dedicated Mean": "97.5%", "Base-Mean": "82.7%", "Base-Last": "91.4%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "102.0%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "64.6%", "Gemma3-Last": "92.8%", "Qwen3.5-Mean": "75.1%", "Qwen3.5-Last": "100.7%", "Dedicated Mean": "100.2%", "Base-Mean": "69.9%", "Base-Last": "96.7%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "91.6%", "Qwen3-Emb": "88.0%", "Gemma3-Mean": "210.3%", "Gemma3-Last": "154.6%", "Qwen3.5-Mean": "181.9%", "Qwen3.5-Last": "201.0%", "Dedicated Mean": "89.8%", "Base-Mean": "196.1%", "Base-Last": "177.8%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "102.6%", "Qwen3-Emb": "98.8%", "Gemma3-Mean": "67.0%", "Gemma3-Last": "95.5%", "Qwen3.5-Mean": "76.9%", "Qwen3.5-Last": "108.4%", "Dedicated Mean": "100.7%", "Base-Mean": "72.0%", "Base-Last": "101.9%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "102.4%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "210.3%", "Gemma3-Last": "151.3%", "Qwen3.5-Mean": "178.5%", "Qwen3.5-Last": "196.9%", "Dedicated Mean": "100.4%", "Base-Mean": "194.4%", "Base-Last": "174.1%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "103.0%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "136.6%", "Gemma3-Last": "118.3%", "Qwen3.5-Mean": "119.6%", "Qwen3.5-Last": "129.1%", "Dedicated Mean": "100.5%", "Base-Mean": "128.1%", "Base-Last": "123.7%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "102.7%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "211.6%", "Gemma3-Last": "154.0%", "Qwen3.5-Mean": "181.5%", "Qwen3.5-Last": "204.9%", "Dedicated Mean": "100.5%", "Base-Mean": "196.5%", "Base-Last": "179.4%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "102.5%", "Qwen3-Emb": "98.5%", "Gemma3-Mean": "202.5%", "Gemma3-Last": "150.7%", "Qwen3.5-Mean": "167.3%", "Qwen3.5-Last": "180.2%", "Dedicated Mean": "100.5%", "Base-Mean": "184.9%", "Base-Last": "165.4%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "103.6%", "Qwen3-Emb": "98.7%", "Gemma3-Mean": "210.0%", "Gemma3-Last": "145.5%", "Qwen3.5-Mean": "175.7%", "Qwen3.5-Last": "190.5%", "Dedicated Mean": "101.1%", "Base-Mean": "192.9%", "Base-Last": "168.0%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "92.0%", "Qwen3-Emb": "94.7%", "Gemma3-Mean": "125.7%", "Gemma3-Last": "105.6%", "Qwen3.5-Mean": "61.5%", "Qwen3.5-Last": "78.3%", "Dedicated Mean": "93.4%", "Base-Mean": "93.6%", "Base-Last": "92.0%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "96.2%", "Qwen3-Emb": "96.2%", "Gemma3-Mean": "59.2%", "Gemma3-Last": "89.9%", "Qwen3.5-Mean": "70.4%", "Qwen3.5-Last": "94.7%", "Dedicated Mean": "96.2%", "Base-Mean": "64.8%", "Base-Last": "92.3%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "92.8%", "Qwen3-Emb": "90.6%", "Gemma3-Mean": "165.4%", "Gemma3-Last": "166.1%", "Qwen3.5-Mean": "145.5%", "Qwen3.5-Last": "166.3%", "Dedicated Mean": "91.7%", "Base-Mean": "155.5%", "Base-Last": "166.2%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "99.1%", "Qwen3-Emb": "96.7%", "Gemma3-Mean": "62.2%", "Gemma3-Last": "91.4%", "Qwen3.5-Mean": "72.6%", "Qwen3.5-Last": "105.7%", "Dedicated Mean": "97.9%", "Base-Mean": "67.4%", "Base-Last": "98.6%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "98.3%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "165.0%", "Gemma3-Last": "161.7%", "Qwen3.5-Mean": "145.5%", "Qwen3.5-Last": "167.2%", "Dedicated Mean": "97.7%", "Base-Mean": "155.2%", "Base-Last": "164.5%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "95.7%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "65.9%", "Gemma3-Last": "92.4%", "Qwen3.5-Mean": "72.7%", "Qwen3.5-Last": "96.7%", "Dedicated Mean": "96.2%", "Base-Mean": "69.3%", "Base-Last": "94.6%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "98.8%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "69.0%", "Gemma3-Last": "90.5%", "Qwen3.5-Mean": "73.8%", "Qwen3.5-Last": "108.2%", "Dedicated Mean": "97.8%", "Base-Mean": "71.4%", "Base-Last": "99.4%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "97.8%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "69.0%", "Gemma3-Last": "90.5%", "Qwen3.5-Mean": "73.8%", "Qwen3.5-Last": "108.2%", "Dedicated Mean": "97.5%", "Base-Mean": "71.4%", "Base-Last": "99.4%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "98.3%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "165.0%", "Gemma3-Last": "161.7%", "Qwen3.5-Mean": "145.5%", "Qwen3.5-Last": "167.2%", "Dedicated Mean": "97.7%", "Base-Mean": "155.2%", "Base-Last": "164.5%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.5%", "Qwen3-Emb": "96.6%", "Gemma3-Mean": "102.3%", "Gemma3-Last": "118.2%", "Qwen3.5-Mean": "98.1%", "Qwen3.5-Last": "118.9%", "Dedicated Mean": "98.0%", "Base-Mean": "100.2%", "Base-Last": "118.5%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.1%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "165.1%", "Gemma3-Last": "163.4%", "Qwen3.5-Mean": "145.8%", "Qwen3.5-Last": "168.2%", "Dedicated Mean": "98.0%", "Base-Mean": "155.4%", "Base-Last": "165.8%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "97.8%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "157.5%", "Gemma3-Last": "150.3%", "Qwen3.5-Mean": "133.6%", "Qwen3.5-Last": "163.7%", "Dedicated Mean": "97.5%", "Base-Mean": "145.6%", "Base-Last": "157.0%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "98.2%", "Qwen3-Emb": "96.7%", "Gemma3-Mean": "165.4%", "Gemma3-Last": "166.0%", "Qwen3.5-Mean": "143.6%", "Qwen3.5-Last": "166.5%", "Dedicated Mean": "97.5%", "Base-Mean": "154.5%", "Base-Last": "166.2%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "78.3%", "Qwen3-Emb": "87.7%", "Gemma3-Mean": "110.1%", "Gemma3-Last": "104.4%", "Qwen3.5-Mean": "60.8%", "Qwen3.5-Last": "107.5%", "Dedicated Mean": "83.0%", "Base-Mean": "85.5%", "Base-Last": "106.0%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "PCA-k", "EmbGemma": "84.7%", "Qwen3-Emb": "91.3%", "Gemma3-Mean": "50.6%", "Gemma3-Last": "90.4%", "Qwen3.5-Mean": "62.0%", "Qwen3.5-Last": "76.8%", "Dedicated Mean": "88.0%", "Base-Mean": "56.3%", "Base-Last": "83.6%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Whitening-k", "EmbGemma": "84.1%", "Qwen3-Emb": "88.3%", "Gemma3-Mean": "100.1%", "Gemma3-Last": "129.7%", "Qwen3.5-Mean": "100.0%", "Qwen3.5-Last": "139.8%", "Dedicated Mean": "86.2%", "Base-Mean": "100.1%", "Base-Last": "134.8%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "SpecTemp", "EmbGemma": "88.7%", "Qwen3-Emb": "91.8%", "Gemma3-Mean": "55.8%", "Gemma3-Last": "91.5%", "Qwen3.5-Mean": "60.7%", "Qwen3.5-Last": "89.5%", "Dedicated Mean": "90.3%", "Base-Mean": "58.3%", "Base-Last": "90.5%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "88.5%", "Qwen3-Emb": "92.2%", "Gemma3-Mean": "102.7%", "Gemma3-Last": "131.1%", "Qwen3.5-Mean": "98.3%", "Qwen3.5-Last": "136.1%", "Dedicated Mean": "90.3%", "Base-Mean": "100.5%", "Base-Last": "133.6%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "84.4%", "Qwen3-Emb": "91.4%", "Gemma3-Mean": "56.1%", "Gemma3-Last": "91.4%", "Qwen3.5-Mean": "64.0%", "Qwen3.5-Last": "82.7%", "Dedicated Mean": "87.9%", "Base-Mean": "60.1%", "Base-Last": "87.1%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "89.0%", "Qwen3-Emb": "91.9%", "Gemma3-Mean": "60.5%", "Gemma3-Last": "91.3%", "Qwen3.5-Mean": "62.0%", "Qwen3.5-Last": "95.5%", "Dedicated Mean": "90.4%", "Base-Mean": "61.3%", "Base-Last": "93.4%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Crowd. 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(Σ, γ*, ε*)", "EmbGemma": "0.3832 (70.1%)", "Qwen3-Emb": "0.4673 (84.8%)", "Gemma3-Mean": "0.0385 (55.0%)", "Gemma3-Last": "0.0189 (63.3%)", "Qwen3.5-Mean": "0.0388 (68.5%)", "Qwen3.5-Last": "0.0020 (58.1%)", "Dedicated Mean": "0.4253 (77.5%)", "Base-Mean": "0.0387 (61.8%)", "Base-Last": "0.0105 (60.7%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.3314 (100.1%)", "Qwen3-Emb": "0.3494 (99.7%)", "Gemma3-Mean": "0.1781 (93.3%)", "Gemma3-Last": "0.0748 (103.4%)", "Qwen3.5-Mean": "0.1976 (95.1%)", "Qwen3.5-Last": "0.0676 (96.7%)", "Dedicated Mean": "0.3404 (99.9%)", "Base-Mean": "0.1879 (94.2%)", "Base-Last": "0.0712 (100.0%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "PCA-k", "EmbGemma": "0.3366 (101.7%)", "Qwen3-Emb": "0.3407 (97.2%)", "Gemma3-Mean": "0.1900 (99.5%)", "Gemma3-Last": "0.0694 (96.0%)", "Qwen3.5-Mean": "0.1927 (92.7%)", "Qwen3.5-Last": "0.0699 (100.0%)", "Dedicated Mean": "0.3387 (99.4%)", "Base-Mean": "0.1914 (96.1%)", "Base-Last": "0.0697 (98.0%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.2970 (89.7%)", "Qwen3-Emb": "0.3079 (87.9%)", "Gemma3-Mean": "0.2324 (121.8%)", "Gemma3-Last": "0.1018 (140.7%)", "Qwen3.5-Mean": "0.2341 (112.6%)", "Qwen3.5-Last": "0.0963 (137.7%)", "Dedicated Mean": "0.3024 (88.8%)", "Base-Mean": "0.2333 (117.2%)", "Base-Last": "0.0990 (139.2%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.3351 (101.2%)", "Qwen3-Emb": "0.3409 (97.3%)", "Gemma3-Mean": "0.1929 (101.1%)", "Gemma3-Last": "0.0710 (98.1%)", "Qwen3.5-Mean": "0.1951 (93.9%)", "Qwen3.5-Last": "0.0715 (102.2%)", "Dedicated Mean": "0.3380 (99.2%)", "Base-Mean": "0.1940 (97.5%)", "Base-Last": "0.0712 (100.2%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.3314 (100.1%)", "Qwen3-Emb": "0.3428 (97.8%)", "Gemma3-Mean": "0.2332 (122.2%)", "Gemma3-Last": "0.1024 (141.6%)", "Qwen3.5-Mean": "0.2354 (113.3%)", "Qwen3.5-Last": "0.0970 (138.7%)", "Dedicated Mean": "0.3371 (98.9%)", "Base-Mean": "0.2343 (117.7%)", "Base-Last": "0.0997 (140.2%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.3297 (99.6%)", "Qwen3-Emb": "0.3430 (97.9%)", "Gemma3-Mean": "0.2267 (118.8%)", "Gemma3-Last": "0.0965 (133.4%)", "Qwen3.5-Mean": "0.2298 (110.5%)", "Qwen3.5-Last": "0.0880 (125.8%)", "Dedicated Mean": "0.3364 (98.7%)", "Base-Mean": "0.2283 (114.7%)", "Base-Last": "0.0922 (129.6%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.3322 (100.3%)", "Qwen3-Emb": "0.3425 (97.7%)", "Gemma3-Mean": "0.2321 (121.6%)", "Gemma3-Last": "0.1019 (140.9%)", "Qwen3.5-Mean": "0.2333 (112.2%)", "Qwen3.5-Last": "0.0961 (137.4%)", "Dedicated Mean": "0.3374 (99.0%)", "Base-Mean": "0.2327 (116.9%)", "Base-Last": "0.0990 (139.2%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.3314 (100.1%)", "Qwen3-Emb": "0.3428 (97.8%)", "Gemma3-Mean": "0.2353 (123.3%)", "Gemma3-Last": "0.1044 (144.3%)", "Qwen3.5-Mean": "0.2382 (114.6%)", "Qwen3.5-Last": "0.0969 (138.5%)", "Dedicated Mean": "0.3371 (99.0%)", "Base-Mean": "0.2368 (119.0%)", "Base-Last": "0.1007 (141.4%)"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.3356 (101.4%)", "Qwen3-Emb": "0.3409 (97.3%)", "Gemma3-Mean": "0.2327 (122.0%)", "Gemma3-Last": "0.1028 (142.1%)", "Qwen3.5-Mean": "0.2351 (113.1%)", "Qwen3.5-Last": "0.0966 (138.1%)", "Dedicated Mean": "0.3382 (99.3%)", "Base-Mean": "0.2339 (117.5%)", "Base-Last": "0.0997 (140.1%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "0.3227 (97.5%)", "Qwen3-Emb": "0.3404 (97.1%)", "Gemma3-Mean": "0.1710 (89.6%)", "Gemma3-Last": "0.0788 (108.9%)", "Qwen3.5-Mean": "0.1844 (88.7%)", "Qwen3.5-Last": "0.0625 (89.4%)", "Dedicated Mean": "0.3316 (97.3%)", "Base-Mean": "0.1777 (89.2%)", "Base-Last": "0.0706 (99.2%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "PCA-k", "EmbGemma": "0.3329 (100.5%)", "Qwen3-Emb": "0.3399 (97.0%)", "Gemma3-Mean": "0.1853 (97.1%)", "Gemma3-Last": "0.0679 (93.9%)", "Qwen3.5-Mean": "0.1918 (92.3%)", "Qwen3.5-Last": "0.0686 (98.1%)", "Dedicated Mean": "0.3364 (98.8%)", "Base-Mean": "0.1885 (94.7%)", "Base-Last": "0.0683 (96.0%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "Whitening-k", "EmbGemma": "0.3075 (92.9%)", "Qwen3-Emb": "0.3221 (91.9%)", "Gemma3-Mean": "0.2358 (123.5%)", "Gemma3-Last": "0.1063 (147.0%)", "Qwen3.5-Mean": "0.2359 (113.5%)", "Qwen3.5-Last": "0.0947 (135.4%)", "Dedicated Mean": "0.3148 (92.4%)", "Base-Mean": "0.2359 (118.5%)", "Base-Last": "0.1005 (141.2%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "SpecTemp", "EmbGemma": "0.3317 (100.2%)", "Qwen3-Emb": "0.3408 (97.2%)", "Gemma3-Mean": "0.1921 (100.7%)", "Gemma3-Last": "0.0720 (99.5%)", "Qwen3.5-Mean": "0.1959 (94.3%)", "Qwen3.5-Last": "0.0716 (102.4%)", "Dedicated Mean": "0.3362 (98.7%)", "Base-Mean": "0.1940 (97.5%)", "Base-Last": "0.0718 (100.9%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "0.3276 (99.0%)", "Qwen3-Emb": "0.3419 (97.5%)", "Gemma3-Mean": "0.2352 (123.2%)", "Gemma3-Last": "0.1057 (146.1%)", "Qwen3.5-Mean": "0.2365 (113.8%)", "Qwen3.5-Last": "0.0942 (134.7%)", "Dedicated Mean": "0.3347 (98.2%)", "Base-Mean": "0.2359 (118.5%)", "Base-Last": "0.1000 (140.4%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.3273 (98.9%)", "Qwen3-Emb": "0.3420 (97.6%)", "Gemma3-Mean": "0.1858 (97.3%)", "Gemma3-Last": "0.0684 (94.6%)", "Qwen3.5-Mean": "0.1923 (92.5%)", "Qwen3.5-Last": "0.0692 (99.0%)", "Dedicated Mean": "0.3347 (98.2%)", "Base-Mean": "0.1890 (94.9%)", "Base-Last": "0.0688 (96.8%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.3282 (99.1%)", "Qwen3-Emb": "0.3425 (97.7%)", "Gemma3-Mean": "0.1918 (100.5%)", "Gemma3-Last": "0.0728 (100.6%)", "Qwen3.5-Mean": "0.1968 (94.7%)", "Qwen3.5-Last": "0.0711 (101.6%)", "Dedicated Mean": "0.3354 (98.4%)", "Base-Mean": "0.1943 (97.6%)", "Base-Last": "0.0720 (101.1%)"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Crowd. 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Proj. (Σ, γ*, ε*)", "EmbGemma": "0.3320 (100.3%)", "Qwen3-Emb": "0.3410 (97.3%)", "Gemma3-Mean": "0.2358 (123.5%)", "Gemma3-Last": "0.1061 (146.7%)", "Qwen3.5-Mean": "0.2360 (113.6%)", "Qwen3.5-Last": "0.0946 (135.3%)", "Dedicated Mean": "0.3365 (98.8%)", "Base-Mean": "0.2359 (118.6%)", "Base-Last": "0.1003 (141.0%)"}, {"Dataset": "ArguAna", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "0.2976 (89.9%)", "Qwen3-Emb": "0.3300 (94.2%)", "Gemma3-Mean": "0.1731 (90.7%)", "Gemma3-Last": "0.0693 (95.8%)", "Qwen3.5-Mean": "0.1732 (83.4%)", "Qwen3.5-Last": "0.0572 (81.8%)", "Dedicated Mean": "0.3138 (92.0%)", "Base-Mean": "0.1731 (87.0%)", "Base-Last": "0.0633 (88.8%)"}, {"Dataset": "ArguAna", "k": "128", "Method": "PCA-k", "EmbGemma": "0.3237 (97.8%)", "Qwen3-Emb": "0.3311 (94.5%)", "Gemma3-Mean": "0.1722 (90.2%)", "Gemma3-Last": "0.0620 (85.7%)", "Qwen3.5-Mean": "0.1837 (88.4%)", "Qwen3.5-Last": "0.0640 (91.6%)", "Dedicated Mean": "0.3274 (96.1%)", "Base-Mean": "0.1779 (89.3%)", "Base-Last": "0.0630 (88.7%)"}, {"Dataset": "ArguAna", "k": "128", "Method": "Whitening-k", "EmbGemma": "0.3076 (92.9%)", "Qwen3-Emb": "0.3209 (91.6%)", "Gemma3-Mean": "0.2158 (113.1%)", "Gemma3-Last": "0.0970 (134.1%)", "Qwen3.5-Mean": "0.2229 (107.3%)", "Qwen3.5-Last": "0.0894 (127.8%)", "Dedicated Mean": "0.3143 (92.2%)", "Base-Mean": "0.2193 (110.2%)", "Base-Last": "0.0932 (130.9%)"}, {"Dataset": "ArguAna", "k": "128", "Method": "SpecTemp", "EmbGemma": "0.3196 (96.5%)", "Qwen3-Emb": "0.3328 (95.0%)", "Gemma3-Mean": "0.1886 (98.8%)", "Gemma3-Last": "0.0696 (96.2%)", "Qwen3.5-Mean": "0.1966 (94.6%)", "Qwen3.5-Last": "0.0681 (97.3%)", "Dedicated Mean": "0.3262 (95.7%)", "Base-Mean": "0.1926 (96.7%)", "Base-Last": "0.0688 (96.8%)"}, {"Dataset": "ArguAna", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "0.3151 (95.2%)", "Qwen3-Emb": "0.3344 (95.4%)", "Gemma3-Mean": "0.2167 (113.5%)", "Gemma3-Last": "0.0977 (135.1%)", "Qwen3.5-Mean": "0.2233 (107.4%)", "Qwen3.5-Last": "0.0890 (127.3%)", "Dedicated Mean": "0.3247 (95.3%)", "Base-Mean": "0.2200 (110.5%)", "Base-Last": "0.0933 (131.2%)"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.3202 (96.7%)", "Qwen3-Emb": "0.3332 (95.1%)", "Gemma3-Mean": "0.2158 (113.1%)", "Gemma3-Last": "0.0969 (134.0%)", "Qwen3.5-Mean": "0.2228 (107.2%)", "Qwen3.5-Last": "0.0893 (127.7%)", "Dedicated Mean": "0.3267 (95.9%)", "Base-Mean": "0.2193 (110.1%)", "Base-Last": "0.0931 (130.9%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.2628 (79.4%)", "Qwen3-Emb": "0.3034 (86.6%)", "Gemma3-Mean": "0.1458 (76.4%)", "Gemma3-Last": "0.0568 (78.5%)", "Qwen3.5-Mean": "0.1256 (60.4%)", "Qwen3.5-Last": "0.0441 (63.1%)", "Dedicated Mean": "0.2831 (83.0%)", "Base-Mean": "0.1357 (68.4%)", "Base-Last": "0.0505 (70.8%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "0.3016 (91.1%)", "Qwen3-Emb": "0.3092 (88.2%)", "Gemma3-Mean": "0.1514 (79.3%)", "Gemma3-Last": "0.0502 (69.4%)", "Qwen3.5-Mean": "0.1685 (81.1%)", "Qwen3.5-Last": "0.0530 (75.8%)", "Dedicated Mean": "0.3054 (89.7%)", "Base-Mean": "0.1600 (80.2%)", "Base-Last": "0.0516 (72.6%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.2791 (84.3%)", "Qwen3-Emb": "0.2999 (85.6%)", "Gemma3-Mean": "0.1805 (94.6%)", "Gemma3-Last": "0.0765 (105.7%)", "Qwen3.5-Mean": "0.1950 (93.8%)", "Qwen3.5-Last": "0.0659 (94.2%)", "Dedicated Mean": "0.2895 (84.9%)", "Base-Mean": "0.1878 (94.2%)", "Base-Last": "0.0712 (100.0%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.2842 (85.8%)", "Qwen3-Emb": "0.3080 (87.9%)", "Gemma3-Mean": "0.1699 (89.0%)", "Gemma3-Last": "0.0600 (82.9%)", "Qwen3.5-Mean": "0.1883 (90.6%)", "Qwen3.5-Last": "0.0597 (85.4%)", "Dedicated Mean": "0.2961 (86.9%)", "Base-Mean": "0.1791 (89.8%)", "Base-Last": "0.0599 (84.2%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.2921 (88.2%)", "Qwen3-Emb": "0.3137 (89.5%)", "Gemma3-Mean": "0.1798 (94.2%)", "Gemma3-Last": "0.0770 (106.5%)", "Qwen3.5-Mean": "0.1935 (93.1%)", "Qwen3.5-Last": "0.0662 (94.6%)", "Dedicated Mean": "0.3029 (88.9%)", "Base-Mean": "0.1866 (93.7%)", "Base-Last": "0.0716 (100.5%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.2921 (88.2%)", "Qwen3-Emb": "0.3134 (89.4%)", "Gemma3-Mean": "0.1690 (88.6%)", "Gemma3-Last": "0.0691 (95.6%)", "Qwen3.5-Mean": "0.1899 (91.4%)", "Qwen3.5-Last": "0.0623 (89.1%)", "Dedicated Mean": "0.3028 (88.8%)", "Base-Mean": "0.1794 (90.0%)", "Base-Last": "0.0657 (92.3%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.2916 (88.1%)", "Qwen3-Emb": "0.3131 (89.3%)", "Gemma3-Mean": "0.1798 (94.2%)", "Gemma3-Last": "0.0771 (106.6%)", "Qwen3.5-Mean": "0.1938 (93.2%)", "Qwen3.5-Last": "0.0662 (94.6%)", "Dedicated Mean": "0.3024 (88.7%)", "Base-Mean": "0.1868 (93.7%)", "Base-Last": "0.0716 (100.6%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.2928 (88.4%)", "Qwen3-Emb": "0.3130 (89.3%)", "Gemma3-Mean": "0.1795 (94.0%)", "Gemma3-Last": "0.0772 (106.7%)", "Qwen3.5-Mean": "0.1936 (93.1%)", "Qwen3.5-Last": "0.0664 (94.9%)", "Dedicated Mean": "0.3029 (88.9%)", "Base-Mean": "0.1865 (93.6%)", "Base-Last": "0.0718 (100.8%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.2878 (86.9%)", "Qwen3-Emb": "0.3088 (88.1%)", "Gemma3-Mean": "0.1807 (94.7%)", "Gemma3-Last": "0.0765 (105.8%)", "Qwen3.5-Mean": "0.1949 (93.8%)", "Qwen3.5-Last": "0.0659 (94.2%)", "Dedicated Mean": "0.2983 (87.5%)", "Base-Mean": "0.1878 (94.3%)", "Base-Last": "0.0712 (100.0%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.3310 (99.0%)", "Qwen3-Emb": "0.3994 (98.1%)", "Gemma3-Mean": "0.0511 (92.7%)", "Gemma3-Last": "0.0099 (86.9%)", "Qwen3.5-Mean": "0.0373 (81.9%)", "Qwen3.5-Last": "0.0069 (80.8%)", "Dedicated Mean": "0.3652 (98.5%)", "Base-Mean": "0.0442 (87.3%)", "Base-Last": "0.0084 (83.8%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "0.3406 (101.8%)", "Qwen3-Emb": "0.3995 (98.1%)", "Gemma3-Mean": "0.0364 (66.2%)", "Gemma3-Last": "0.0109 (95.7%)", "Qwen3.5-Mean": "0.0334 (73.3%)", "Qwen3.5-Last": "0.0086 (101.3%)", "Dedicated Mean": "0.3700 (100.0%)", "Base-Mean": "0.0349 (69.8%)", "Base-Last": "0.0097 (98.5%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.3145 (94.0%)", "Qwen3-Emb": "0.3669 (90.1%)", "Gemma3-Mean": "0.1109 (201.3%)", "Gemma3-Last": "0.0170 (149.5%)", "Qwen3.5-Mean": "0.0831 (182.3%)", "Qwen3.5-Last": "0.0182 (213.7%)", "Dedicated Mean": "0.3407 (92.1%)", "Base-Mean": "0.0970 (191.8%)", "Base-Last": "0.0176 (181.6%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.3429 (102.5%)", "Qwen3-Emb": "0.4009 (98.4%)", "Gemma3-Mean": "0.0370 (67.1%)", "Gemma3-Last": "0.0111 (97.5%)", "Qwen3.5-Mean": "0.0340 (74.7%)", "Qwen3.5-Last": "0.0096 (112.9%)", "Dedicated Mean": "0.3719 (100.5%)", "Base-Mean": "0.0355 (70.9%)", "Base-Last": "0.0103 (105.2%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.3417 (102.2%)", "Qwen3-Emb": "0.4001 (98.3%)", "Gemma3-Mean": "0.1109 (201.3%)", "Gemma3-Last": "0.0171 (149.9%)", "Qwen3.5-Mean": "0.0822 (180.3%)", "Qwen3.5-Last": "0.0172 (202.4%)", "Dedicated Mean": "0.3709 (100.2%)", "Base-Mean": "0.0965 (190.8%)", "Base-Last": "0.0171 (176.2%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.3362 (100.5%)", "Qwen3-Emb": "0.4004 (98.3%)", "Gemma3-Mean": "0.0411 (74.7%)", "Gemma3-Last": "0.0115 (101.1%)", "Qwen3.5-Mean": "0.0352 (77.2%)", "Qwen3.5-Last": "0.0088 (103.7%)", "Dedicated Mean": "0.3683 (99.4%)", "Base-Mean": "0.0382 (75.9%)", "Base-Last": "0.0101 (102.4%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.3387 (101.3%)", "Qwen3-Emb": "0.3988 (97.9%)", "Gemma3-Mean": "0.0407 (73.9%)", "Gemma3-Last": "0.0114 (99.6%)", "Qwen3.5-Mean": "0.0354 (77.6%)", "Qwen3.5-Last": "0.0096 (112.6%)", "Dedicated Mean": "0.3688 (99.6%)", "Base-Mean": "0.0381 (75.8%)", "Base-Last": "0.0105 (106.1%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.3378 (101.0%)", "Qwen3-Emb": "0.3994 (98.1%)", "Gemma3-Mean": "0.0407 (73.9%)", "Gemma3-Last": "0.0114 (99.6%)", "Qwen3.5-Mean": "0.0354 (77.6%)", "Qwen3.5-Last": "0.0096 (112.6%)", "Dedicated Mean": "0.3686 (99.5%)", "Base-Mean": "0.0381 (75.8%)", "Base-Last": "0.0105 (106.1%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.3417 (102.2%)", "Qwen3-Emb": "0.4001 (98.3%)", "Gemma3-Mean": "0.1109 (201.3%)", "Gemma3-Last": "0.0171 (149.9%)", "Qwen3.5-Mean": "0.0822 (180.3%)", "Qwen3.5-Last": "0.0172 (202.4%)", "Dedicated Mean": "0.3709 (100.2%)", "Base-Mean": "0.0965 (190.8%)", "Base-Last": "0.0171 (176.2%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.3429 (102.5%)", "Qwen3-Emb": "0.3976 (97.7%)", "Gemma3-Mean": "0.0695 (126.2%)", "Gemma3-Last": "0.0140 (122.8%)", "Qwen3.5-Mean": "0.0522 (114.6%)", "Qwen3.5-Last": "0.0123 (144.6%)", "Dedicated Mean": "0.3702 (100.1%)", "Base-Mean": "0.0609 (120.4%)", "Base-Last": "0.0132 (133.7%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.3444 (103.0%)", "Qwen3-Emb": "0.3990 (98.0%)", "Gemma3-Mean": "0.1113 (202.2%)", "Gemma3-Last": "0.0170 (149.2%)", "Qwen3.5-Mean": "0.0833 (182.9%)", "Qwen3.5-Last": "0.0185 (218.1%)", "Dedicated Mean": "0.3717 (100.5%)", "Base-Mean": "0.0973 (192.5%)", "Base-Last": "0.0178 (183.7%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.3429 (102.5%)", "Qwen3-Emb": "0.4006 (98.4%)", "Gemma3-Mean": "0.1051 (190.9%)", "Gemma3-Last": "0.0170 (148.7%)", "Qwen3.5-Mean": "0.0771 (169.1%)", "Qwen3.5-Last": "0.0160 (187.8%)", "Dedicated Mean": "0.3718 (100.5%)", "Base-Mean": "0.0911 (180.0%)", "Base-Last": "0.0165 (168.2%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.3441 (102.9%)", "Qwen3-Emb": "0.4011 (98.5%)", "Gemma3-Mean": "0.1115 (202.4%)", "Gemma3-Last": "0.0168 (147.3%)", "Qwen3.5-Mean": "0.0800 (175.6%)", "Qwen3.5-Last": "0.0168 (197.3%)", "Dedicated Mean": "0.3726 (100.7%)", "Base-Mean": "0.0958 (189.0%)", "Base-Last": "0.0168 (172.3%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "0.3200 (95.7%)", "Qwen3-Emb": "0.3877 (95.2%)", "Gemma3-Mean": "0.0677 (122.9%)", "Gemma3-Last": "0.0129 (113.0%)", "Qwen3.5-Mean": "0.0300 (65.7%)", "Qwen3.5-Last": "0.0062 (72.9%)", "Dedicated Mean": "0.3538 (95.4%)", "Base-Mean": "0.0488 (94.3%)", "Base-Last": "0.0095 (92.9%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "0.3230 (96.6%)", "Qwen3-Emb": "0.3936 (96.7%)", "Gemma3-Mean": "0.0323 (58.6%)", "Gemma3-Last": "0.0106 (92.9%)", "Qwen3.5-Mean": "0.0314 (69.0%)", "Qwen3.5-Last": "0.0082 (96.6%)", "Dedicated Mean": "0.3583 (96.6%)", "Base-Mean": "0.0319 (63.8%)", "Base-Last": "0.0094 (94.8%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "0.3147 (94.1%)", "Qwen3-Emb": "0.3761 (92.4%)", "Gemma3-Mean": "0.0866 (157.3%)", "Gemma3-Last": "0.0184 (161.6%)", "Qwen3.5-Mean": "0.0686 (150.5%)", "Qwen3.5-Last": "0.0147 (173.5%)", "Dedicated Mean": "0.3454 (93.2%)", "Base-Mean": "0.0776 (153.9%)", "Base-Last": "0.0165 (167.5%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "0.3324 (99.4%)", "Qwen3-Emb": "0.3941 (96.8%)", "Gemma3-Mean": "0.0336 (60.9%)", "Gemma3-Last": "0.0110 (96.7%)", "Qwen3.5-Mean": "0.0318 (69.8%)", "Qwen3.5-Last": "0.0088 (104.0%)", "Dedicated Mean": "0.3632 (98.1%)", "Base-Mean": "0.0327 (65.3%)", "Base-Last": "0.0099 (100.4%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "0.3250 (97.2%)", "Qwen3-Emb": "0.3963 (97.3%)", "Gemma3-Mean": "0.0868 (157.7%)", "Gemma3-Last": "0.0181 (158.4%)", "Qwen3.5-Mean": "0.0678 (148.7%)", "Qwen3.5-Last": "0.0148 (174.7%)", "Dedicated Mean": "0.3607 (97.2%)", "Base-Mean": "0.0773 (153.2%)", "Base-Last": "0.0164 (166.6%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.3308", "Qwen3-Emb": "0.3429", "Gemma3-Mean": "0.1905", "Gemma3-Last": "0.0698", "Qwen3.5-Mean": "0.1935", "Qwen3.5-Last": "0.0699", "Dedicated Mean": "0.3368", "Base-Mean": "0.1920", "Base-Last": "0.0698"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.3314", "Qwen3-Emb": "0.3427", "Gemma3-Mean": "0.1919", "Gemma3-Last": "0.0713", "Qwen3.5-Mean": "0.1958", "Qwen3.5-Last": "0.0712", "Dedicated Mean": "0.3370", "Base-Mean": "0.1938", "Base-Last": "0.0713"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Crowd. 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Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.3276", "Qwen3-Emb": "0.3419", "Gemma3-Mean": "0.1917", "Gemma3-Last": "0.0725", "Qwen3.5-Mean": "0.1975", "Qwen3.5-Last": "0.0711", "Dedicated Mean": "0.3347", "Base-Mean": "0.1946", "Base-Last": "0.0718"}, {"Dataset": "ArguAna", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.3272", "Qwen3-Emb": "0.3417", "Gemma3-Mean": "0.2352", "Gemma3-Last": "0.1057", "Qwen3.5-Mean": "0.2365", "Qwen3.5-Last": "0.0942", "Dedicated Mean": "0.3345", "Base-Mean": "0.2359", "Base-Last": "0.1000"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o SNR Sched. 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(Σ, γ*, ε*)", "EmbGemma": "0.3320", "Qwen3-Emb": "0.3410", "Gemma3-Mean": "0.2358", "Gemma3-Last": "0.1061", "Qwen3.5-Mean": "0.2360", "Qwen3.5-Last": "0.0946", "Dedicated Mean": "0.3365", "Base-Mean": "0.2359", "Base-Last": "0.1003"}, {"Dataset": "ArguAna", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "0.2976", "Qwen3-Emb": "0.3300", "Gemma3-Mean": "0.1731", "Gemma3-Last": "0.0693", "Qwen3.5-Mean": "0.1732", "Qwen3.5-Last": "0.0572", "Dedicated Mean": "0.3138", "Base-Mean": "0.1731", "Base-Last": "0.0633"}, {"Dataset": "ArguAna", "k": "128", "Method": "PCA-k", "EmbGemma": "0.3237", "Qwen3-Emb": "0.3311", "Gemma3-Mean": "0.1722", "Gemma3-Last": "0.0620", "Qwen3.5-Mean": "0.1837", "Qwen3.5-Last": "0.0640", "Dedicated Mean": "0.3274", "Base-Mean": "0.1779", "Base-Last": "0.0630"}, {"Dataset": "ArguAna", "k": "128", "Method": "Whitening-k", "EmbGemma": "0.3076", "Qwen3-Emb": "0.3209", "Gemma3-Mean": "0.2158", "Gemma3-Last": "0.0970", "Qwen3.5-Mean": "0.2229", "Qwen3.5-Last": "0.0894", "Dedicated Mean": "0.3143", "Base-Mean": "0.2193", "Base-Last": "0.0932"}, {"Dataset": "ArguAna", "k": "128", "Method": "SpecTemp", "EmbGemma": "0.3196", "Qwen3-Emb": "0.3328", "Gemma3-Mean": "0.1886", "Gemma3-Last": "0.0696", "Qwen3.5-Mean": "0.1966", "Qwen3.5-Last": "0.0681", "Dedicated Mean": "0.3262", "Base-Mean": "0.1926", "Base-Last": "0.0688"}, {"Dataset": "ArguAna", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "0.3151", "Qwen3-Emb": "0.3344", "Gemma3-Mean": "0.2167", "Gemma3-Last": "0.0977", "Qwen3.5-Mean": "0.2233", "Qwen3.5-Last": "0.0890", "Dedicated Mean": "0.3247", "Base-Mean": "0.2200", "Base-Last": "0.0933"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.3145", "Qwen3-Emb": "0.3326", "Gemma3-Mean": "0.1715", "Gemma3-Last": "0.0616", "Qwen3.5-Mean": "0.1851", "Qwen3.5-Last": "0.0645", "Dedicated Mean": "0.3236", "Base-Mean": "0.1783", "Base-Last": "0.0630"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.3166", "Qwen3-Emb": "0.3339", "Gemma3-Mean": "0.1887", "Gemma3-Last": "0.0707", "Qwen3.5-Mean": "0.1964", "Qwen3.5-Last": "0.0666", "Dedicated Mean": "0.3252", "Base-Mean": "0.1925", "Base-Last": "0.0687"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Crowd. 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(Σ, γ*, ε*)", "EmbGemma": "0.2878", "Qwen3-Emb": "0.3088", "Gemma3-Mean": "0.1807", "Gemma3-Last": "0.0765", "Qwen3.5-Mean": "0.1949", "Qwen3.5-Last": "0.0659", "Dedicated Mean": "0.2983", "Base-Mean": "0.1878", "Base-Last": "0.0712"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.3310", "Qwen3-Emb": "0.3994", "Gemma3-Mean": "0.0511", "Gemma3-Last": "0.0099", "Qwen3.5-Mean": "0.0373", "Qwen3.5-Last": "0.0069", "Dedicated Mean": "0.3652", "Base-Mean": "0.0442", "Base-Last": "0.0084"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "0.3406", "Qwen3-Emb": "0.3995", "Gemma3-Mean": "0.0364", "Gemma3-Last": "0.0109", "Qwen3.5-Mean": "0.0334", "Qwen3.5-Last": "0.0086", "Dedicated Mean": "0.3700", "Base-Mean": "0.0349", "Base-Last": "0.0097"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.3145", "Qwen3-Emb": "0.3669", "Gemma3-Mean": "0.1109", "Gemma3-Last": "0.0170", "Qwen3.5-Mean": "0.0831", "Qwen3.5-Last": "0.0182", "Dedicated Mean": "0.3407", "Base-Mean": "0.0970", "Base-Last": "0.0176"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.3429", "Qwen3-Emb": "0.4009", "Gemma3-Mean": "0.0370", "Gemma3-Last": "0.0111", "Qwen3.5-Mean": "0.0340", "Qwen3.5-Last": "0.0096", "Dedicated Mean": "0.3719", "Base-Mean": "0.0355", "Base-Last": "0.0103"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.3417", "Qwen3-Emb": "0.4001", "Gemma3-Mean": "0.1109", "Gemma3-Last": "0.0171", "Qwen3.5-Mean": "0.0822", "Qwen3.5-Last": "0.0172", "Dedicated Mean": "0.3709", "Base-Mean": "0.0965", "Base-Last": "0.0171"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.3362", "Qwen3-Emb": "0.4004", "Gemma3-Mean": "0.0411", "Gemma3-Last": "0.0115", "Qwen3.5-Mean": "0.0352", "Qwen3.5-Last": "0.0088", "Dedicated Mean": "0.3683", "Base-Mean": "0.0382", "Base-Last": "0.0101"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.3387", "Qwen3-Emb": "0.3988", "Gemma3-Mean": "0.0407", "Gemma3-Last": "0.0114", "Qwen3.5-Mean": "0.0354", "Qwen3.5-Last": "0.0096", "Dedicated Mean": "0.3688", "Base-Mean": "0.0381", "Base-Last": "0.0105"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.3378", "Qwen3-Emb": "0.3994", "Gemma3-Mean": "0.0407", "Gemma3-Last": "0.0114", "Qwen3.5-Mean": "0.0354", "Qwen3.5-Last": "0.0096", "Dedicated Mean": "0.3686", "Base-Mean": "0.0381", "Base-Last": "0.0105"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.3417", "Qwen3-Emb": "0.4001", "Gemma3-Mean": "0.1109", "Gemma3-Last": "0.0171", "Qwen3.5-Mean": "0.0822", "Qwen3.5-Last": "0.0172", "Dedicated Mean": "0.3709", "Base-Mean": "0.0965", "Base-Last": "0.0171"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.3429", "Qwen3-Emb": "0.3976", "Gemma3-Mean": "0.0695", "Gemma3-Last": "0.0140", "Qwen3.5-Mean": "0.0522", "Qwen3.5-Last": "0.0123", "Dedicated Mean": "0.3702", "Base-Mean": "0.0609", "Base-Last": "0.0132"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.3444", "Qwen3-Emb": "0.3990", "Gemma3-Mean": "0.1113", "Gemma3-Last": "0.0170", "Qwen3.5-Mean": "0.0833", "Qwen3.5-Last": "0.0185", "Dedicated Mean": "0.3717", "Base-Mean": "0.0973", "Base-Last": "0.0178"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.3429", "Qwen3-Emb": "0.4006", "Gemma3-Mean": "0.1051", "Gemma3-Last": "0.0170", "Qwen3.5-Mean": "0.0771", "Qwen3.5-Last": "0.0160", "Dedicated Mean": "0.3718", "Base-Mean": "0.0911", "Base-Last": "0.0165"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Orth. Proj. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.2812", "Qwen3-Emb": "0.3758", "Gemma3-Mean": "0.0317", "Gemma3-Last": "0.0113", "Qwen3.5-Mean": "0.0293", "Qwen3.5-Last": "0.0069", "Dedicated Mean": "0.3285", "Base-Mean": "0.0305", "Base-Last": "0.0091"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.2972", "Qwen3-Emb": "0.3781", "Gemma3-Mean": "0.0322", "Gemma3-Last": "0.0113", "Qwen3.5-Mean": "0.0294", "Qwen3.5-Last": "0.0078", "Dedicated Mean": "0.3377", "Base-Mean": "0.0308", "Base-Last": "0.0095"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Crowd. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "90.6%", "Qwen3-Emb": "94.3%", "Gemma3-Mean": "59.7%", "Gemma3-Last": "73.0%", "Qwen3.5-Mean": "65.8%", "Qwen3.5-Last": "104.5%", "Dedicated Mean": "92.5%", "Base-Mean": "62.8%", "Base-Last": "88.8%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "92.2%", "Qwen3-Emb": "96.5%", "Gemma3-Mean": "70.0%", "Gemma3-Last": "85.7%", "Qwen3.5-Mean": "67.4%", "Qwen3.5-Last": "100.0%", "Dedicated Mean": "94.3%", "Base-Mean": "68.7%", "Base-Last": "92.9%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "91.5%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "70.0%", "Gemma3-Last": "85.7%", "Qwen3.5-Mean": "67.4%", "Qwen3.5-Last": "100.0%", "Dedicated Mean": "94.2%", "Base-Mean": "68.7%", "Base-Last": "92.9%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "91.5%", "Qwen3-Emb": "95.7%", "Gemma3-Mean": "86.2%", "Gemma3-Last": "80.5%", "Qwen3.5-Mean": "84.5%", "Qwen3.5-Last": "161.8%", "Dedicated Mean": "93.6%", "Base-Mean": "85.4%", "Base-Last": "121.2%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "92.1%", "Qwen3-Emb": "96.6%", "Gemma3-Mean": "84.2%", "Gemma3-Last": "82.3%", "Qwen3.5-Mean": "80.2%", "Qwen3.5-Last": "116.5%", "Dedicated Mean": "94.4%", "Base-Mean": "82.2%", "Base-Last": "99.4%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "92.2%", "Qwen3-Emb": "96.5%", "Gemma3-Mean": "86.2%", "Gemma3-Last": "80.5%", "Qwen3.5-Mean": "84.6%", "Qwen3.5-Last": "161.8%", "Dedicated Mean": "94.3%", "Base-Mean": "85.4%", "Base-Last": "121.2%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "91.6%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "86.3%", "Gemma3-Last": "80.4%", "Qwen3.5-Mean": "84.9%", "Qwen3.5-Last": "156.0%", "Dedicated Mean": "94.2%", "Base-Mean": "85.6%", "Base-Last": "118.2%"}, {"Dataset": "FiQA-2018", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "89.8%", "Qwen3-Emb": "96.3%", "Gemma3-Mean": "89.0%", "Gemma3-Last": "81.0%", "Qwen3.5-Mean": "81.5%", "Qwen3.5-Last": "205.5%", "Dedicated Mean": "93.0%", "Base-Mean": "85.2%", "Base-Last": "143.3%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "65.5%", "Qwen3-Emb": "80.9%", "Gemma3-Mean": "51.9%", "Gemma3-Last": "37.9%", "Qwen3.5-Mean": "25.2%", "Qwen3.5-Last": "81.9%", "Dedicated Mean": "73.2%", "Base-Mean": "38.5%", "Base-Last": "59.9%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "PCA-k", "EmbGemma": "67.6%", "Qwen3-Emb": "85.4%", "Gemma3-Mean": "37.2%", "Gemma3-Last": "61.8%", "Qwen3.5-Mean": "51.2%", "Qwen3.5-Last": "51.7%", "Dedicated Mean": "76.5%", "Base-Mean": "44.2%", "Base-Last": "56.8%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Whitening-k", "EmbGemma": "70.6%", "Qwen3-Emb": "83.7%", "Gemma3-Mean": "54.8%", "Gemma3-Last": "63.3%", "Qwen3.5-Mean": "68.5%", "Qwen3.5-Last": "58.1%", "Dedicated Mean": "77.2%", "Base-Mean": "61.6%", "Base-Last": "60.7%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "SpecTemp", "EmbGemma": "70.7%", "Qwen3-Emb": "84.3%", "Gemma3-Mean": "49.6%", "Gemma3-Last": "66.0%", "Qwen3.5-Mean": "62.6%", "Qwen3.5-Last": "45.2%", "Dedicated Mean": "77.5%", "Base-Mean": "56.1%", "Base-Last": "55.6%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "74.0%", "Qwen3-Emb": "86.6%", "Gemma3-Mean": "57.0%", "Gemma3-Last": "66.4%", "Qwen3.5-Mean": "72.3%", "Qwen3.5-Last": "64.8%", "Dedicated Mean": "80.3%", "Base-Mean": "64.7%", "Base-Last": "65.6%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "71.2%", "Qwen3-Emb": "86.3%", "Gemma3-Mean": "38.0%", "Gemma3-Last": "63.0%", "Qwen3.5-Mean": "58.6%", "Qwen3.5-Last": "63.0%", "Dedicated Mean": "78.8%", "Base-Mean": "48.3%", "Base-Last": "63.0%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "74.3%", "Qwen3-Emb": "85.7%", "Gemma3-Mean": "49.2%", "Gemma3-Last": "67.9%", "Qwen3.5-Mean": "67.3%", "Qwen3.5-Last": "56.5%", "Dedicated Mean": "80.0%", "Base-Mean": "58.3%", "Base-Last": "62.2%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "74.0%", "Qwen3-Emb": "86.6%", "Gemma3-Mean": "49.2%", "Gemma3-Last": "67.9%", "Qwen3.5-Mean": "67.3%", "Qwen3.5-Last": "56.5%", "Dedicated Mean": "80.3%", "Base-Mean": "58.3%", "Base-Last": "62.2%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "71.8%", "Qwen3-Emb": "86.8%", "Gemma3-Mean": "57.0%", "Gemma3-Last": "66.4%", "Qwen3.5-Mean": "72.3%", "Qwen3.5-Last": "64.8%", "Dedicated Mean": "79.3%", "Base-Mean": "64.7%", "Base-Last": "65.6%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "73.6%", "Qwen3-Emb": "86.7%", "Gemma3-Mean": "53.4%", "Gemma3-Last": "64.7%", "Qwen3.5-Mean": "68.8%", "Qwen3.5-Last": "67.8%", "Dedicated Mean": "80.1%", "Base-Mean": "61.1%", "Base-Last": "66.3%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "74.3%", "Qwen3-Emb": "85.7%", "Gemma3-Mean": "57.0%", "Gemma3-Last": "66.4%", "Qwen3.5-Mean": "72.3%", "Qwen3.5-Last": "64.8%", "Dedicated Mean": "80.0%", "Base-Mean": "64.7%", "Base-Last": "65.6%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "73.7%", "Qwen3-Emb": "86.8%", "Gemma3-Mean": "56.9%", "Gemma3-Last": "64.4%", "Qwen3.5-Mean": "73.0%", "Qwen3.5-Last": "60.3%", "Dedicated Mean": "80.2%", "Base-Mean": "64.9%", "Base-Last": "62.4%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "70.1%", "Qwen3-Emb": "84.8%", "Gemma3-Mean": "55.0%", "Gemma3-Last": "63.3%", "Qwen3.5-Mean": "68.5%", "Qwen3.5-Last": "58.1%", "Dedicated Mean": "77.5%", "Base-Mean": "61.8%", "Base-Last": "60.7%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "93.3%", "Gemma3-Last": "103.4%", "Qwen3.5-Mean": "95.1%", "Qwen3.5-Last": "96.7%", "Dedicated Mean": "99.9%", "Base-Mean": "94.2%", "Base-Last": "100.0%"}, {"Dataset": "ArguAna", "k": "512", "Method": "PCA-k", "EmbGemma": "101.7%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "99.5%", "Gemma3-Last": "96.0%", "Qwen3.5-Mean": "92.7%", "Qwen3.5-Last": "100.0%", "Dedicated Mean": "99.4%", "Base-Mean": "96.1%", "Base-Last": "98.0%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Whitening-k", "EmbGemma": "89.7%", "Qwen3-Emb": "87.9%", "Gemma3-Mean": "121.8%", "Gemma3-Last": "140.7%", "Qwen3.5-Mean": "112.6%", "Qwen3.5-Last": "137.7%", "Dedicated Mean": "88.8%", "Base-Mean": "117.2%", "Base-Last": "139.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "SpecTemp", "EmbGemma": "101.2%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "101.1%", "Gemma3-Last": "98.1%", "Qwen3.5-Mean": "93.9%", "Qwen3.5-Last": "102.2%", "Dedicated Mean": "99.2%", "Base-Mean": "97.5%", "Base-Last": "100.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "100.1%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "122.2%", "Gemma3-Last": "141.6%", "Qwen3.5-Mean": "113.3%", "Qwen3.5-Last": "138.7%", "Dedicated Mean": "98.9%", "Base-Mean": "117.7%", "Base-Last": "140.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.9%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "99.8%", "Gemma3-Last": "96.5%", "Qwen3.5-Mean": "93.1%", "Qwen3.5-Last": "100.0%", "Dedicated Mean": "98.9%", "Base-Mean": "96.5%", "Base-Last": "98.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "100.5%", "Gemma3-Last": "98.6%", "Qwen3.5-Mean": "94.2%", "Qwen3.5-Last": "101.8%", "Dedicated Mean": "98.9%", "Base-Mean": "97.4%", "Base-Last": "100.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.0%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "100.8%", "Gemma3-Last": "98.6%", "Qwen3.5-Mean": "94.2%", "Qwen3.5-Last": "101.7%", "Dedicated Mean": "99.0%", "Base-Mean": "97.5%", "Base-Last": "100.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "122.2%", "Gemma3-Last": "141.6%", "Qwen3.5-Mean": "113.3%", "Qwen3.5-Last": "138.7%", "Dedicated Mean": "99.0%", "Base-Mean": "117.7%", "Base-Last": "140.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "118.8%", "Gemma3-Last": "133.4%", "Qwen3.5-Mean": "110.5%", "Qwen3.5-Last": "125.8%", "Dedicated Mean": "98.7%", "Base-Mean": "114.7%", "Base-Last": "129.6%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.3%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "121.6%", "Gemma3-Last": "140.9%", "Qwen3.5-Mean": "112.2%", "Qwen3.5-Last": "137.4%", "Dedicated Mean": "99.0%", "Base-Mean": "116.9%", "Base-Last": "139.2%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.1%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "123.3%", "Gemma3-Last": "144.3%", "Qwen3.5-Mean": "114.6%", "Qwen3.5-Last": "138.5%", "Dedicated Mean": "99.0%", "Base-Mean": "119.0%", "Base-Last": "141.4%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "101.4%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "122.0%", "Gemma3-Last": "142.1%", "Qwen3.5-Mean": "113.1%", "Qwen3.5-Last": "138.1%", "Dedicated Mean": "99.3%", "Base-Mean": "117.5%", "Base-Last": "140.1%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "97.5%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "89.6%", "Gemma3-Last": "108.9%", "Qwen3.5-Mean": "88.7%", "Qwen3.5-Last": "89.4%", "Dedicated Mean": "97.3%", "Base-Mean": "89.2%", "Base-Last": "99.2%"}, {"Dataset": "ArguAna", "k": "256", "Method": "PCA-k", "EmbGemma": "100.5%", "Qwen3-Emb": "97.0%", "Gemma3-Mean": "97.1%", "Gemma3-Last": "93.9%", "Qwen3.5-Mean": "92.3%", "Qwen3.5-Last": "98.1%", "Dedicated Mean": "98.8%", "Base-Mean": "94.7%", "Base-Last": "96.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Whitening-k", "EmbGemma": "92.9%", "Qwen3-Emb": "91.9%", "Gemma3-Mean": "123.5%", "Gemma3-Last": "147.0%", "Qwen3.5-Mean": "113.5%", "Qwen3.5-Last": "135.4%", "Dedicated Mean": "92.4%", "Base-Mean": "118.5%", "Base-Last": "141.2%"}, {"Dataset": "ArguAna", "k": "256", "Method": "SpecTemp", "EmbGemma": "100.2%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "100.7%", "Gemma3-Last": "99.5%", "Qwen3.5-Mean": "94.3%", "Qwen3.5-Last": "102.4%", "Dedicated Mean": "98.7%", "Base-Mean": "97.5%", "Base-Last": "100.9%"}, {"Dataset": "ArguAna", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "99.0%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "123.2%", "Gemma3-Last": "146.1%", "Qwen3.5-Mean": "113.8%", "Qwen3.5-Last": "134.7%", "Dedicated Mean": "98.2%", "Base-Mean": "118.5%", "Base-Last": "140.4%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "98.9%", "Qwen3-Emb": "97.6%", "Gemma3-Mean": "97.3%", "Gemma3-Last": "94.6%", "Qwen3.5-Mean": "92.5%", "Qwen3.5-Last": "99.0%", "Dedicated Mean": "98.2%", "Base-Mean": "94.9%", "Base-Last": "96.8%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.1%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "100.5%", "Gemma3-Last": "100.6%", "Qwen3.5-Mean": "94.7%", "Qwen3.5-Last": "101.6%", "Dedicated Mean": "98.4%", "Base-Mean": "97.6%", "Base-Last": "101.1%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.0%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "100.4%", "Gemma3-Last": "100.2%", "Qwen3.5-Mean": "95.0%", "Qwen3.5-Last": "101.6%", "Dedicated Mean": "98.2%", "Base-Mean": "97.7%", "Base-Last": "100.9%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "98.8%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "123.2%", "Gemma3-Last": "146.1%", "Qwen3.5-Mean": "113.8%", "Qwen3.5-Last": "134.7%", "Dedicated Mean": "98.2%", "Base-Mean": "118.5%", "Base-Last": "140.4%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.0%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "117.0%", "Gemma3-Last": "131.4%", "Qwen3.5-Mean": "110.3%", "Qwen3.5-Last": "124.2%", "Dedicated Mean": "98.2%", "Base-Mean": "113.6%", "Base-Last": "127.8%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.1%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "123.3%", "Gemma3-Last": "146.2%", "Qwen3.5-Mean": "113.7%", "Qwen3.5-Last": "134.4%", "Dedicated Mean": "98.4%", "Base-Mean": "118.5%", "Base-Last": "140.3%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.0%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "123.4%", "Gemma3-Last": "144.8%", "Qwen3.5-Mean": "113.6%", "Qwen3.5-Last": "134.1%", "Dedicated Mean": "98.2%", "Base-Mean": "118.5%", "Base-Last": "139.4%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Orth. Proj. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "95.0%", "Qwen3-Emb": "94.9%", "Gemma3-Mean": "89.8%", "Gemma3-Last": "85.2%", "Qwen3.5-Mean": "89.1%", "Qwen3.5-Last": "92.3%", "Dedicated Mean": "95.0%", "Base-Mean": "89.5%", "Base-Last": "88.7%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "95.6%", "Qwen3-Emb": "95.3%", "Gemma3-Mean": "98.9%", "Gemma3-Last": "97.7%", "Qwen3.5-Mean": "94.5%", "Qwen3.5-Last": "95.2%", "Dedicated Mean": "95.5%", "Base-Mean": "96.7%", "Base-Last": "96.4%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "95.2%", "Qwen3-Emb": "95.4%", "Gemma3-Mean": "98.7%", "Gemma3-Last": "97.5%", "Qwen3.5-Mean": "94.4%", "Qwen3.5-Last": "95.2%", "Dedicated Mean": "95.3%", "Base-Mean": "96.6%", "Base-Last": "96.3%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "95.2%", "Qwen3-Emb": "95.2%", "Gemma3-Mean": "113.5%", "Gemma3-Last": "135.1%", "Qwen3.5-Mean": "107.4%", "Qwen3.5-Last": "127.3%", "Dedicated Mean": "95.2%", "Base-Mean": "110.5%", "Base-Last": "131.2%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "95.6%", "Qwen3-Emb": "95.0%", "Gemma3-Mean": "108.4%", "Gemma3-Last": "117.7%", "Qwen3.5-Mean": "103.0%", "Qwen3.5-Last": "111.8%", "Dedicated Mean": "95.3%", "Base-Mean": "105.7%", "Base-Last": "114.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "95.6%", "Qwen3-Emb": "95.3%", "Gemma3-Mean": "113.3%", "Gemma3-Last": "135.1%", "Qwen3.5-Mean": "107.5%", "Qwen3.5-Last": "127.4%", "Dedicated Mean": "95.5%", "Base-Mean": "110.4%", "Base-Last": "131.3%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "95.2%", "Qwen3-Emb": "95.4%", "Gemma3-Mean": "113.5%", "Gemma3-Last": "132.9%", "Qwen3.5-Mean": "107.3%", "Qwen3.5-Last": "125.1%", "Dedicated Mean": "95.3%", "Base-Mean": "110.4%", "Base-Last": "129.0%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "96.7%", "Qwen3-Emb": "95.1%", "Gemma3-Mean": "113.1%", "Gemma3-Last": "134.0%", "Qwen3.5-Mean": "107.2%", "Qwen3.5-Last": "127.7%", "Dedicated Mean": "95.9%", "Base-Mean": "110.1%", "Base-Last": "130.9%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "79.4%", "Qwen3-Emb": "86.6%", "Gemma3-Mean": "76.4%", "Gemma3-Last": "78.5%", "Qwen3.5-Mean": "60.4%", "Qwen3.5-Last": "63.1%", "Dedicated Mean": "83.0%", "Base-Mean": "68.4%", "Base-Last": "70.8%"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "91.1%", "Qwen3-Emb": "88.2%", "Gemma3-Mean": "79.3%", "Gemma3-Last": "69.4%", "Qwen3.5-Mean": "81.1%", "Qwen3.5-Last": "75.8%", "Dedicated Mean": "89.7%", "Base-Mean": "80.2%", "Base-Last": "72.6%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "84.3%", "Qwen3-Emb": "85.6%", "Gemma3-Mean": "94.6%", "Gemma3-Last": "105.7%", "Qwen3.5-Mean": "93.8%", "Qwen3.5-Last": "94.2%", "Dedicated Mean": "84.9%", "Base-Mean": "94.2%", "Base-Last": "100.0%"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "85.8%", "Qwen3-Emb": "87.9%", "Gemma3-Mean": "89.0%", "Gemma3-Last": "82.9%", "Qwen3.5-Mean": "90.6%", "Qwen3.5-Last": "85.4%", "Dedicated Mean": "86.9%", "Base-Mean": "89.8%", "Base-Last": "84.2%"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "88.2%", "Qwen3-Emb": "89.5%", "Gemma3-Mean": "94.2%", "Gemma3-Last": "106.5%", "Qwen3.5-Mean": "93.1%", "Qwen3.5-Last": "94.6%", "Dedicated Mean": "88.9%", "Base-Mean": "93.7%", "Base-Last": "100.5%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "88.4%", "Qwen3-Emb": "89.7%", "Gemma3-Mean": "79.6%", "Gemma3-Last": "70.7%", "Qwen3.5-Mean": "81.2%", "Qwen3.5-Last": "77.1%", "Dedicated Mean": "89.0%", "Base-Mean": "80.4%", "Base-Last": "73.9%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "88.1%", "Qwen3-Emb": "89.3%", "Gemma3-Mean": "89.0%", "Gemma3-Last": "85.6%", "Qwen3.5-Mean": "90.7%", "Qwen3.5-Last": "82.1%", "Dedicated Mean": "88.7%", "Base-Mean": "89.8%", "Base-Last": "83.8%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "88.2%", "Qwen3-Emb": "89.5%", "Gemma3-Mean": "88.9%", "Gemma3-Last": "85.2%", "Qwen3.5-Mean": "90.9%", "Qwen3.5-Last": "82.1%", "Dedicated Mean": "88.9%", "Base-Mean": "89.9%", "Base-Last": "83.6%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "88.4%", "Qwen3-Emb": "89.6%", "Gemma3-Mean": "94.2%", "Gemma3-Last": "106.5%", "Qwen3.5-Mean": "93.1%", "Qwen3.5-Last": "94.6%", "Dedicated Mean": "89.0%", "Base-Mean": "93.7%", "Base-Last": "100.5%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "88.2%", "Qwen3-Emb": "89.4%", "Gemma3-Mean": "88.6%", "Gemma3-Last": "95.6%", "Qwen3.5-Mean": "91.4%", "Qwen3.5-Last": "89.1%", "Dedicated Mean": "88.8%", "Base-Mean": "90.0%", "Base-Last": "92.3%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "88.1%", "Qwen3-Emb": "89.3%", "Gemma3-Mean": "94.2%", "Gemma3-Last": "106.6%", "Qwen3.5-Mean": "93.2%", "Qwen3.5-Last": "94.6%", "Dedicated Mean": "88.7%", "Base-Mean": "93.7%", "Base-Last": "100.6%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "88.4%", "Qwen3-Emb": "89.3%", "Gemma3-Mean": "94.0%", "Gemma3-Last": "106.7%", "Qwen3.5-Mean": "93.1%", "Qwen3.5-Last": "94.9%", "Dedicated Mean": "88.9%", "Base-Mean": "93.6%", "Base-Last": "100.8%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "86.9%", "Qwen3-Emb": "88.1%", "Gemma3-Mean": "94.7%", "Gemma3-Last": "105.8%", "Qwen3.5-Mean": "93.8%", "Qwen3.5-Last": "94.2%", "Dedicated Mean": "87.5%", "Base-Mean": "94.3%", "Base-Last": "100.0%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "99.0%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "92.7%", "Gemma3-Last": "86.9%", "Qwen3.5-Mean": "81.9%", "Qwen3.5-Last": "80.8%", "Dedicated Mean": "98.5%", "Base-Mean": "87.3%", "Base-Last": "83.8%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "101.8%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "66.2%", "Gemma3-Last": "95.7%", "Qwen3.5-Mean": "73.3%", "Qwen3.5-Last": "101.3%", "Dedicated Mean": "100.0%", "Base-Mean": "69.8%", "Base-Last": "98.5%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "94.0%", "Qwen3-Emb": "90.1%", "Gemma3-Mean": "201.3%", "Gemma3-Last": "149.5%", "Qwen3.5-Mean": "182.3%", "Qwen3.5-Last": "213.7%", "Dedicated Mean": "92.1%", "Base-Mean": "191.8%", "Base-Last": "181.6%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "102.5%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "67.1%", "Gemma3-Last": "97.5%", "Qwen3.5-Mean": "74.7%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "100.5%", "Base-Mean": "70.9%", "Base-Last": "105.2%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "102.2%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "201.3%", "Gemma3-Last": "149.9%", "Qwen3.5-Mean": "180.3%", "Qwen3.5-Last": "202.4%", "Dedicated Mean": "100.2%", "Base-Mean": "190.8%", "Base-Last": "176.2%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.5%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "74.7%", "Gemma3-Last": "101.1%", "Qwen3.5-Mean": "77.2%", "Qwen3.5-Last": "103.7%", "Dedicated Mean": "99.4%", "Base-Mean": "75.9%", "Base-Last": "102.4%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "101.3%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "73.9%", "Gemma3-Last": "99.6%", "Qwen3.5-Mean": "77.6%", "Qwen3.5-Last": "112.6%", "Dedicated Mean": "99.6%", "Base-Mean": "75.8%", "Base-Last": "106.1%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "101.0%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "73.9%", "Gemma3-Last": "99.6%", "Qwen3.5-Mean": "77.6%", "Qwen3.5-Last": "112.6%", "Dedicated Mean": "99.5%", "Base-Mean": "75.8%", "Base-Last": "106.1%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "102.2%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "201.3%", "Gemma3-Last": "149.9%", "Qwen3.5-Mean": "180.3%", "Qwen3.5-Last": "202.4%", "Dedicated Mean": "100.2%", "Base-Mean": "190.8%", "Base-Last": "176.2%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "102.5%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "126.2%", "Gemma3-Last": "122.8%", "Qwen3.5-Mean": "114.6%", "Qwen3.5-Last": "144.6%", "Dedicated Mean": "100.1%", "Base-Mean": "120.4%", "Base-Last": "133.7%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "103.0%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "202.2%", "Gemma3-Last": "149.2%", "Qwen3.5-Mean": "182.9%", "Qwen3.5-Last": "218.1%", "Dedicated Mean": "100.5%", "Base-Mean": "192.5%", "Base-Last": "183.7%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "102.5%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "190.9%", "Gemma3-Last": "148.7%", "Qwen3.5-Mean": "169.1%", "Qwen3.5-Last": "187.8%", "Dedicated Mean": "100.5%", "Base-Mean": "180.0%", "Base-Last": "168.2%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "102.9%", "Qwen3-Emb": "98.5%", "Gemma3-Mean": "202.4%", "Gemma3-Last": "147.3%", "Qwen3.5-Mean": "175.6%", "Qwen3.5-Last": "197.3%", "Dedicated Mean": "100.7%", "Base-Mean": "189.0%", "Base-Last": "172.3%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "95.7%", "Qwen3-Emb": "95.2%", "Gemma3-Mean": "122.9%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "65.7%", "Qwen3.5-Last": "72.9%", "Dedicated Mean": "95.4%", "Base-Mean": "94.3%", "Base-Last": "92.9%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "96.6%", "Qwen3-Emb": "96.7%", "Gemma3-Mean": "58.6%", "Gemma3-Last": "92.9%", "Qwen3.5-Mean": "69.0%", "Qwen3.5-Last": "96.6%", "Dedicated Mean": "96.6%", "Base-Mean": "63.8%", "Base-Last": "94.8%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "94.1%", "Qwen3-Emb": "92.4%", "Gemma3-Mean": "157.3%", "Gemma3-Last": "161.6%", "Qwen3.5-Mean": "150.5%", "Qwen3.5-Last": "173.5%", "Dedicated Mean": "93.2%", "Base-Mean": "153.9%", "Base-Last": "167.5%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "99.4%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "60.9%", "Gemma3-Last": "96.7%", "Qwen3.5-Mean": "69.8%", "Qwen3.5-Last": "104.0%", "Dedicated Mean": "98.1%", "Base-Mean": "65.3%", "Base-Last": "100.4%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "97.2%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "157.7%", "Gemma3-Last": "158.4%", "Qwen3.5-Mean": "148.7%", "Qwen3.5-Last": "174.7%", "Dedicated Mean": "97.2%", "Base-Mean": "153.2%", "Base-Last": "166.6%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.9936 (100.0%)", "Qwen3-Emb": "0.9929 (99.7%)", "Gemma3-Mean": "0.9765 (107.0%)", "Gemma3-Last": "0.5882 (151.2%)", "Qwen3.5-Mean": "0.9659 (102.7%)", "Qwen3.5-Last": "0.5405 (152.3%)", "Dedicated Mean": "0.9932 (99.9%)", "Base-Mean": "0.9712 (104.9%)", "Base-Last": "0.5643 (151.8%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.9644 (97.1%)", "Qwen3-Emb": "0.9858 (99.0%)", "Gemma3-Mean": "0.8293 (90.9%)", "Gemma3-Last": "0.3350 (86.1%)", "Qwen3.5-Mean": "0.7831 (83.3%)", "Qwen3.5-Last": "0.2937 (82.8%)", "Dedicated Mean": "0.9751 (98.0%)", "Base-Mean": "0.8062 (87.1%)", "Base-Last": "0.3144 (84.4%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "0.9893 (99.6%)", "Qwen3-Emb": "0.9922 (99.6%)", "Gemma3-Mean": "0.8912 (97.7%)", "Gemma3-Last": "0.3385 (87.0%)", "Qwen3.5-Mean": "0.8969 (95.4%)", "Qwen3.5-Last": "0.3307 (93.2%)", "Dedicated Mean": "0.9908 (99.6%)", "Base-Mean": "0.8941 (96.5%)", "Base-Last": "0.3346 (90.1%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.9879 (99.4%)", "Qwen3-Emb": "0.9858 (99.0%)", "Gemma3-Mean": "0.9523 (104.4%)", "Gemma3-Last": "0.4922 (126.5%)", "Qwen3.5-Mean": "0.9580 (101.9%)", "Qwen3.5-Last": "0.4438 (125.0%)", "Dedicated Mean": "0.9869 (99.2%)", "Base-Mean": "0.9551 (103.1%)", "Base-Last": "0.4680 (125.8%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.9886 (99.5%)", "Qwen3-Emb": "0.9900 (99.4%)", "Gemma3-Mean": "0.9481 (103.9%)", "Gemma3-Last": "0.3812 (98.0%)", "Qwen3.5-Mean": "0.9459 (100.6%)", "Qwen3.5-Last": "0.3649 (102.8%)", "Dedicated Mean": "0.9893 (99.5%)", "Base-Mean": "0.9470 (102.3%)", "Base-Last": "0.3730 (100.4%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.9908 (99.7%)", "Qwen3-Emb": "0.9908 (99.5%)", "Gemma3-Mean": "0.9531 (104.4%)", "Gemma3-Last": "0.4900 (126.0%)", "Qwen3.5-Mean": "0.9552 (101.6%)", "Qwen3.5-Last": "0.4495 (126.7%)", "Dedicated Mean": "0.9908 (99.6%)", "Base-Mean": "0.9542 (103.0%)", "Base-Last": "0.4698 (126.3%)"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.9900 (99.6%)", "Qwen3-Emb": "0.9908 (99.5%)", "Gemma3-Mean": "0.9523 (104.4%)", "Gemma3-Last": "0.4922 (126.5%)", "Qwen3.5-Mean": "0.9580 (101.9%)", "Qwen3.5-Last": "0.4438 (125.0%)", "Dedicated Mean": "0.9904 (99.6%)", "Base-Mean": "0.9551 (103.1%)", "Base-Last": "0.4680 (125.8%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.4135 (97.8%)", "Qwen3-Emb": "0.5282 (99.8%)", "Gemma3-Mean": "0.0931 (84.1%)", "Gemma3-Last": "0.0338 (92.3%)", "Qwen3.5-Mean": "0.1062 (91.2%)", "Qwen3.5-Last": "0.0276 (102.2%)", "Dedicated Mean": "0.4708 (98.8%)", "Base-Mean": "0.0997 (87.6%)", "Base-Last": "0.0307 (97.3%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "0.4430 (104.7%)", "Qwen3-Emb": "0.5208 (98.4%)", "Gemma3-Mean": "0.0875 (79.0%)", "Gemma3-Last": "0.0289 (79.0%)", "Qwen3.5-Mean": "0.0916 (78.7%)", "Qwen3.5-Last": "0.0243 (89.8%)", "Dedicated Mean": "0.4819 (101.6%)", "Base-Mean": "0.0895 (78.8%)", "Base-Last": "0.0266 (84.4%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.3717 (87.9%)", "Qwen3-Emb": "0.4475 (84.6%)", "Gemma3-Mean": "0.2207 (199.2%)", "Gemma3-Last": "0.0803 (219.5%)", "Qwen3.5-Mean": "0.2048 (175.8%)", "Qwen3.5-Last": "0.0713 (263.5%)", "Dedicated Mean": "0.4096 (86.2%)", "Base-Mean": "0.2127 (187.5%)", "Base-Last": "0.0758 (241.5%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.4452 (105.2%)", "Qwen3-Emb": "0.5210 (98.5%)", "Gemma3-Mean": "0.0882 (79.6%)", "Gemma3-Last": "0.0291 (79.5%)", "Qwen3.5-Mean": "0.0927 (79.6%)", "Qwen3.5-Last": "0.0241 (89.1%)", "Dedicated Mean": "0.4831 (101.8%)", "Base-Mean": "0.0905 (79.6%)", "Base-Last": "0.0266 (84.3%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.4414 (104.4%)", "Qwen3-Emb": "0.5193 (98.1%)", "Gemma3-Mean": "0.2222 (200.6%)", "Gemma3-Last": "0.0796 (217.4%)", "Qwen3.5-Mean": "0.2058 (176.7%)", "Qwen3.5-Last": "0.0699 (258.3%)", "Dedicated Mean": "0.4803 (101.2%)", "Base-Mean": "0.2140 (188.7%)", "Base-Last": "0.0748 (237.9%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.4407 (104.2%)", "Qwen3-Emb": "0.5191 (98.1%)", "Gemma3-Mean": "0.1574 (142.0%)", "Gemma3-Last": "0.0459 (125.5%)", "Qwen3.5-Mean": "0.1346 (115.6%)", "Qwen3.5-Last": "0.0399 (147.5%)", "Dedicated Mean": "0.4799 (101.1%)", "Base-Mean": "0.1460 (128.8%)", "Base-Last": "0.0429 (136.5%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.4426 (104.7%)", "Qwen3-Emb": "0.5187 (98.0%)", "Gemma3-Mean": "0.2205 (199.1%)", "Gemma3-Last": "0.0803 (219.5%)", "Qwen3.5-Mean": "0.2051 (176.1%)", "Qwen3.5-Last": "0.0713 (263.5%)", "Dedicated Mean": "0.4807 (101.3%)", "Base-Mean": "0.2128 (187.6%)", "Base-Last": "0.0758 (241.5%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.4406 (104.2%)", "Qwen3-Emb": "0.5191 (98.1%)", "Gemma3-Mean": "0.2241 (202.3%)", "Gemma3-Last": "0.0746 (203.8%)", "Qwen3.5-Mean": "0.1979 (169.9%)", "Qwen3.5-Last": "0.0658 (243.2%)", "Dedicated Mean": "0.4798 (101.1%)", "Base-Mean": "0.2110 (186.1%)", "Base-Last": "0.0702 (223.5%)"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.4432 (104.8%)", "Qwen3-Emb": "0.5207 (98.4%)", "Gemma3-Mean": "0.2230 (201.3%)", "Gemma3-Last": "0.0794 (216.9%)", "Qwen3.5-Mean": "0.2054 (176.4%)", "Qwen3.5-Last": "0.0689 (254.8%)", "Dedicated Mean": "0.4819 (101.6%)", "Base-Mean": "0.2142 (188.8%)", "Base-Last": "0.0741 (235.8%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "0.3990 (94.3%)", "Qwen3-Emb": "0.5051 (95.4%)", "Gemma3-Mean": "0.1442 (130.1%)", "Gemma3-Last": "0.0337 (92.0%)", "Qwen3.5-Mean": "0.0908 (78.0%)", "Qwen3.5-Last": "0.0289 (106.8%)", "Dedicated Mean": "0.4521 (94.9%)", "Base-Mean": "0.1175 (104.1%)", "Base-Last": "0.0313 (99.4%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "0.4348 (102.8%)", "Qwen3-Emb": "0.5172 (97.7%)", "Gemma3-Mean": "0.0839 (75.7%)", "Gemma3-Last": "0.0282 (77.2%)", "Qwen3.5-Mean": "0.0862 (74.0%)", "Qwen3.5-Last": "0.0239 (88.4%)", "Dedicated Mean": "0.4760 (100.3%)", "Base-Mean": "0.0851 (74.9%)", "Base-Last": "0.0261 (82.8%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "0.3965 (93.7%)", "Qwen3-Emb": "0.4739 (89.5%)", "Gemma3-Mean": "0.1948 (175.8%)", "Gemma3-Last": "0.0646 (176.6%)", "Qwen3.5-Mean": "0.1661 (142.6%)", "Qwen3.5-Last": "0.0578 (213.8%)", "Dedicated Mean": "0.4352 (91.6%)", "Base-Mean": "0.1804 (159.2%)", "Base-Last": "0.0612 (195.2%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "0.4383 (103.6%)", "Qwen3-Emb": "0.5174 (97.8%)", "Gemma3-Mean": "0.0868 (78.4%)", "Gemma3-Last": "0.0284 (77.6%)", "Qwen3.5-Mean": "0.0866 (74.4%)", "Qwen3.5-Last": "0.0247 (91.3%)", "Dedicated Mean": "0.4778 (100.7%)", "Base-Mean": "0.0867 (76.4%)", "Base-Last": "0.0266 (84.5%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "0.4368 (103.3%)", "Qwen3-Emb": "0.5164 (97.6%)", "Gemma3-Mean": "0.1964 (177.3%)", "Gemma3-Last": "0.0647 (176.9%)", "Qwen3.5-Mean": "0.1651 (141.8%)", "Qwen3.5-Last": "0.0574 (212.3%)", "Dedicated Mean": "0.4766 (100.4%)", "Base-Mean": "0.1807 (159.5%)", "Base-Last": "0.0610 (194.6%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.4295 (101.5%)", "Qwen3-Emb": "0.5164 (97.6%)", "Gemma3-Mean": "0.0927 (83.7%)", "Gemma3-Last": "0.0295 (80.5%)", "Qwen3.5-Mean": "0.0910 (78.2%)", "Qwen3.5-Last": "0.0247 (91.3%)", "Dedicated Mean": "0.4729 (99.6%)", "Base-Mean": "0.0919 (80.9%)", "Base-Last": "0.0271 (85.9%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.4375 (103.4%)", "Qwen3-Emb": "0.5156 (97.4%)", "Gemma3-Mean": "0.0956 (86.3%)", "Gemma3-Last": "0.0294 (80.3%)", "Qwen3.5-Mean": "0.0917 (78.8%)", "Qwen3.5-Last": "0.0255 (94.3%)", "Dedicated Mean": "0.4765 (100.4%)", "Base-Mean": "0.0937 (82.5%)", "Base-Last": "0.0274 (87.3%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.4333 (102.4%)", "Qwen3-Emb": "0.5165 (97.6%)", "Gemma3-Mean": "0.1235 (111.5%)", "Gemma3-Last": "0.0379 (103.4%)", "Qwen3.5-Mean": "0.1061 (91.1%)", "Qwen3.5-Last": "0.0332 (122.7%)", "Dedicated Mean": "0.4749 (100.0%)", "Base-Mean": "0.1148 (101.3%)", "Base-Last": "0.0355 (113.1%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.4371 (103.3%)", "Qwen3-Emb": "0.5156 (97.4%)", "Gemma3-Mean": "0.1966 (177.4%)", "Gemma3-Last": "0.0645 (176.3%)", "Qwen3.5-Mean": "0.1659 (142.5%)", "Qwen3.5-Last": "0.0578 (213.8%)", "Dedicated Mean": "0.4763 (100.4%)", "Base-Mean": "0.1812 (159.9%)", "Base-Last": "0.0611 (195.1%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.4361 (103.1%)", "Qwen3-Emb": "0.5160 (97.5%)", "Gemma3-Mean": "0.1892 (170.8%)", "Gemma3-Last": "0.0603 (164.7%)", "Qwen3.5-Mean": "0.1542 (132.4%)", "Qwen3.5-Last": "0.0532 (196.7%)", "Dedicated Mean": "0.4760 (100.3%)", "Base-Mean": "0.1717 (151.6%)", "Base-Last": "0.0567 (180.7%)"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.4380 (103.5%)", "Qwen3-Emb": "0.5180 (97.9%)", "Gemma3-Mean": "0.1946 (175.6%)", "Gemma3-Last": "0.0642 (175.5%)", "Qwen3.5-Mean": "0.1649 (141.6%)", "Qwen3.5-Last": "0.0576 (213.1%)", "Dedicated Mean": "0.4780 (100.7%)", "Base-Mean": "0.1797 (158.6%)", "Base-Last": "0.0609 (194.3%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "0.3548 (83.9%)", "Qwen3-Emb": "0.4788 (90.5%)", "Gemma3-Mean": "0.1424 (128.5%)", "Gemma3-Last": "0.0414 (113.1%)", "Qwen3.5-Mean": "0.0932 (80.0%)", "Qwen3.5-Last": "0.0283 (104.6%)", "Dedicated Mean": "0.4168 (87.2%)", "Base-Mean": "0.1178 (104.3%)", "Base-Last": "0.0348 (108.8%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "PCA-k", "EmbGemma": "0.4126 (97.6%)", "Qwen3-Emb": "0.5049 (95.4%)", "Gemma3-Mean": "0.0769 (69.4%)", "Gemma3-Last": "0.0278 (76.1%)", "Qwen3.5-Mean": "0.0829 (71.2%)", "Qwen3.5-Last": "0.0236 (87.4%)", "Dedicated Mean": "0.4587 (96.5%)", "Base-Mean": "0.0799 (70.3%)", "Base-Last": "0.0257 (81.8%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Whitening-k", "EmbGemma": "0.3920 (92.7%)", "Qwen3-Emb": "0.4758 (89.9%)", "Gemma3-Mean": "0.1283 (115.8%)", "Gemma3-Last": "0.0463 (126.5%)", "Qwen3.5-Mean": "0.1127 (96.8%)", "Qwen3.5-Last": "0.0414 (153.0%)", "Dedicated Mean": "0.4339 (91.3%)", "Base-Mean": "0.1205 (106.3%)", "Base-Last": "0.0439 (139.8%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "SpecTemp", "EmbGemma": "0.4196 (99.2%)", "Qwen3-Emb": "0.5062 (95.6%)", "Gemma3-Mean": "0.0819 (73.9%)", "Gemma3-Last": "0.0286 (78.1%)", "Qwen3.5-Mean": "0.0825 (70.9%)", "Qwen3.5-Last": "0.0248 (91.9%)", "Dedicated Mean": "0.4629 (97.4%)", "Base-Mean": "0.0822 (72.4%)", "Base-Last": "0.0267 (85.0%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "0.4154 (98.2%)", "Qwen3-Emb": "0.5044 (95.3%)", "Gemma3-Mean": "0.1305 (117.8%)", "Gemma3-Last": "0.0469 (128.2%)", "Qwen3.5-Mean": "0.1122 (96.4%)", "Qwen3.5-Last": "0.0411 (151.8%)", "Dedicated Mean": "0.4599 (96.8%)", "Base-Mean": "0.1213 (107.1%)", "Base-Last": "0.0440 (140.0%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.4077 (96.4%)", "Qwen3-Emb": "0.5018 (94.8%)", "Gemma3-Mean": "0.0854 (77.1%)", "Gemma3-Last": "0.0293 (79.9%)", "Qwen3.5-Mean": "0.0876 (75.2%)", "Qwen3.5-Last": "0.0241 (89.1%)", "Dedicated Mean": "0.4547 (95.6%)", "Base-Mean": "0.0865 (76.2%)", "Base-Last": "0.0267 (84.5%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.4166 (98.5%)", "Qwen3-Emb": "0.5048 (95.4%)", "Gemma3-Mean": "0.0896 (80.9%)", "Gemma3-Last": "0.0300 (82.0%)", "Qwen3.5-Mean": "0.0848 (72.8%)", "Qwen3.5-Last": "0.0259 (95.8%)", "Dedicated Mean": "0.4607 (96.9%)", "Base-Mean": "0.0872 (76.8%)", "Base-Last": "0.0279 (88.9%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.4158 (98.3%)", "Qwen3-Emb": "0.5054 (95.5%)", "Gemma3-Mean": "0.0955 (86.2%)", "Gemma3-Last": "0.0332 (90.7%)", "Qwen3.5-Mean": "0.0859 (73.8%)", "Qwen3.5-Last": "0.0287 (106.1%)", "Dedicated Mean": "0.4606 (96.9%)", "Base-Mean": "0.0907 (80.0%)", "Base-Last": "0.0309 (98.4%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.4166 (98.5%)", "Qwen3-Emb": "0.5048 (95.4%)", "Gemma3-Mean": "0.1303 (117.6%)", "Gemma3-Last": "0.0469 (128.2%)", "Qwen3.5-Mean": "0.1124 (96.5%)", "Qwen3.5-Last": "0.0411 (151.8%)", "Dedicated Mean": "0.4607 (96.9%)", "Base-Mean": "0.1213 (107.1%)", "Base-Last": "0.0440 (140.0%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.4137 (97.8%)", "Qwen3-Emb": "0.5034 (95.1%)", "Gemma3-Mean": "0.1259 (113.6%)", "Gemma3-Last": "0.0448 (122.5%)", "Qwen3.5-Mean": "0.1037 (89.0%)", "Qwen3.5-Last": "0.0408 (150.8%)", "Dedicated Mean": "0.4586 (96.5%)", "Base-Mean": "0.1148 (101.3%)", "Base-Last": "0.0428 (136.7%)"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Orth. Proj. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.4077", "Qwen3-Emb": "0.5018", "Gemma3-Mean": "0.0854", "Gemma3-Last": "0.0293", "Qwen3.5-Mean": "0.0876", "Qwen3.5-Last": "0.0241", "Dedicated Mean": "0.4547", "Base-Mean": "0.0865", "Base-Last": "0.0267"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.4166", "Qwen3-Emb": "0.5048", "Gemma3-Mean": "0.0896", "Gemma3-Last": "0.0300", "Qwen3.5-Mean": "0.0848", "Qwen3.5-Last": "0.0259", "Dedicated Mean": "0.4607", "Base-Mean": "0.0872", "Base-Last": "0.0279"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.4158", "Qwen3-Emb": "0.5054", "Gemma3-Mean": "0.0955", "Gemma3-Last": "0.0332", "Qwen3.5-Mean": "0.0859", "Qwen3.5-Last": "0.0287", "Dedicated Mean": "0.4606", "Base-Mean": "0.0907", "Base-Last": "0.0309"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.4166", "Qwen3-Emb": "0.5048", "Gemma3-Mean": "0.1303", "Gemma3-Last": "0.0469", "Qwen3.5-Mean": "0.1124", "Qwen3.5-Last": "0.0411", "Dedicated Mean": "0.4607", "Base-Mean": "0.1213", "Base-Last": "0.0440"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.4137", "Qwen3-Emb": "0.5034", "Gemma3-Mean": "0.1259", "Gemma3-Last": "0.0448", "Qwen3.5-Mean": "0.1037", "Qwen3.5-Last": "0.0408", "Dedicated Mean": "0.4586", "Base-Mean": "0.1148", "Base-Last": "0.0428"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.4192", "Qwen3-Emb": "0.5064", "Gemma3-Mean": "0.1285", "Gemma3-Last": "0.0463", "Qwen3.5-Mean": "0.1127", "Qwen3.5-Last": "0.0414", "Dedicated Mean": "0.4628", "Base-Mean": "0.1206", "Base-Last": "0.0439"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.2498", "Qwen3-Emb": "0.4237", "Gemma3-Mean": "0.1046", "Gemma3-Last": "0.0344", "Qwen3.5-Mean": "0.0812", "Qwen3.5-Last": "0.0265", "Dedicated Mean": "0.3367", "Base-Mean": "0.0929", "Base-Last": "0.0304"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "PCA-k", "EmbGemma": "0.3670", "Qwen3-Emb": "0.4783", "Gemma3-Mean": "0.0678", "Gemma3-Last": "0.0271", "Qwen3.5-Mean": "0.0753", "Qwen3.5-Last": "0.0230", "Dedicated Mean": "0.4226", "Base-Mean": "0.0716", "Base-Last": "0.0250"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.3451", "Qwen3-Emb": "0.4611", "Gemma3-Mean": "0.0732", "Gemma3-Last": "0.0312", "Qwen3.5-Mean": "0.0594", "Qwen3.5-Last": "0.0301", "Dedicated Mean": "0.4031", "Base-Mean": "0.0663", "Base-Last": "0.0306"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.3620", "Qwen3-Emb": "0.4750", "Gemma3-Mean": "0.0698", "Gemma3-Last": "0.0268", "Qwen3.5-Mean": "0.0669", "Qwen3.5-Last": "0.0240", "Dedicated Mean": "0.4185", "Base-Mean": "0.0683", "Base-Last": "0.0254"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.3684", "Qwen3-Emb": "0.4802", "Gemma3-Mean": "0.0740", "Gemma3-Last": "0.0314", "Qwen3.5-Mean": "0.0600", "Qwen3.5-Last": "0.0306", "Dedicated Mean": "0.4243", "Base-Mean": "0.0670", "Base-Last": "0.0310"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.3666", "Qwen3-Emb": "0.4797", "Gemma3-Mean": "0.0752", "Gemma3-Last": "0.0278", "Qwen3.5-Mean": "0.0790", "Qwen3.5-Last": "0.0243", "Dedicated Mean": "0.4232", "Base-Mean": "0.0771", "Base-Last": "0.0260"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.3680", "Qwen3-Emb": "0.4824", "Gemma3-Mean": "0.0751", "Gemma3-Last": "0.0274", "Qwen3.5-Mean": "0.0674", "Qwen3.5-Last": "0.0250", "Dedicated Mean": "0.4252", "Base-Mean": "0.0713", "Base-Last": "0.0262"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.3684", "Qwen3-Emb": "0.4802", "Gemma3-Mean": "0.0751", "Gemma3-Last": "0.0274", "Qwen3.5-Mean": "0.0674", "Qwen3.5-Last": "0.0250", "Dedicated Mean": "0.4243", "Base-Mean": "0.0713", "Base-Last": "0.0262"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.3710", "Qwen3-Emb": "0.4791", "Gemma3-Mean": "0.0740", "Gemma3-Last": "0.0314", "Qwen3.5-Mean": "0.0600", "Qwen3.5-Last": "0.0306", "Dedicated Mean": "0.4251", "Base-Mean": "0.0670", "Base-Last": "0.0310"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.3700", "Qwen3-Emb": "0.4806", "Gemma3-Mean": "0.0733", "Gemma3-Last": "0.0270", "Qwen3.5-Mean": "0.0655", "Qwen3.5-Last": "0.0250", "Dedicated Mean": "0.4253", "Base-Mean": "0.0694", "Base-Last": "0.0260"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.3680", "Qwen3-Emb": "0.4824", "Gemma3-Mean": "0.0740", "Gemma3-Last": "0.0314", "Qwen3.5-Mean": "0.0600", "Qwen3.5-Last": "0.0306", "Dedicated Mean": "0.4252", "Base-Mean": "0.0670", "Base-Last": "0.0310"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.3702", "Qwen3-Emb": "0.4808", "Gemma3-Mean": "0.0732", "Gemma3-Last": "0.0306", "Qwen3.5-Mean": "0.0602", "Qwen3.5-Last": "0.0297", "Dedicated Mean": "0.4255", "Base-Mean": "0.0667", "Base-Last": "0.0301"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.3638", "Qwen3-Emb": "0.4772", "Gemma3-Mean": "0.0735", "Gemma3-Last": "0.0312", "Qwen3.5-Mean": "0.0594", "Qwen3.5-Last": "0.0301", "Dedicated Mean": "0.4205", "Base-Mean": "0.0664", "Base-Last": "0.0306"}], "task_comp::Retrieval (IR)::Recall@100::Retention %": [{"Dataset": "FiQA-2018", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "97.8%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "81.5%", "Gemma3-Last": "81.0%", "Qwen3.5-Mean": "92.0%", "Qwen3.5-Last": "96.0%", "Dedicated Mean": "99.1%", "Base-Mean": "86.7%", "Base-Last": "88.5%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "PCA-k", "EmbGemma": "99.6%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "86.9%", "Gemma3-Last": "95.6%", "Qwen3.5-Mean": "100.4%", "Qwen3.5-Last": "91.3%", "Dedicated Mean": "99.5%", "Base-Mean": "93.7%", "Base-Last": "93.4%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "Whitening-k", "EmbGemma": "90.1%", "Qwen3-Emb": "88.8%", "Gemma3-Mean": "133.4%", "Gemma3-Last": "159.5%", "Qwen3.5-Mean": "137.5%", "Qwen3.5-Last": "304.4%", "Dedicated Mean": "89.4%", "Base-Mean": "135.4%", "Base-Last": "231.9%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "SpecTemp", "EmbGemma": "99.7%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "90.2%", "Gemma3-Last": "96.2%", "Qwen3.5-Mean": "101.9%", "Qwen3.5-Last": "92.8%", "Dedicated Mean": "99.5%", "Base-Mean": "96.0%", "Base-Last": "94.5%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "134.7%", "Gemma3-Last": "166.4%", "Qwen3.5-Mean": "141.3%", "Qwen3.5-Last": "311.1%", "Dedicated Mean": "99.6%", "Base-Mean": "138.0%", "Base-Last": "238.7%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "Orth. 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Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "94.8%", "Gemma3-Last": "96.2%", "Qwen3.5-Mean": "100.2%", "Qwen3.5-Last": "120.6%", "Dedicated Mean": "99.7%", "Base-Mean": "97.5%", "Base-Last": "108.4%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "134.7%", "Gemma3-Last": "166.4%", "Qwen3.5-Mean": "141.3%", "Qwen3.5-Last": "311.1%", "Dedicated Mean": "99.6%", "Base-Mean": "138.0%", "Base-Last": "238.8%"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "w/o SNR Sched. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "87.8%", "Qwen3-Emb": "93.3%", "Gemma3-Mean": "60.7%", "Gemma3-Last": "55.5%", "Qwen3.5-Mean": "72.5%", "Qwen3.5-Last": "72.9%", "Dedicated Mean": "90.6%", "Base-Mean": "66.6%", "Base-Last": "64.2%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "89.6%", "Qwen3-Emb": "93.1%", "Gemma3-Mean": "70.5%", "Gemma3-Last": "63.7%", "Qwen3.5-Mean": "83.9%", "Qwen3.5-Last": "84.1%", "Dedicated Mean": "91.3%", "Base-Mean": "77.2%", "Base-Last": "73.9%"}, {"Dataset": "FiQA-2018", "k": "64", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.7%", "Gemma3-Last": "140.0%", "Qwen3.5-Mean": "103.7%", "Qwen3.5-Last": "137.7%", "Dedicated Mean": "99.9%", "Base-Mean": "105.2%", "Base-Last": "138.9%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.0%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "105.9%", "Gemma3-Last": "160.0%", "Qwen3.5-Mean": "102.1%", "Qwen3.5-Last": "162.7%", "Dedicated Mean": "99.9%", "Base-Mean": "104.0%", "Base-Last": "161.3%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.0%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.5%", "Gemma3-Last": "162.9%", "Qwen3.5-Mean": "103.1%", "Qwen3.5-Last": "165.1%", "Dedicated Mean": "99.9%", "Base-Mean": "104.8%", "Base-Last": "164.0%"}, {"Dataset": "ArguAna", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "106.0%", "Gemma3-Last": "161.8%", "Qwen3.5-Mean": "103.0%", "Qwen3.5-Last": "166.1%", "Dedicated Mean": "100.0%", "Base-Mean": "104.5%", "Base-Last": "164.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "99.8%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "95.4%", "Gemma3-Last": "99.1%", "Qwen3.5-Mean": "94.9%", "Qwen3.5-Last": "95.0%", "Dedicated Mean": "99.8%", "Base-Mean": "95.2%", "Base-Last": "97.0%"}, {"Dataset": "ArguAna", "k": "256", "Method": "PCA-k", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "101.7%", "Gemma3-Last": "99.3%", "Qwen3.5-Mean": "98.6%", "Qwen3.5-Last": "103.2%", "Dedicated Mean": "99.9%", "Base-Mean": "100.2%", "Base-Last": "101.2%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Whitening-k", "EmbGemma": "99.2%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "107.2%", "Gemma3-Last": "164.5%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "164.1%", "Dedicated Mean": "99.2%", "Base-Mean": "105.0%", "Base-Last": "164.3%"}, {"Dataset": "ArguAna", "k": "256", "Method": "SpecTemp", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "103.2%", "Gemma3-Last": "104.4%", "Qwen3.5-Mean": "99.8%", "Qwen3.5-Last": "104.4%", "Dedicated Mean": "99.9%", "Base-Mean": "101.5%", "Base-Last": "104.4%"}, {"Dataset": "ArguAna", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.9%", "Gemma3-Last": "164.7%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "163.9%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "164.3%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "102.0%", "Gemma3-Last": "100.5%", "Qwen3.5-Mean": "98.5%", "Qwen3.5-Last": "103.2%", "Dedicated Mean": "99.9%", "Base-Mean": "100.2%", "Base-Last": "101.9%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "103.3%", "Gemma3-Last": "105.1%", "Qwen3.5-Mean": "99.8%", "Qwen3.5-Last": "104.2%", "Dedicated Mean": "99.9%", "Base-Mean": "101.5%", "Base-Last": "104.7%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "103.3%", "Gemma3-Last": "105.1%", "Qwen3.5-Mean": "99.8%", "Qwen3.5-Last": "104.2%", "Dedicated Mean": "99.9%", "Base-Mean": "101.5%", "Base-Last": "104.7%"}, {"Dataset": "ArguAna", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.9%", "Gemma3-Last": "164.7%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "163.9%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "164.3%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.8%", "Gemma3-Last": "137.3%", "Qwen3.5-Mean": "103.3%", "Qwen3.5-Last": "134.9%", "Dedicated Mean": "99.9%", "Base-Mean": "105.0%", "Base-Last": "136.1%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.9%", "Gemma3-Last": "164.7%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "164.1%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "164.4%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "107.1%", "Gemma3-Last": "163.2%", "Qwen3.5-Mean": "103.1%", "Qwen3.5-Last": "163.1%", "Dedicated Mean": "99.9%", "Base-Mean": "105.1%", "Base-Last": "163.2%"}, {"Dataset": "ArguAna", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "107.2%", "Gemma3-Last": "164.5%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "164.5%", "Dedicated Mean": "100.0%", "Base-Mean": "105.0%", "Base-Last": "164.5%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "99.4%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "96.8%", "Gemma3-Last": "93.8%", "Qwen3.5-Mean": "94.9%", "Qwen3.5-Last": "93.8%", "Dedicated Mean": "99.5%", "Base-Mean": "95.9%", "Base-Last": "93.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "PCA-k", "EmbGemma": "100.1%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "100.6%", "Gemma3-Last": "95.1%", "Qwen3.5-Mean": "97.5%", "Qwen3.5-Last": "99.6%", "Dedicated Mean": "99.9%", "Base-Mean": "99.1%", "Base-Last": "97.3%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Whitening-k", "EmbGemma": "99.6%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "107.1%", "Gemma3-Last": "151.2%", "Qwen3.5-Mean": "102.7%", "Qwen3.5-Last": "152.3%", "Dedicated Mean": "99.7%", "Base-Mean": "104.9%", "Base-Last": "151.7%"}, {"Dataset": "ArguAna", "k": "128", "Method": "SpecTemp", "EmbGemma": "99.9%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "104.2%", "Gemma3-Last": "102.9%", "Qwen3.5-Mean": "100.6%", "Qwen3.5-Last": "104.4%", "Dedicated Mean": "99.9%", "Base-Mean": "102.4%", "Base-Last": "103.7%"}, {"Dataset": "ArguAna", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "107.1%", "Gemma3-Last": "150.6%", "Qwen3.5-Mean": "102.6%", "Qwen3.5-Last": "152.3%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "151.5%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "100.6%", "Gemma3-Last": "96.0%", "Qwen3.5-Mean": "97.3%", "Qwen3.5-Last": "100.0%", "Dedicated Mean": "99.9%", "Base-Mean": "99.0%", "Base-Last": "98.0%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "103.7%", "Qwen3.5-Mean": "100.5%", "Qwen3.5-Last": "102.2%", "Dedicated Mean": "99.9%", "Base-Mean": "102.5%", "Base-Last": "102.9%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "103.7%", "Qwen3.5-Mean": "100.5%", "Qwen3.5-Last": "102.2%", "Dedicated Mean": "99.9%", "Base-Mean": "102.5%", "Base-Last": "102.9%"}, {"Dataset": "ArguAna", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "107.1%", "Gemma3-Last": "150.6%", "Qwen3.5-Mean": "102.7%", "Qwen3.5-Last": "152.3%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "151.5%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "106.2%", "Gemma3-Last": "124.9%", "Qwen3.5-Mean": "103.0%", "Qwen3.5-Last": "122.7%", "Dedicated Mean": "99.9%", "Base-Mean": "104.6%", "Base-Last": "123.8%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "107.1%", "Gemma3-Last": "150.6%", "Qwen3.5-Mean": "102.7%", "Qwen3.5-Last": "152.5%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "151.6%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.1%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "107.1%", "Gemma3-Last": "149.5%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "150.3%", "Dedicated Mean": "99.9%", "Base-Mean": "105.0%", "Base-Last": "149.9%"}, {"Dataset": "ArguAna", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.0%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "107.0%", "Gemma3-Last": "151.2%", "Qwen3.5-Mean": "102.7%", "Qwen3.5-Last": "152.3%", "Dedicated Mean": "99.9%", "Base-Mean": "104.9%", "Base-Last": "151.8%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "97.1%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "90.9%", "Gemma3-Last": "86.1%", "Qwen3.5-Mean": "83.3%", "Qwen3.5-Last": "82.8%", "Dedicated Mean": "98.0%", "Base-Mean": "87.1%", "Base-Last": "84.4%"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "99.6%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "97.7%", "Gemma3-Last": "87.0%", "Qwen3.5-Mean": "95.4%", "Qwen3.5-Last": "93.2%", "Dedicated Mean": "99.6%", "Base-Mean": "96.5%", "Base-Last": "90.1%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "99.4%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "126.5%", "Qwen3.5-Mean": "101.9%", "Qwen3.5-Last": "125.0%", "Dedicated Mean": "99.2%", "Base-Mean": "103.1%", "Base-Last": "125.8%"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "99.5%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "103.9%", "Gemma3-Last": "98.0%", "Qwen3.5-Mean": "100.6%", "Qwen3.5-Last": "102.8%", "Dedicated Mean": "99.5%", "Base-Mean": "102.3%", "Base-Last": "100.4%"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "99.7%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "126.0%", "Qwen3.5-Mean": "101.6%", "Qwen3.5-Last": "126.7%", "Dedicated Mean": "99.6%", "Base-Mean": "103.0%", "Base-Last": "126.3%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "97.7%", "Gemma3-Last": "87.4%", "Qwen3.5-Mean": "95.2%", "Qwen3.5-Last": "94.4%", "Dedicated Mean": "99.6%", "Base-Mean": "96.5%", "Base-Last": "90.9%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.8%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "103.7%", "Gemma3-Last": "99.5%", "Qwen3.5-Mean": "100.6%", "Qwen3.5-Last": "97.4%", "Dedicated Mean": "99.6%", "Base-Mean": "102.2%", "Base-Last": "98.4%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.7%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "103.7%", "Gemma3-Last": "99.5%", "Qwen3.5-Mean": "100.6%", "Qwen3.5-Last": "97.4%", "Dedicated Mean": "99.6%", "Base-Mean": "102.2%", "Base-Last": "98.4%"}, {"Dataset": "ArguAna", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "126.0%", "Qwen3.5-Mean": "101.6%", "Qwen3.5-Last": "126.7%", "Dedicated Mean": "99.6%", "Base-Mean": "103.0%", "Base-Last": "126.3%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.7%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "103.7%", "Gemma3-Last": "107.1%", "Qwen3.5-Mean": "101.1%", "Qwen3.5-Last": "110.0%", "Dedicated Mean": "99.6%", "Base-Mean": "102.4%", "Base-Last": "108.6%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.8%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "126.0%", "Qwen3.5-Mean": "101.6%", "Qwen3.5-Last": "126.7%", "Dedicated Mean": "99.6%", "Base-Mean": "103.0%", "Base-Last": "126.3%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.7%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "125.0%", "Qwen3.5-Mean": "101.6%", "Qwen3.5-Last": "125.0%", "Dedicated Mean": "99.6%", "Base-Mean": "103.0%", "Base-Last": "125.0%"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "104.4%", "Gemma3-Last": "126.5%", "Qwen3.5-Mean": "101.9%", "Qwen3.5-Last": "125.0%", "Dedicated Mean": "99.6%", "Base-Mean": "103.1%", "Base-Last": "125.8%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "97.8%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "84.1%", "Gemma3-Last": "92.3%", "Qwen3.5-Mean": "91.2%", "Qwen3.5-Last": "102.2%", "Dedicated Mean": "98.8%", "Base-Mean": "87.6%", "Base-Last": "97.3%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "104.7%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "79.0%", "Gemma3-Last": "79.0%", "Qwen3.5-Mean": "78.7%", "Qwen3.5-Last": "89.8%", "Dedicated Mean": "101.6%", "Base-Mean": "78.8%", "Base-Last": "84.4%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "87.9%", "Qwen3-Emb": "84.6%", "Gemma3-Mean": "199.2%", "Gemma3-Last": "219.5%", "Qwen3.5-Mean": "175.8%", "Qwen3.5-Last": "263.5%", "Dedicated Mean": "86.2%", "Base-Mean": "187.5%", "Base-Last": "241.5%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "105.2%", "Qwen3-Emb": "98.5%", "Gemma3-Mean": "79.6%", "Gemma3-Last": "79.5%", "Qwen3.5-Mean": "79.6%", "Qwen3.5-Last": "89.1%", "Dedicated Mean": "101.8%", "Base-Mean": "79.6%", "Base-Last": "84.3%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "104.4%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "200.6%", "Gemma3-Last": "217.4%", "Qwen3.5-Mean": "176.7%", "Qwen3.5-Last": "258.3%", "Dedicated Mean": "101.2%", "Base-Mean": "188.7%", "Base-Last": "237.9%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "103.9%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "87.3%", "Gemma3-Last": "82.8%", "Qwen3.5-Mean": "83.2%", "Qwen3.5-Last": "92.0%", "Dedicated Mean": "101.0%", "Base-Mean": "85.3%", "Base-Last": "87.4%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "104.3%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "88.7%", "Gemma3-Last": "82.8%", "Qwen3.5-Mean": "83.4%", "Qwen3.5-Last": "92.8%", "Dedicated Mean": "101.2%", "Base-Mean": "86.0%", "Base-Last": "87.8%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "104.5%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "88.7%", "Gemma3-Last": "82.8%", "Qwen3.5-Mean": "83.4%", "Qwen3.5-Last": "92.8%", "Dedicated Mean": "101.3%", "Base-Mean": "86.0%", "Base-Last": "87.8%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "104.4%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "200.6%", "Gemma3-Last": "217.4%", "Qwen3.5-Mean": "176.8%", "Qwen3.5-Last": "258.3%", "Dedicated Mean": "101.2%", "Base-Mean": "188.7%", "Base-Last": "237.9%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "104.2%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "142.0%", "Gemma3-Last": "125.5%", "Qwen3.5-Mean": "115.6%", "Qwen3.5-Last": "147.5%", "Dedicated Mean": "101.1%", "Base-Mean": "128.8%", "Base-Last": "136.5%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "104.7%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "199.1%", "Gemma3-Last": "219.5%", "Qwen3.5-Mean": "176.1%", "Qwen3.5-Last": "263.5%", "Dedicated Mean": "101.3%", "Base-Mean": "187.6%", "Base-Last": "241.5%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "104.2%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "202.3%", "Gemma3-Last": "203.8%", "Qwen3.5-Mean": "169.9%", "Qwen3.5-Last": "243.2%", "Dedicated Mean": "101.1%", "Base-Mean": "186.1%", "Base-Last": "223.5%"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "104.8%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "201.3%", "Gemma3-Last": "216.9%", "Qwen3.5-Mean": "176.4%", "Qwen3.5-Last": "254.8%", "Dedicated Mean": "101.6%", "Base-Mean": "188.8%", "Base-Last": "235.8%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "94.3%", "Qwen3-Emb": "95.4%", "Gemma3-Mean": "130.1%", "Gemma3-Last": "92.0%", "Qwen3.5-Mean": "78.0%", "Qwen3.5-Last": "106.8%", "Dedicated Mean": "94.9%", "Base-Mean": "104.1%", "Base-Last": "99.4%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "102.8%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "75.7%", "Gemma3-Last": "77.2%", "Qwen3.5-Mean": "74.0%", "Qwen3.5-Last": "88.4%", "Dedicated Mean": "100.3%", "Base-Mean": "74.9%", "Base-Last": "82.8%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "93.7%", "Qwen3-Emb": "89.5%", "Gemma3-Mean": "175.8%", "Gemma3-Last": "176.6%", "Qwen3.5-Mean": "142.6%", "Qwen3.5-Last": "213.8%", "Dedicated Mean": "91.6%", "Base-Mean": "159.2%", "Base-Last": "195.2%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "103.6%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "78.4%", "Gemma3-Last": "77.6%", "Qwen3.5-Mean": "74.4%", "Qwen3.5-Last": "91.3%", "Dedicated Mean": "100.7%", "Base-Mean": "76.4%", "Base-Last": "84.5%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "103.3%", "Qwen3-Emb": "97.6%", "Gemma3-Mean": "177.3%", "Gemma3-Last": "176.9%", "Qwen3.5-Mean": "141.8%", "Qwen3.5-Last": "212.3%", "Dedicated Mean": "100.4%", "Base-Mean": "159.5%", "Base-Last": "194.6%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "101.5%", "Qwen3-Emb": "97.6%", "Gemma3-Mean": "83.7%", "Gemma3-Last": "80.5%", "Qwen3.5-Mean": "78.2%", "Qwen3.5-Last": "91.3%", "Dedicated Mean": "99.6%", "Base-Mean": "80.9%", "Base-Last": "85.9%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "103.4%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "86.3%", "Gemma3-Last": "80.3%", "Qwen3.5-Mean": "78.8%", "Qwen3.5-Last": "94.3%", "Dedicated Mean": "100.4%", "Base-Mean": "82.5%", "Base-Last": "87.3%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "103.2%", "Qwen3-Emb": "97.6%", "Gemma3-Mean": "86.3%", "Gemma3-Last": "80.3%", "Qwen3.5-Mean": "78.8%", "Qwen3.5-Last": "94.3%", "Dedicated Mean": "100.4%", "Base-Mean": "82.5%", "Base-Last": "87.3%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "103.3%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "177.3%", "Gemma3-Last": "176.9%", "Qwen3.5-Mean": "141.8%", "Qwen3.5-Last": "212.3%", "Dedicated Mean": "100.4%", "Base-Mean": "159.5%", "Base-Last": "194.6%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "102.4%", "Qwen3-Emb": "97.6%", "Gemma3-Mean": "111.5%", "Gemma3-Last": "103.4%", "Qwen3.5-Mean": "91.1%", "Qwen3.5-Last": "122.7%", "Dedicated Mean": "100.0%", "Base-Mean": "101.3%", "Base-Last": "113.1%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "103.3%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "177.4%", "Gemma3-Last": "176.3%", "Qwen3.5-Mean": "142.5%", "Qwen3.5-Last": "213.8%", "Dedicated Mean": "100.4%", "Base-Mean": "159.9%", "Base-Last": "195.1%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "103.1%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "170.8%", "Gemma3-Last": "164.7%", "Qwen3.5-Mean": "132.4%", "Qwen3.5-Last": "196.7%", "Dedicated Mean": "100.3%", "Base-Mean": "151.6%", "Base-Last": "180.7%"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "103.5%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "175.6%", "Gemma3-Last": "175.5%", "Qwen3.5-Mean": "141.6%", "Qwen3.5-Last": "213.1%", "Dedicated Mean": "100.7%", "Base-Mean": "158.6%", "Base-Last": "194.3%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "83.9%", "Qwen3-Emb": "90.5%", "Gemma3-Mean": "128.5%", "Gemma3-Last": "113.1%", "Qwen3.5-Mean": "80.0%", "Qwen3.5-Last": "104.6%", "Dedicated Mean": "87.2%", "Base-Mean": "104.3%", "Base-Last": "108.8%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "PCA-k", "EmbGemma": "97.6%", "Qwen3-Emb": "95.4%", "Gemma3-Mean": "69.4%", "Gemma3-Last": "76.1%", "Qwen3.5-Mean": "71.2%", "Qwen3.5-Last": "87.4%", "Dedicated Mean": "96.5%", "Base-Mean": "70.3%", "Base-Last": "81.8%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Whitening-k", "EmbGemma": "92.7%", "Qwen3-Emb": "89.9%", "Gemma3-Mean": "115.8%", "Gemma3-Last": "126.5%", "Qwen3.5-Mean": "96.8%", "Qwen3.5-Last": "153.0%", "Dedicated Mean": "91.3%", "Base-Mean": "106.3%", "Base-Last": "139.8%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "SpecTemp", "EmbGemma": "99.2%", "Qwen3-Emb": "95.6%", "Gemma3-Mean": "73.9%", "Gemma3-Last": "78.1%", "Qwen3.5-Mean": "70.9%", "Qwen3.5-Last": "91.9%", "Dedicated Mean": "97.4%", "Base-Mean": "72.4%", "Base-Last": "85.0%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "98.2%", "Qwen3-Emb": "95.3%", "Gemma3-Mean": "117.8%", "Gemma3-Last": "128.2%", "Qwen3.5-Mean": "96.4%", "Qwen3.5-Last": "151.8%", "Dedicated Mean": "96.8%", "Base-Mean": "107.1%", "Base-Last": "140.0%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "96.4%", "Qwen3-Emb": "94.8%", "Gemma3-Mean": "77.1%", "Gemma3-Last": "79.9%", "Qwen3.5-Mean": "75.2%", "Qwen3.5-Last": "89.1%", "Dedicated Mean": "95.6%", "Base-Mean": "76.2%", "Base-Last": "84.5%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "98.5%", "Qwen3-Emb": "95.4%", "Gemma3-Mean": "80.9%", "Gemma3-Last": "82.0%", "Qwen3.5-Mean": "72.8%", "Qwen3.5-Last": "95.8%", "Dedicated Mean": "96.9%", "Base-Mean": "76.8%", "Base-Last": "88.9%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "98.2%", "Qwen3-Emb": "95.3%", "Gemma3-Mean": "80.9%", "Gemma3-Last": "82.0%", "Qwen3.5-Mean": "72.8%", "Qwen3.5-Last": "95.8%", "Dedicated Mean": "96.8%", "Base-Mean": "76.8%", "Base-Last": "88.9%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "97.6%", "Qwen3-Emb": "95.0%", "Gemma3-Mean": "117.8%", "Gemma3-Last": "128.2%", "Qwen3.5-Mean": "96.4%", "Qwen3.5-Last": "151.8%", "Dedicated Mean": "96.3%", "Base-Mean": "107.1%", "Base-Last": "140.0%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "98.3%", "Qwen3-Emb": "95.5%", "Gemma3-Mean": "86.2%", "Gemma3-Last": "90.7%", "Qwen3.5-Mean": "73.8%", "Qwen3.5-Last": "106.1%", "Dedicated Mean": "96.9%", "Base-Mean": "80.0%", "Base-Last": "98.4%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "98.5%", "Qwen3-Emb": "95.4%", "Gemma3-Mean": "117.6%", "Gemma3-Last": "128.2%", "Qwen3.5-Mean": "96.5%", "Qwen3.5-Last": "151.8%", "Dedicated Mean": "96.9%", "Base-Mean": "107.1%", "Base-Last": "140.0%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "97.8%", "Qwen3-Emb": "95.1%", "Gemma3-Mean": "113.6%", "Gemma3-Last": "122.5%", "Qwen3.5-Mean": "89.0%", "Qwen3.5-Last": "150.8%", "Dedicated Mean": "96.5%", "Base-Mean": "101.3%", "Base-Last": "136.7%"}, {"Dataset": "SCIDOCS", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.1%", "Qwen3-Emb": "95.7%", "Gemma3-Mean": "116.0%", "Gemma3-Last": "126.5%", "Qwen3.5-Mean": "96.8%", "Qwen3.5-Last": "153.1%", "Dedicated Mean": "97.4%", "Base-Mean": "106.4%", "Base-Last": "139.8%"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "59.1%", "Qwen3-Emb": "80.1%", "Gemma3-Mean": "94.4%", "Gemma3-Last": "93.9%", "Qwen3.5-Mean": "69.7%", "Qwen3.5-Last": "98.0%", "Dedicated Mean": "69.6%", "Base-Mean": "82.0%", "Base-Last": "96.0%"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "PCA-k", "EmbGemma": "86.8%", "Qwen3-Emb": "90.4%", "Gemma3-Mean": "61.1%", "Gemma3-Last": "74.0%", "Qwen3.5-Mean": "64.7%", "Qwen3.5-Last": "85.2%", "Dedicated Mean": "88.6%", "Base-Mean": "62.9%", "Base-Last": "79.6%"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Whitening-k", "EmbGemma": "81.6%", "Qwen3-Emb": "87.1%", "Gemma3-Mean": "66.1%", "Gemma3-Last": "85.1%", "Qwen3.5-Mean": "51.0%", "Qwen3.5-Last": "111.3%", "Dedicated Mean": "84.4%", "Base-Mean": "58.6%", "Base-Last": "98.2%"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "SpecTemp", "EmbGemma": "85.6%", "Qwen3-Emb": "89.8%", "Gemma3-Mean": "63.0%", "Gemma3-Last": "73.2%", "Qwen3.5-Mean": "57.4%", "Qwen3.5-Last": "88.9%", "Dedicated Mean": "87.7%", "Base-Mean": "60.2%", "Base-Last": "81.1%"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "87.1%", "Qwen3-Emb": "90.7%", "Gemma3-Mean": "66.8%", "Gemma3-Last": "85.8%", "Qwen3.5-Mean": "51.5%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "88.9%", "Base-Mean": "59.2%", "Base-Last": "99.4%"}, {"Dataset": "SCIDOCS", "k": "64", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "83.35 (98.2%)", "Qwen3-Emb": "85.14 (100.6%)", "Gemma3-Mean": "49.34 (129.0%)", "Gemma3-Last": "55.20 (134.2%)", "Qwen3.5-Mean": "51.18 (124.5%)", "Qwen3.5-Last": "50.79 (140.1%)", "Dedicated Mean": "84.25 (99.4%)", "Base-Mean": "50.26 (126.8%)", "Base-Last": "53.00 (137.1%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "83.15 (98.0%)", "Qwen3-Emb": "85.24 (100.8%)", "Gemma3-Mean": "53.76 (140.6%)", "Gemma3-Last": "60.69 (147.5%)", "Qwen3.5-Mean": "54.83 (133.4%)", "Qwen3.5-Last": "57.10 (157.5%)", "Dedicated Mean": "84.19 (99.4%)", "Base-Mean": "54.30 (137.0%)", "Base-Last": "58.89 (152.5%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "82.53 (97.3%)", "Qwen3-Emb": "85.25 (100.8%)", "Gemma3-Mean": "53.48 (139.8%)", "Gemma3-Last": "60.15 (146.2%)", "Qwen3.5-Mean": "54.58 (132.8%)", "Qwen3.5-Last": "56.56 (156.0%)", "Dedicated Mean": "83.89 (99.0%)", "Base-Mean": "54.03 (136.3%)", "Base-Last": "58.36 (151.1%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "82.67 (97.4%)", "Qwen3-Emb": "85.22 (100.7%)", "Gemma3-Mean": "53.75 (140.5%)", "Gemma3-Last": "60.70 (147.5%)", "Qwen3.5-Mean": "54.87 (133.5%)", "Qwen3.5-Last": "57.03 (157.3%)", "Dedicated Mean": "83.94 (99.1%)", "Base-Mean": "54.31 (137.0%)", "Base-Last": "58.87 (152.4%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "81.30 (95.8%)", "Qwen3-Emb": "82.66 (97.7%)", "Gemma3-Mean": "43.21 (113.0%)", "Gemma3-Last": "44.08 (107.1%)", "Qwen3.5-Mean": "35.03 (85.2%)", "Qwen3.5-Last": "32.68 (90.1%)", "Dedicated Mean": "81.98 (96.8%)", "Base-Mean": "39.12 (99.1%)", "Base-Last": "38.38 (98.6%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "PCA-k", "EmbGemma": "76.35 (90.0%)", "Qwen3-Emb": "83.18 (98.3%)", "Gemma3-Mean": "35.74 (93.4%)", "Gemma3-Last": "39.87 (96.9%)", "Qwen3.5-Mean": "38.49 (93.7%)", "Qwen3.5-Last": "35.86 (98.9%)", "Dedicated Mean": "79.77 (94.2%)", "Base-Mean": "37.12 (93.5%)", "Base-Last": "37.86 (97.9%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Whitening-k", "EmbGemma": "80.99 (95.4%)", "Qwen3-Emb": "83.88 (99.2%)", "Gemma3-Mean": "47.40 (123.9%)", "Gemma3-Last": "54.36 (132.1%)", "Qwen3.5-Mean": "50.16 (122.1%)", "Qwen3.5-Last": "51.35 (141.6%)", "Dedicated Mean": "82.44 (97.3%)", "Base-Mean": "48.78 (123.0%)", "Base-Last": "52.86 (136.9%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "SpecTemp", "EmbGemma": "79.67 (93.9%)", "Qwen3-Emb": "84.17 (99.5%)", "Gemma3-Mean": "42.64 (111.5%)", "Gemma3-Last": "47.03 (114.3%)", "Qwen3.5-Mean": "45.03 (109.6%)", "Qwen3.5-Last": "42.14 (116.2%)", "Dedicated Mean": "81.92 (96.7%)", "Base-Mean": "43.84 (110.5%)", "Base-Last": "44.59 (115.2%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "78.76 (92.8%)", "Qwen3-Emb": "84.28 (99.6%)", "Gemma3-Mean": "47.50 (124.2%)", "Gemma3-Last": "54.45 (132.3%)", "Qwen3.5-Mean": "50.10 (121.9%)", "Qwen3.5-Last": "51.40 (141.8%)", "Dedicated Mean": "81.52 (96.2%)", "Base-Mean": "48.80 (123.0%)", "Base-Last": "52.92 (137.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "76.45 (90.1%)", "Qwen3-Emb": "83.42 (98.6%)", "Gemma3-Mean": "36.04 (94.2%)", "Gemma3-Last": "40.34 (98.0%)", "Qwen3.5-Mean": "38.82 (94.5%)", "Qwen3.5-Last": "36.07 (99.5%)", "Dedicated Mean": "79.94 (94.3%)", "Base-Mean": "37.43 (94.3%)", "Base-Last": "38.20 (98.8%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "79.45 (93.6%)", "Qwen3-Emb": "84.28 (99.6%)", "Gemma3-Mean": "41.66 (108.9%)", "Gemma3-Last": "45.12 (109.6%)", "Qwen3.5-Mean": "45.10 (109.8%)", "Qwen3.5-Last": "41.89 (115.5%)", "Dedicated Mean": "81.87 (96.6%)", "Base-Mean": "43.38 (109.3%)", "Base-Last": "43.50 (112.6%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "78.96 (93.1%)", "Qwen3-Emb": "84.26 (99.6%)", "Gemma3-Mean": "43.72 (114.3%)", "Gemma3-Last": "49.29 (119.8%)", "Qwen3.5-Mean": "46.71 (113.7%)", "Qwen3.5-Last": "45.73 (126.1%)", "Dedicated Mean": "81.61 (96.3%)", "Base-Mean": "45.22 (114.0%)", "Base-Last": "47.51 (123.0%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "79.45 (93.6%)", "Qwen3-Emb": "84.28 (99.6%)", "Gemma3-Mean": "47.50 (124.2%)", "Gemma3-Last": "54.45 (132.3%)", "Qwen3.5-Mean": "50.10 (121.9%)", "Qwen3.5-Last": "51.40 (141.8%)", "Dedicated Mean": "81.87 (96.6%)", "Base-Mean": "48.80 (123.0%)", "Base-Last": "52.92 (137.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "78.53 (92.5%)", "Qwen3-Emb": "84.24 (99.6%)", "Gemma3-Mean": "47.37 (123.8%)", "Gemma3-Last": "54.13 (131.6%)", "Qwen3.5-Mean": "49.99 (121.7%)", "Qwen3.5-Last": "51.10 (140.9%)", "Dedicated Mean": "81.38 (96.1%)", "Base-Mean": "48.68 (122.8%)", "Base-Last": "52.62 (136.2%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Orth. 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(Σ, γ*, ε*)", "EmbGemma": "79.00 (93.1%)", "Qwen3-Emb": "84.16 (99.5%)", "Gemma3-Mean": "47.40 (123.9%)", "Gemma3-Last": "54.36 (132.1%)", "Qwen3.5-Mean": "50.16 (122.1%)", "Qwen3.5-Last": "51.35 (141.6%)", "Dedicated Mean": "81.58 (96.3%)", "Base-Mean": "48.78 (123.0%)", "Base-Last": "52.86 (136.9%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "80.22 (100.0%)", "Qwen3-Emb": "81.63 (100.6%)", "Gemma3-Mean": "45.92 (98.4%)", "Gemma3-Last": "49.50 (97.9%)", "Qwen3.5-Mean": "48.05 (99.7%)", "Qwen3.5-Last": "48.53 (100.0%)", "Dedicated Mean": "80.92 (100.3%)", "Base-Mean": "46.98 (99.0%)", "Base-Last": "49.02 (99.0%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "PCA-k", "EmbGemma": "79.73 (99.5%)", "Qwen3-Emb": "81.09 (99.9%)", "Gemma3-Mean": "51.52 (110.4%)", "Gemma3-Last": "53.16 (105.1%)", "Qwen3.5-Mean": "51.87 (107.6%)", "Qwen3.5-Last": "51.98 (107.1%)", "Dedicated Mean": "80.41 (99.7%)", "Base-Mean": "51.70 (109.0%)", "Base-Last": "52.57 (106.1%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Whitening-k", "EmbGemma": "70.29 (87.7%)", "Qwen3-Emb": "69.91 (86.1%)", "Gemma3-Mean": "59.32 (127.1%)", "Gemma3-Last": "57.50 (113.7%)", "Qwen3.5-Mean": "59.56 (123.6%)", "Qwen3.5-Last": "55.31 (114.0%)", "Dedicated Mean": "70.10 (86.9%)", "Base-Mean": "59.44 (125.3%)", "Base-Last": "56.41 (113.8%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "SpecTemp", "EmbGemma": "79.79 (99.5%)", "Qwen3-Emb": "81.00 (99.8%)", "Gemma3-Mean": "51.88 (111.2%)", "Gemma3-Last": "53.48 (105.8%)", "Qwen3.5-Mean": "52.27 (108.4%)", "Qwen3.5-Last": "52.24 (107.7%)", "Dedicated Mean": "80.40 (99.7%)", "Base-Mean": "52.08 (109.8%)", "Base-Last": "52.86 (106.7%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "79.34 (99.0%)", "Qwen3-Emb": "79.13 (97.5%)", "Gemma3-Mean": "59.36 (127.2%)", "Gemma3-Last": "57.72 (114.1%)", "Qwen3.5-Mean": "59.74 (123.9%)", "Qwen3.5-Last": "55.76 (114.9%)", "Dedicated Mean": "79.23 (98.2%)", "Base-Mean": "59.55 (125.6%)", "Base-Last": "56.74 (114.5%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "79.76 (99.5%)", "Qwen3-Emb": "81.09 (99.9%)", "Gemma3-Mean": "51.55 (110.5%)", "Gemma3-Last": "53.29 (105.4%)", "Qwen3.5-Mean": "51.91 (107.7%)", "Qwen3.5-Last": "52.18 (107.5%)", "Dedicated Mean": "80.43 (99.7%)", "Base-Mean": "51.73 (109.1%)", "Base-Last": "52.73 (106.5%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "79.81 (99.5%)", "Qwen3-Emb": "81.00 (99.8%)", "Gemma3-Mean": "51.92 (111.3%)", "Gemma3-Last": "53.55 (105.9%)", "Qwen3.5-Mean": "52.32 (108.5%)", "Qwen3.5-Last": "52.34 (107.9%)", "Dedicated Mean": "80.41 (99.7%)", "Base-Mean": "52.12 (109.9%)", "Base-Last": "52.95 (106.9%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "79.80 (99.5%)", "Qwen3-Emb": "81.03 (99.8%)", "Gemma3-Mean": "51.91 (111.2%)", "Gemma3-Last": "53.55 (105.9%)", "Qwen3.5-Mean": "52.31 (108.5%)", "Qwen3.5-Last": "52.34 (107.9%)", "Dedicated Mean": "80.41 (99.7%)", "Base-Mean": "52.11 (109.9%)", "Base-Last": "52.95 (106.9%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "79.34 (99.0%)", "Qwen3-Emb": "79.13 (97.5%)", "Gemma3-Mean": "59.36 (127.2%)", "Gemma3-Last": "57.72 (114.1%)", "Qwen3.5-Mean": "59.74 (123.9%)", "Qwen3.5-Last": "55.76 (114.9%)", "Dedicated Mean": "79.23 (98.2%)", "Base-Mean": "59.55 (125.6%)", "Base-Last": "56.74 (114.5%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "78.54 (98.0%)", "Qwen3-Emb": "77.59 (95.6%)", "Gemma3-Mean": "59.10 (126.7%)", "Gemma3-Last": "57.46 (113.6%)", "Qwen3.5-Mean": "59.99 (124.5%)", "Qwen3.5-Last": "55.82 (115.0%)", "Dedicated Mean": "78.06 (96.8%)", "Base-Mean": "59.55 (125.6%)", "Base-Last": "56.64 (114.3%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "77.90 (97.2%)", "Qwen3-Emb": "77.97 (96.1%)", "Gemma3-Mean": "59.31 (127.1%)", "Gemma3-Last": "57.53 (113.8%)", "Qwen3.5-Mean": "59.57 (123.6%)", "Qwen3.5-Last": "55.32 (114.0%)", "Dedicated Mean": "77.94 (96.6%)", "Base-Mean": "59.44 (125.3%)", "Base-Last": "56.42 (113.9%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "79.49 (99.2%)", "Qwen3-Emb": "79.39 (97.8%)", "Gemma3-Mean": "59.47 (127.4%)", "Gemma3-Last": "58.05 (114.8%)", "Qwen3.5-Mean": "59.92 (124.3%)", "Qwen3.5-Last": "56.20 (115.8%)", "Dedicated Mean": "79.44 (98.5%)", "Base-Mean": "59.70 (125.9%)", "Base-Last": "57.12 (115.3%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "79.35 (99.0%)", "Qwen3-Emb": "79.16 (97.5%)", "Gemma3-Mean": "59.36 (127.2%)", "Gemma3-Last": "57.69 (114.1%)", "Qwen3.5-Mean": "59.73 (123.9%)", "Qwen3.5-Last": "55.75 (114.9%)", "Dedicated Mean": "79.25 (98.2%)", "Base-Mean": "59.55 (125.6%)", "Base-Last": "56.72 (114.5%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "79.92 (99.7%)", "Qwen3-Emb": "81.18 (100.0%)", "Gemma3-Mean": "44.71 (95.8%)", "Gemma3-Last": "47.37 (93.7%)", "Qwen3.5-Mean": "47.29 (98.1%)", "Qwen3.5-Last": "48.93 (100.8%)", "Dedicated Mean": "80.55 (99.8%)", "Base-Mean": "46.00 (97.0%)", "Base-Last": "48.15 (97.2%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "PCA-k", "EmbGemma": "79.51 (99.2%)", "Qwen3-Emb": "81.41 (100.3%)", "Gemma3-Mean": "50.83 (108.9%)", "Gemma3-Last": "52.87 (104.5%)", "Qwen3.5-Mean": "51.23 (106.3%)", "Qwen3.5-Last": "51.71 (106.6%)", "Dedicated Mean": "80.46 (99.7%)", "Base-Mean": "51.03 (107.6%)", "Base-Last": "52.29 (105.5%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Whitening-k", "EmbGemma": "72.65 (90.6%)", "Qwen3-Emb": "71.81 (88.5%)", "Gemma3-Mean": "58.50 (125.4%)", "Gemma3-Last": "57.22 (113.2%)", "Qwen3.5-Mean": "59.04 (122.5%)", "Qwen3.5-Last": "55.38 (114.1%)", "Dedicated Mean": "72.23 (89.5%)", "Base-Mean": "58.77 (123.9%)", "Base-Last": "56.30 (113.6%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "SpecTemp", "EmbGemma": "79.86 (99.6%)", "Qwen3-Emb": "81.00 (99.8%)", "Gemma3-Mean": "52.00 (111.4%)", "Gemma3-Last": "53.89 (106.6%)", "Qwen3.5-Mean": "52.56 (109.0%)", "Qwen3.5-Last": "52.59 (108.4%)", "Dedicated Mean": "80.43 (99.7%)", "Base-Mean": "52.28 (110.2%)", "Base-Last": "53.24 (107.5%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "79.55 (99.2%)", "Qwen3-Emb": "79.57 (98.0%)", "Gemma3-Mean": "58.52 (125.4%)", "Gemma3-Last": "57.25 (113.2%)", "Qwen3.5-Mean": "59.07 (122.5%)", "Qwen3.5-Last": "55.42 (114.2%)", "Dedicated Mean": "79.56 (98.6%)", "Base-Mean": "58.80 (124.0%)", "Base-Last": "56.34 (113.7%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "79.53 (99.2%)", "Qwen3-Emb": "81.41 (100.3%)", "Gemma3-Mean": "50.87 (109.0%)", "Gemma3-Last": "53.01 (104.8%)", "Qwen3.5-Mean": "51.27 (106.4%)", "Qwen3.5-Last": "51.92 (107.0%)", "Dedicated Mean": "80.47 (99.8%)", "Base-Mean": "51.07 (107.7%)", "Base-Last": "52.47 (105.9%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "79.88 (99.6%)", "Qwen3-Emb": "80.99 (99.8%)", "Gemma3-Mean": "52.04 (111.5%)", "Gemma3-Last": "53.83 (106.5%)", "Qwen3.5-Mean": "52.61 (109.1%)", "Qwen3.5-Last": "52.45 (108.1%)", "Dedicated Mean": "80.44 (99.7%)", "Base-Mean": "52.33 (110.3%)", "Base-Last": "53.14 (107.3%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "79.85 (99.6%)", "Qwen3-Emb": "81.09 (99.9%)", "Gemma3-Mean": "52.04 (111.5%)", "Gemma3-Last": "53.83 (106.5%)", "Qwen3.5-Mean": "52.61 (109.1%)", "Qwen3.5-Last": "52.45 (108.1%)", "Dedicated Mean": "80.47 (99.8%)", "Base-Mean": "52.33 (110.3%)", "Base-Last": "53.14 (107.3%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "79.55 (99.2%)", "Qwen3-Emb": "79.57 (98.0%)", "Gemma3-Mean": "58.52 (125.4%)", "Gemma3-Last": "57.25 (113.2%)", "Qwen3.5-Mean": "59.07 (122.5%)", "Qwen3.5-Last": "55.42 (114.2%)", "Dedicated Mean": "79.56 (98.6%)", "Base-Mean": "58.80 (124.0%)", "Base-Last": "56.34 (113.7%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "78.76 (98.2%)", "Qwen3-Emb": "78.02 (96.1%)", "Gemma3-Mean": "58.08 (124.5%)", "Gemma3-Last": "56.83 (112.4%)", "Qwen3.5-Mean": "59.16 (122.7%)", "Qwen3.5-Last": "55.38 (114.1%)", "Dedicated Mean": "78.39 (97.2%)", "Base-Mean": "58.62 (123.6%)", "Base-Last": "56.11 (113.2%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "78.94 (98.5%)", "Qwen3-Emb": "79.01 (97.3%)", "Gemma3-Mean": "58.52 (125.4%)", "Gemma3-Last": "57.24 (113.2%)", "Qwen3.5-Mean": "59.06 (122.5%)", "Qwen3.5-Last": "55.39 (114.1%)", "Dedicated Mean": "78.97 (97.9%)", "Base-Mean": "58.79 (124.0%)", "Base-Last": "56.31 (113.7%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "79.82 (99.6%)", "Qwen3-Emb": "79.96 (98.5%)", "Gemma3-Mean": "58.53 (125.4%)", "Gemma3-Last": "57.52 (113.7%)", "Qwen3.5-Mean": "59.18 (122.8%)", "Qwen3.5-Last": "55.76 (114.9%)", "Dedicated Mean": "79.89 (99.0%)", "Base-Mean": "58.86 (124.1%)", "Base-Last": "56.64 (114.3%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "79.56 (99.2%)", "Qwen3-Emb": "79.60 (98.1%)", "Gemma3-Mean": "58.50 (125.4%)", "Gemma3-Last": "57.24 (113.2%)", "Qwen3.5-Mean": "59.05 (122.5%)", "Qwen3.5-Last": "55.41 (114.2%)", "Dedicated Mean": "79.58 (98.7%)", "Base-Mean": "58.77 (123.9%)", "Base-Last": "56.33 (113.7%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "79.55 (99.2%)", "Qwen3-Emb": "81.02 (99.8%)", "Gemma3-Mean": "46.50 (99.7%)", "Gemma3-Last": "51.15 (101.2%)", "Qwen3.5-Mean": "46.39 (96.2%)", "Qwen3.5-Last": "49.40 (101.8%)", "Dedicated Mean": "80.28 (99.5%)", "Base-Mean": "46.45 (97.9%)", "Base-Last": "50.27 (101.5%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "PCA-k", "EmbGemma": "78.47 (97.9%)", "Qwen3-Emb": "81.83 (100.8%)", "Gemma3-Mean": "49.64 (106.4%)", "Gemma3-Last": "52.32 (103.5%)", "Qwen3.5-Mean": "50.08 (103.9%)", "Qwen3.5-Last": "51.16 (105.4%)", "Dedicated Mean": "80.15 (99.3%)", "Base-Mean": "49.86 (105.1%)", "Base-Last": "51.74 (104.5%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Whitening-k", "EmbGemma": "75.63 (94.3%)", "Qwen3-Emb": "74.95 (92.3%)", "Gemma3-Mean": "57.04 (122.2%)", "Gemma3-Last": "57.12 (113.0%)", "Qwen3.5-Mean": "57.97 (120.2%)", "Qwen3.5-Last": "55.26 (113.9%)", "Dedicated Mean": "75.29 (93.3%)", "Base-Mean": "57.50 (121.2%)", "Base-Last": "56.19 (113.4%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "SpecTemp", "EmbGemma": "79.71 (99.4%)", "Qwen3-Emb": "80.78 (99.5%)", "Gemma3-Mean": "52.28 (112.0%)", "Gemma3-Last": "54.56 (107.9%)", "Qwen3.5-Mean": "53.17 (110.3%)", "Qwen3.5-Last": "53.16 (109.5%)", "Dedicated Mean": "80.25 (99.5%)", "Base-Mean": "52.73 (111.2%)", "Base-Last": "53.86 (108.7%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "79.86 (99.6%)", "Qwen3-Emb": "80.78 (99.5%)", "Gemma3-Mean": "57.06 (122.3%)", "Gemma3-Last": "57.12 (113.0%)", "Qwen3.5-Mean": "58.00 (120.3%)", "Qwen3.5-Last": "55.28 (113.9%)", "Dedicated Mean": "80.32 (99.6%)", "Base-Mean": "57.53 (121.3%)", "Base-Last": "56.20 (113.4%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "78.52 (97.9%)", "Qwen3-Emb": "81.86 (100.9%)", "Gemma3-Mean": "49.67 (106.5%)", "Gemma3-Last": "52.47 (103.8%)", "Qwen3.5-Mean": "50.13 (104.0%)", "Qwen3.5-Last": "51.39 (105.9%)", "Dedicated Mean": "80.19 (99.4%)", "Base-Mean": "49.90 (105.2%)", "Base-Last": "51.93 (104.8%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "79.75 (99.5%)", "Qwen3-Emb": "80.78 (99.5%)", "Gemma3-Mean": "52.33 (112.1%)", "Gemma3-Last": "54.30 (107.4%)", "Qwen3.5-Mean": "53.20 (110.4%)", "Qwen3.5-Last": "52.63 (108.5%)", "Dedicated Mean": "80.27 (99.5%)", "Base-Mean": "52.77 (111.2%)", "Base-Last": "53.47 (107.9%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "79.49 (99.2%)", "Qwen3-Emb": "79.56 (98.0%)", "Gemma3-Mean": "56.54 (121.2%)", "Gemma3-Last": "56.09 (110.9%)", "Qwen3.5-Mean": "57.70 (119.7%)", "Qwen3.5-Last": "54.70 (112.7%)", "Dedicated Mean": "79.53 (98.6%)", "Base-Mean": "57.12 (120.4%)", "Base-Last": "55.40 (111.8%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "79.77 (99.5%)", "Qwen3-Emb": "80.60 (99.3%)", "Gemma3-Mean": "57.06 (122.3%)", "Gemma3-Last": "57.12 (113.0%)", "Qwen3.5-Mean": "58.00 (120.3%)", "Qwen3.5-Last": "55.28 (113.9%)", "Dedicated Mean": "80.19 (99.4%)", "Base-Mean": "57.53 (121.3%)", "Base-Last": "56.20 (113.4%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "79.93 (99.7%)", "Qwen3-Emb": "81.07 (99.9%)", "Gemma3-Mean": "57.08 (122.3%)", "Gemma3-Last": "57.16 (113.0%)", "Qwen3.5-Mean": "58.05 (120.4%)", "Qwen3.5-Last": "55.40 (114.2%)", "Dedicated Mean": "80.50 (99.8%)", "Base-Mean": "57.56 (121.4%)", "Base-Last": "56.28 (113.6%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "79.84 (99.6%)", "Qwen3-Emb": "80.77 (99.5%)", "Gemma3-Mean": "57.03 (122.2%)", "Gemma3-Last": "57.12 (113.0%)", "Qwen3.5-Mean": "57.97 (120.2%)", "Qwen3.5-Last": "55.26 (113.9%)", "Dedicated Mean": "80.31 (99.5%)", "Base-Mean": "57.50 (121.2%)", "Base-Last": "56.19 (113.4%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "77.49 (96.7%)", "Qwen3-Emb": "80.37 (99.0%)", "Gemma3-Mean": "44.93 (96.3%)", "Gemma3-Last": "49.93 (98.7%)", "Qwen3.5-Mean": "44.01 (91.3%)", "Qwen3.5-Last": "47.68 (98.3%)", "Dedicated Mean": "78.93 (97.8%)", "Base-Mean": "44.47 (93.8%)", "Base-Last": "48.80 (98.5%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "PCA-k", "EmbGemma": "75.91 (94.7%)", "Qwen3-Emb": "81.76 (100.7%)", "Gemma3-Mean": "47.82 (102.5%)", "Gemma3-Last": "51.15 (101.1%)", "Qwen3.5-Mean": "48.53 (100.7%)", "Qwen3.5-Last": "50.05 (103.2%)", "Dedicated Mean": "78.84 (97.7%)", "Base-Mean": "48.17 (101.6%)", "Base-Last": "50.60 (102.2%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Whitening-k", "EmbGemma": "78.15 (97.5%)", "Qwen3-Emb": "78.56 (96.8%)", "Gemma3-Mean": "55.36 (118.7%)", "Gemma3-Last": "56.13 (111.0%)", "Qwen3.5-Mean": "56.78 (117.8%)", "Qwen3.5-Last": "54.83 (113.0%)", "Dedicated Mean": "78.36 (97.1%)", "Base-Mean": "56.07 (118.2%)", "Base-Last": "55.48 (112.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "SpecTemp", "EmbGemma": "79.00 (98.5%)", "Qwen3-Emb": "80.18 (98.8%)", "Gemma3-Mean": "52.74 (113.0%)", "Gemma3-Last": "54.94 (108.6%)", "Qwen3.5-Mean": "54.52 (113.1%)", "Qwen3.5-Last": "53.68 (110.6%)", "Dedicated Mean": "79.59 (98.7%)", "Base-Mean": "53.63 (113.0%)", "Base-Last": "54.31 (109.6%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "78.98 (98.5%)", "Qwen3-Emb": "80.40 (99.1%)", "Gemma3-Mean": "55.37 (118.7%)", "Gemma3-Last": "56.18 (111.1%)", "Qwen3.5-Mean": "56.80 (117.8%)", "Qwen3.5-Last": "54.84 (113.0%)", "Dedicated Mean": "79.69 (98.8%)", "Base-Mean": "56.08 (118.2%)", "Base-Last": "55.51 (112.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "75.95 (94.7%)", "Qwen3-Emb": "81.82 (100.8%)", "Gemma3-Mean": "47.86 (102.6%)", "Gemma3-Last": "51.31 (101.5%)", "Qwen3.5-Mean": "48.58 (100.8%)", "Qwen3.5-Last": "50.31 (103.7%)", "Dedicated Mean": "78.88 (97.8%)", "Base-Mean": "48.22 (101.7%)", "Base-Last": "50.81 (102.6%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "79.03 (98.6%)", "Qwen3-Emb": "80.26 (98.9%)", "Gemma3-Mean": "52.79 (113.1%)", "Gemma3-Last": "54.51 (107.8%)", "Qwen3.5-Mean": "54.57 (113.2%)", "Qwen3.5-Last": "52.69 (108.6%)", "Dedicated Mean": "79.65 (98.7%)", "Base-Mean": "53.68 (113.2%)", "Base-Last": "53.60 (108.2%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "78.98 (98.5%)", "Qwen3-Emb": "80.40 (99.1%)", "Gemma3-Mean": "52.79 (113.1%)", "Gemma3-Last": "54.51 (107.8%)", "Qwen3.5-Mean": "54.58 (113.2%)", "Qwen3.5-Last": "52.69 (108.6%)", "Dedicated Mean": "79.69 (98.8%)", "Base-Mean": "53.69 (113.2%)", "Base-Last": "53.60 (108.2%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "78.75 (98.2%)", "Qwen3-Emb": "81.99 (101.0%)", "Gemma3-Mean": "55.37 (118.7%)", "Gemma3-Last": "56.18 (111.1%)", "Qwen3.5-Mean": "56.80 (117.8%)", "Qwen3.5-Last": "54.84 (113.0%)", "Dedicated Mean": "80.37 (99.6%)", "Base-Mean": "56.08 (118.2%)", "Base-Last": "55.51 (112.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "79.14 (98.7%)", "Qwen3-Emb": "81.41 (100.3%)", "Gemma3-Mean": "54.24 (116.2%)", "Gemma3-Last": "54.60 (108.0%)", "Qwen3.5-Mean": "55.83 (115.8%)", "Qwen3.5-Last": "53.56 (110.4%)", "Dedicated Mean": "80.28 (99.5%)", "Base-Mean": "55.03 (116.0%)", "Base-Last": "54.08 (109.2%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "79.03 (98.6%)", "Qwen3-Emb": "80.26 (98.9%)", "Gemma3-Mean": "55.37 (118.7%)", "Gemma3-Last": "56.18 (111.1%)", "Qwen3.5-Mean": "56.80 (117.8%)", "Qwen3.5-Last": "54.84 (113.0%)", "Dedicated Mean": "79.65 (98.7%)", "Base-Mean": "56.08 (118.2%)", "Base-Last": "55.51 (112.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "78.75 (98.2%)", "Qwen3-Emb": "80.89 (99.7%)", "Gemma3-Mean": "55.39 (118.7%)", "Gemma3-Last": "56.13 (111.0%)", "Qwen3.5-Mean": "56.83 (117.9%)", "Qwen3.5-Last": "54.82 (113.0%)", "Dedicated Mean": "79.82 (98.9%)", "Base-Mean": "56.11 (118.3%)", "Base-Last": "55.48 (112.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "78.95 (98.5%)", "Qwen3-Emb": "80.32 (99.0%)", "Gemma3-Mean": "55.36 (118.6%)", "Gemma3-Last": "56.13 (111.0%)", "Qwen3.5-Mean": "56.78 (117.8%)", "Qwen3.5-Last": "54.83 (113.0%)", "Dedicated Mean": "79.63 (98.7%)", "Base-Mean": "56.07 (118.2%)", "Base-Last": "55.48 (112.0%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "66.45 (99.8%)", "Qwen3-Emb": "69.00 (99.1%)", "Gemma3-Mean": "58.77 (100.0%)", "Gemma3-Last": "9.65 (80.0%)", "Qwen3.5-Mean": "59.56 (98.9%)", "Qwen3.5-Last": "14.48 (89.0%)", "Dedicated Mean": "67.72 (99.5%)", "Base-Mean": "59.17 (99.5%)", "Base-Last": "12.07 (84.5%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "PCA-k", "EmbGemma": "65.90 (99.0%)", "Qwen3-Emb": "67.61 (97.1%)", "Gemma3-Mean": "55.45 (94.3%)", "Gemma3-Last": "13.39 (111.0%)", "Qwen3.5-Mean": "58.16 (96.6%)", "Qwen3.5-Last": "15.36 (94.4%)", "Dedicated Mean": "66.75 (98.1%)", "Base-Mean": "56.80 (95.5%)", "Base-Last": "14.38 (102.7%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Whitening-k", "EmbGemma": "68.08 (102.3%)", "Qwen3-Emb": "67.43 (96.9%)", "Gemma3-Mean": "65.03 (110.6%)", "Gemma3-Last": "22.96 (190.2%)", "Qwen3.5-Mean": "63.93 (106.2%)", "Qwen3.5-Last": "34.70 (213.3%)", "Dedicated Mean": "67.75 (99.6%)", "Base-Mean": "64.48 (108.4%)", "Base-Last": "28.83 (201.8%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "SpecTemp", "EmbGemma": "65.90 (99.0%)", "Qwen3-Emb": "67.61 (97.1%)", "Gemma3-Mean": "55.45 (94.3%)", "Gemma3-Last": "13.39 (111.0%)", "Qwen3.5-Mean": "58.16 (96.6%)", "Qwen3.5-Last": "15.36 (94.4%)", "Dedicated Mean": "66.75 (98.1%)", "Base-Mean": "56.80 (95.5%)", "Base-Last": "14.38 (102.7%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "66.06 (99.3%)", "Qwen3-Emb": "67.63 (97.2%)", "Gemma3-Mean": "64.31 (109.4%)", "Gemma3-Last": "20.79 (172.3%)", "Qwen3.5-Mean": "64.03 (106.3%)", "Qwen3.5-Last": "34.94 (214.8%)", "Dedicated Mean": "66.84 (98.2%)", "Base-Mean": "64.17 (107.9%)", "Base-Last": "27.86 (193.6%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "66.70 (100.2%)", "Qwen3-Emb": "67.65 (97.2%)", "Gemma3-Mean": "60.42 (102.8%)", "Gemma3-Last": "19.33 (160.2%)", "Qwen3.5-Mean": "61.91 (102.8%)", "Qwen3.5-Last": "28.55 (175.5%)", "Dedicated Mean": "67.18 (98.7%)", "Base-Mean": "61.16 (102.8%)", "Base-Last": "23.94 (167.8%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.04 (99.2%)", "Qwen3-Emb": "67.60 (97.1%)", "Gemma3-Mean": "64.85 (110.3%)", "Gemma3-Last": "20.35 (168.6%)", "Qwen3.5-Mean": "63.84 (106.0%)", "Qwen3.5-Last": "34.90 (214.6%)", "Dedicated Mean": "66.82 (98.2%)", "Base-Mean": "64.34 (108.2%)", "Base-Last": "27.62 (191.6%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "66.06 (99.3%)", "Qwen3-Emb": "67.63 (97.2%)", "Gemma3-Mean": "64.31 (109.4%)", "Gemma3-Last": "20.79 (172.3%)", "Qwen3.5-Mean": "64.03 (106.3%)", "Qwen3.5-Last": "34.94 (214.8%)", "Dedicated Mean": "66.84 (98.2%)", "Base-Mean": "64.17 (107.9%)", "Base-Last": "27.86 (193.6%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "65.90 (99.0%)", "Qwen3-Emb": "67.67 (97.2%)", "Gemma3-Mean": "64.28 (109.4%)", "Gemma3-Last": "19.48 (161.4%)", "Qwen3.5-Mean": "64.00 (106.3%)", "Qwen3.5-Last": "34.49 (212.0%)", "Dedicated Mean": "66.78 (98.1%)", "Base-Mean": "64.14 (107.8%)", "Base-Last": "26.98 (186.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "66.54 (100.0%)", "Qwen3-Emb": "69.82 (100.3%)", "Gemma3-Mean": "58.70 (99.9%)", "Gemma3-Last": "6.74 (55.9%)", "Qwen3.5-Mean": "59.50 (98.8%)", "Qwen3.5-Last": "15.34 (94.3%)", "Dedicated Mean": "68.18 (100.2%)", "Base-Mean": "59.10 (99.3%)", "Base-Last": "11.04 (75.1%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "PCA-k", "EmbGemma": "66.04 (99.2%)", "Qwen3-Emb": "67.78 (97.4%)", "Gemma3-Mean": "56.02 (95.3%)", "Gemma3-Last": "13.48 (111.7%)", "Qwen3.5-Mean": "58.42 (97.0%)", "Qwen3.5-Last": "15.60 (95.9%)", "Dedicated Mean": "66.91 (98.3%)", "Base-Mean": "57.22 (96.2%)", "Base-Last": "14.54 (103.8%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Whitening-k", "EmbGemma": "67.92 (102.1%)", "Qwen3-Emb": "67.79 (97.4%)", "Gemma3-Mean": "63.34 (107.8%)", "Gemma3-Last": "18.68 (154.8%)", "Qwen3.5-Mean": "63.55 (105.5%)", "Qwen3.5-Last": "32.14 (197.6%)", "Dedicated Mean": "67.86 (99.7%)", "Base-Mean": "63.45 (106.7%)", "Base-Last": "25.41 (176.2%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "SpecTemp", "EmbGemma": "66.26 (99.6%)", "Qwen3-Emb": "67.75 (97.3%)", "Gemma3-Mean": "56.52 (96.2%)", "Gemma3-Last": "14.91 (123.5%)", "Qwen3.5-Mean": "58.76 (97.6%)", "Qwen3.5-Last": "17.21 (105.8%)", "Dedicated Mean": "67.00 (98.5%)", "Base-Mean": "57.64 (96.9%)", "Base-Last": "16.06 (114.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "66.25 (99.6%)", "Qwen3-Emb": "67.75 (97.3%)", "Gemma3-Mean": "63.56 (108.1%)", "Gemma3-Last": "20.27 (167.9%)", "Qwen3.5-Mean": "63.58 (105.6%)", "Qwen3.5-Last": "33.65 (206.9%)", "Dedicated Mean": "67.00 (98.5%)", "Base-Mean": "63.57 (106.9%)", "Base-Last": "26.96 (187.4%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "66.11 (99.3%)", "Qwen3-Emb": "67.74 (97.3%)", "Gemma3-Mean": "55.98 (95.2%)", "Gemma3-Last": "14.39 (119.2%)", "Qwen3.5-Mean": "58.50 (97.2%)", "Qwen3.5-Last": "16.30 (100.2%)", "Dedicated Mean": "66.92 (98.3%)", "Base-Mean": "57.24 (96.2%)", "Base-Last": "15.35 (109.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.38 (99.8%)", "Qwen3-Emb": "67.63 (97.2%)", "Gemma3-Mean": "56.76 (96.6%)", "Gemma3-Last": "15.81 (131.0%)", "Qwen3.5-Mean": "58.78 (97.6%)", "Qwen3.5-Last": "17.95 (110.3%)", "Dedicated Mean": "67.00 (98.5%)", "Base-Mean": "57.77 (97.1%)", "Base-Last": "16.88 (120.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "66.25 (99.6%)", "Qwen3-Emb": "67.75 (97.3%)", "Gemma3-Mean": "56.74 (96.5%)", "Gemma3-Last": "15.70 (130.1%)", "Qwen3.5-Mean": "58.79 (97.6%)", "Qwen3.5-Last": "17.89 (110.0%)", "Dedicated Mean": "67.00 (98.5%)", "Base-Mean": "57.77 (97.1%)", "Base-Last": "16.80 (120.0%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "66.17 (99.4%)", "Qwen3-Emb": "67.72 (97.3%)", "Gemma3-Mean": "63.56 (108.1%)", "Gemma3-Last": "20.27 (167.9%)", "Qwen3.5-Mean": "63.58 (105.6%)", "Qwen3.5-Last": "33.65 (206.9%)", "Dedicated Mean": "66.94 (98.4%)", "Base-Mean": "63.57 (106.9%)", "Base-Last": "26.96 (187.4%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "66.75 (100.3%)", "Qwen3-Emb": "67.58 (97.1%)", "Gemma3-Mean": "61.01 (103.8%)", "Gemma3-Last": "19.29 (159.8%)", "Qwen3.5-Mean": "62.45 (103.7%)", "Qwen3.5-Last": "29.67 (182.4%)", "Dedicated Mean": "67.16 (98.7%)", "Base-Mean": "61.73 (103.8%)", "Base-Last": "24.48 (171.1%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.38 (99.8%)", "Qwen3-Emb": "67.63 (97.2%)", "Gemma3-Mean": "63.58 (108.2%)", "Gemma3-Last": "19.91 (165.0%)", "Qwen3.5-Mean": "63.29 (105.1%)", "Qwen3.5-Last": "32.27 (198.4%)", "Dedicated Mean": "67.00 (98.5%)", "Base-Mean": "63.44 (106.7%)", "Base-Last": "26.09 (181.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "66.25 (99.6%)", "Qwen3-Emb": "67.75 (97.3%)", "Gemma3-Mean": "63.63 (108.3%)", "Gemma3-Last": "19.99 (165.7%)", "Qwen3.5-Mean": "63.86 (106.1%)", "Qwen3.5-Last": "34.10 (209.7%)", "Dedicated Mean": "67.00 (98.5%)", "Base-Mean": "63.75 (107.2%)", "Base-Last": "27.05 (187.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "66.20 (99.5%)", "Qwen3-Emb": "67.76 (97.4%)", "Gemma3-Mean": "63.33 (107.8%)", "Gemma3-Last": "19.57 (162.1%)", "Qwen3.5-Mean": "63.69 (105.8%)", "Qwen3.5-Last": "33.40 (205.3%)", "Dedicated Mean": "66.98 (98.4%)", "Base-Mean": "63.51 (106.8%)", "Base-Last": "26.48 (183.7%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "66.88 (100.5%)", "Qwen3-Emb": "68.48 (98.4%)", "Gemma3-Mean": "57.93 (98.6%)", "Gemma3-Last": "17.87 (148.0%)", "Qwen3.5-Mean": "57.59 (95.7%)", "Qwen3.5-Last": "17.22 (105.9%)", "Dedicated Mean": "67.68 (99.4%)", "Base-Mean": "57.76 (97.1%)", "Base-Last": "17.55 (127.0%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "65.73 (98.8%)", "Qwen3-Emb": "67.60 (97.1%)", "Gemma3-Mean": "53.04 (90.2%)", "Gemma3-Last": "12.84 (106.4%)", "Qwen3.5-Mean": "57.01 (94.7%)", "Qwen3.5-Last": "15.03 (92.4%)", "Dedicated Mean": "66.66 (98.0%)", "Base-Mean": "55.02 (92.5%)", "Base-Last": "13.93 (99.4%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "67.39 (101.3%)", "Qwen3-Emb": "67.35 (96.8%)", "Gemma3-Mean": "60.18 (102.4%)", "Gemma3-Last": "16.89 (139.9%)", "Qwen3.5-Mean": "62.83 (104.4%)", "Qwen3.5-Last": "33.06 (203.2%)", "Dedicated Mean": "67.37 (99.0%)", "Base-Mean": "61.50 (103.4%)", "Base-Last": "24.98 (171.6%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "66.47 (99.9%)", "Qwen3-Emb": "67.44 (96.9%)", "Gemma3-Mean": "55.31 (94.1%)", "Gemma3-Last": "15.51 (128.5%)", "Qwen3.5-Mean": "58.39 (97.0%)", "Qwen3.5-Last": "21.01 (129.2%)", "Dedicated Mean": "66.95 (98.4%)", "Base-Mean": "56.85 (95.5%)", "Base-Last": "18.26 (128.8%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "66.38 (99.8%)", "Qwen3-Emb": "67.59 (97.1%)", "Gemma3-Mean": "60.29 (102.6%)", "Gemma3-Last": "17.08 (141.5%)", "Qwen3.5-Mean": "62.81 (104.3%)", "Qwen3.5-Last": "33.39 (205.3%)", "Dedicated Mean": "66.98 (98.4%)", "Base-Mean": "61.55 (103.5%)", "Base-Last": "25.23 (173.4%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "65.77 (98.8%)", "Qwen3-Emb": "67.52 (97.0%)", "Gemma3-Mean": "53.11 (90.3%)", "Gemma3-Last": "13.80 (114.4%)", "Qwen3.5-Mean": "56.98 (94.6%)", "Qwen3.5-Last": "15.26 (93.8%)", "Dedicated Mean": "66.64 (97.9%)", "Base-Mean": "55.05 (92.5%)", "Base-Last": "14.53 (104.1%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.61 (100.1%)", "Qwen3-Emb": "67.54 (97.0%)", "Gemma3-Mean": "55.69 (94.8%)", "Gemma3-Last": "16.24 (134.5%)", "Qwen3.5-Mean": "58.31 (96.8%)", "Qwen3.5-Last": "21.80 (134.0%)", "Dedicated Mean": "67.08 (98.6%)", "Base-Mean": "57.00 (95.8%)", "Base-Last": "19.02 (134.3%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "66.38 (99.8%)", "Qwen3-Emb": "67.59 (97.1%)", "Gemma3-Mean": "55.68 (94.7%)", "Gemma3-Last": "16.23 (134.4%)", "Qwen3.5-Mean": "58.32 (96.9%)", "Qwen3.5-Last": "21.72 (133.6%)", "Dedicated Mean": "66.98 (98.4%)", "Base-Mean": "57.00 (95.8%)", "Base-Last": "18.98 (134.0%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "65.79 (98.9%)", "Qwen3-Emb": "67.55 (97.0%)", "Gemma3-Mean": "60.29 (102.6%)", "Gemma3-Last": "17.08 (141.5%)", "Qwen3.5-Mean": "62.81 (104.3%)", "Qwen3.5-Last": "33.39 (205.3%)", "Dedicated Mean": "66.67 (98.0%)", "Base-Mean": "61.55 (103.5%)", "Base-Last": "25.23 (173.4%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "66.41 (99.8%)", "Qwen3-Emb": "67.50 (97.0%)", "Gemma3-Mean": "56.97 (96.9%)", "Gemma3-Last": "17.03 (141.1%)", "Qwen3.5-Mean": "60.44 (100.4%)", "Qwen3.5-Last": "28.42 (174.7%)", "Dedicated Mean": "66.95 (98.4%)", "Base-Mean": "58.70 (98.7%)", "Base-Last": "22.73 (157.9%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.61 (100.1%)", "Qwen3-Emb": "67.54 (97.0%)", "Gemma3-Mean": "60.31 (102.6%)", "Gemma3-Last": "17.09 (141.6%)", "Qwen3.5-Mean": "62.84 (104.4%)", "Qwen3.5-Last": "33.33 (204.9%)", "Dedicated Mean": "67.08 (98.6%)", "Base-Mean": "61.58 (103.5%)", "Base-Last": "25.21 (173.2%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "66.36 (99.7%)", "Qwen3-Emb": "67.57 (97.1%)", "Gemma3-Mean": "60.03 (102.1%)", "Gemma3-Last": "17.03 (141.1%)", "Qwen3.5-Mean": "62.58 (103.9%)", "Qwen3.5-Last": "33.08 (203.4%)", "Dedicated Mean": "66.97 (98.4%)", "Base-Mean": "61.30 (103.0%)", "Base-Last": "25.05 (172.2%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "66.21 (99.5%)", "Qwen3-Emb": "67.65 (97.2%)", "Gemma3-Mean": "60.16 (102.3%)", "Gemma3-Last": "16.30 (135.1%)", "Qwen3.5-Mean": "62.84 (104.4%)", "Qwen3.5-Last": "33.03 (203.1%)", "Dedicated Mean": "66.93 (98.3%)", "Base-Mean": "61.50 (103.4%)", "Base-Last": "24.66 (169.1%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "65.79 (98.9%)", "Qwen3-Emb": "67.66 (97.2%)", "Gemma3-Mean": "58.49 (99.5%)", "Gemma3-Last": "17.34 (143.7%)", "Qwen3.5-Mean": "55.95 (92.9%)", "Qwen3.5-Last": "16.19 (99.5%)", "Dedicated Mean": "66.72 (98.0%)", "Base-Mean": "57.22 (96.2%)", "Base-Last": "16.77 (121.6%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "PCA-k", "EmbGemma": "64.03 (96.2%)", "Qwen3-Emb": "67.56 (97.1%)", "Gemma3-Mean": "49.69 (84.5%)", "Gemma3-Last": "11.44 (94.8%)", "Qwen3.5-Mean": "54.88 (91.2%)", "Qwen3.5-Last": "10.46 (64.3%)", "Dedicated Mean": "65.80 (96.7%)", "Base-Mean": "52.28 (87.8%)", "Base-Last": "10.95 (79.5%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Whitening-k", "EmbGemma": "66.34 (99.7%)", "Qwen3-Emb": "67.75 (97.3%)", "Gemma3-Mean": "54.97 (93.5%)", "Gemma3-Last": "19.50 (161.6%)", "Qwen3.5-Mean": "59.34 (98.6%)", "Qwen3.5-Last": "26.24 (161.3%)", "Dedicated Mean": "67.05 (98.5%)", "Base-Mean": "57.16 (96.0%)", "Base-Last": "22.87 (161.4%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "SpecTemp", "EmbGemma": "66.11 (99.3%)", "Qwen3-Emb": "67.75 (97.3%)", "Gemma3-Mean": "53.72 (91.4%)", "Gemma3-Last": "17.47 (144.7%)", "Qwen3.5-Mean": "57.82 (96.0%)", "Qwen3.5-Last": "21.53 (132.4%)", "Dedicated Mean": "66.93 (98.3%)", "Base-Mean": "55.77 (93.7%)", "Base-Last": "19.50 (138.6%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "65.57 (98.5%)", "Qwen3-Emb": "68.09 (97.8%)", "Gemma3-Mean": "55.34 (94.2%)", "Gemma3-Last": "18.08 (149.8%)", "Qwen3.5-Mean": "59.18 (98.3%)", "Qwen3.5-Last": "26.44 (162.6%)", "Dedicated Mean": "66.83 (98.2%)", "Base-Mean": "57.26 (96.2%)", "Base-Last": "22.26 (156.2%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "64.19 (96.5%)", "Qwen3-Emb": "67.73 (97.3%)", "Gemma3-Mean": "49.89 (84.9%)", "Gemma3-Last": "11.96 (99.1%)", "Qwen3.5-Mean": "54.98 (91.3%)", "Qwen3.5-Last": "10.66 (65.5%)", "Dedicated Mean": "65.96 (96.9%)", "Base-Mean": "52.44 (88.1%)", "Base-Last": "11.31 (82.3%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.00 (99.2%)", "Qwen3-Emb": "68.05 (97.8%)", "Gemma3-Mean": "54.31 (92.4%)", "Gemma3-Last": "17.90 (148.3%)", "Qwen3.5-Mean": "57.62 (95.7%)", "Qwen3.5-Last": "21.80 (134.0%)", "Dedicated Mean": "67.03 (98.5%)", "Base-Mean": "55.97 (94.1%)", "Base-Last": "19.85 (141.2%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "65.57 (98.5%)", "Qwen3-Emb": "68.09 (97.8%)", "Gemma3-Mean": "54.31 (92.4%)", "Gemma3-Last": "17.85 (147.9%)", "Qwen3.5-Mean": "57.61 (95.7%)", "Qwen3.5-Last": "21.80 (134.0%)", "Dedicated Mean": "66.83 (98.2%)", "Base-Mean": "55.96 (94.0%)", "Base-Last": "19.83 (141.0%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "64.32 (96.7%)", "Qwen3-Emb": "67.73 (97.3%)", "Gemma3-Mean": "55.34 (94.2%)", "Gemma3-Last": "18.08 (149.8%)", "Qwen3.5-Mean": "59.18 (98.3%)", "Qwen3.5-Last": "26.44 (162.6%)", "Dedicated Mean": "66.03 (97.0%)", "Base-Mean": "57.26 (96.2%)", "Base-Last": "22.26 (156.2%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "65.06 (97.8%)", "Qwen3-Emb": "68.04 (97.8%)", "Gemma3-Mean": "53.52 (91.1%)", "Gemma3-Last": "17.20 (142.6%)", "Qwen3.5-Mean": "57.68 (95.8%)", "Qwen3.5-Last": "21.69 (133.4%)", "Dedicated Mean": "66.55 (97.8%)", "Base-Mean": "55.60 (93.4%)", "Base-Last": "19.45 (138.0%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.00 (99.2%)", "Qwen3-Emb": "68.05 (97.8%)", "Gemma3-Mean": "55.34 (94.2%)", "Gemma3-Last": "18.13 (150.2%)", "Qwen3.5-Mean": "59.18 (98.3%)", "Qwen3.5-Last": "26.44 (162.6%)", "Dedicated Mean": "67.03 (98.5%)", "Base-Mean": "57.26 (96.2%)", "Base-Last": "22.29 (156.4%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "65.51 (98.5%)", "Qwen3-Emb": "68.07 (97.8%)", "Gemma3-Mean": "55.30 (94.1%)", "Gemma3-Last": "17.79 (147.4%)", "Qwen3.5-Mean": "59.14 (98.2%)", "Qwen3.5-Last": "26.15 (160.8%)", "Dedicated Mean": "66.79 (98.1%)", "Base-Mean": "57.22 (96.2%)", "Base-Last": "21.97 (154.1%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "65.43 (98.3%)", "Qwen3-Emb": "67.95 (97.6%)", "Gemma3-Mean": "54.97 (93.5%)", "Gemma3-Last": "17.50 (145.0%)", "Qwen3.5-Mean": "59.35 (98.6%)", "Qwen3.5-Last": "26.22 (161.2%)", "Dedicated Mean": "66.69 (98.0%)", "Base-Mean": "57.16 (96.0%)", "Base-Last": "21.86 (153.1%)"}], "task_comp::Similarity (STS)::Spearman (ρ × 100)::Absolute Score": [{"Dataset": "STSBenchmark", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "85.06", "Qwen3-Emb": "84.76", "Gemma3-Mean": "36.61", "Gemma3-Last": "41.92", "Qwen3.5-Mean": "40.33", "Qwen3.5-Last": "35.41", "Dedicated Mean": "84.91", "Base-Mean": "38.47", "Base-Last": "38.66"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "PCA-k", "EmbGemma": "85.24", "Qwen3-Emb": "84.86", "Gemma3-Mean": "44.11", "Gemma3-Last": "46.97", "Qwen3.5-Mean": "44.71", "Qwen3.5-Last": "40.44", "Dedicated Mean": "85.05", "Base-Mean": "44.41", "Base-Last": "43.70"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Whitening-k", "EmbGemma": "81.77", "Qwen3-Emb": "79.22", "Gemma3-Mean": "60.36", "Gemma3-Last": "65.13", "Qwen3.5-Mean": "60.51", "Qwen3.5-Last": "60.46", "Dedicated Mean": "80.50", "Base-Mean": "60.44", "Base-Last": "62.80"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "SpecTemp", "EmbGemma": "85.43", "Qwen3-Emb": "84.86", "Gemma3-Mean": "45.08", "Gemma3-Last": "47.72", "Qwen3.5-Mean": "45.38", "Qwen3.5-Last": "40.87", "Dedicated Mean": "85.15", "Base-Mean": "45.23", "Base-Last": "44.30"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "85.63", "Qwen3-Emb": "84.94", "Gemma3-Mean": "60.28", "Gemma3-Last": "65.17", "Qwen3.5-Mean": "60.34", "Qwen3.5-Last": "60.54", "Dedicated Mean": "85.28", "Base-Mean": "60.31", "Base-Last": "62.86"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "85.36", "Qwen3-Emb": "84.92", "Gemma3-Mean": "44.40", "Gemma3-Last": "47.60", "Qwen3.5-Mean": "45.01", "Qwen3.5-Last": "40.60", "Dedicated Mean": "85.14", "Base-Mean": "44.70", "Base-Last": "44.10"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "85.55", "Qwen3-Emb": "84.92", "Gemma3-Mean": "45.16", "Gemma3-Last": "48.07", "Qwen3.5-Mean": "45.62", "Qwen3.5-Last": "41.05", "Dedicated Mean": "85.23", "Base-Mean": "45.39", "Base-Last": "44.56"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "85.46", "Qwen3-Emb": "84.93", "Gemma3-Mean": "45.15", "Gemma3-Last": "48.05", "Qwen3.5-Mean": "45.61", "Qwen3.5-Last": "41.03", "Dedicated Mean": "85.19", "Base-Mean": "45.38", "Base-Last": "44.54"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "85.63", "Qwen3-Emb": "84.94", "Gemma3-Mean": "60.28", "Gemma3-Last": "65.17", "Qwen3.5-Mean": "60.34", "Qwen3.5-Last": "60.54", "Dedicated Mean": "85.28", "Base-Mean": "60.31", "Base-Last": "62.86"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "85.99", "Qwen3-Emb": "84.41", "Gemma3-Mean": "56.54", "Gemma3-Last": "61.00", "Qwen3.5-Mean": "56.95", "Qwen3.5-Last": "55.37", "Dedicated Mean": "85.20", "Base-Mean": "56.75", "Base-Last": "58.19"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "85.84", "Qwen3-Emb": "84.76", "Gemma3-Mean": "60.36", "Gemma3-Last": "65.16", "Qwen3.5-Mean": "60.51", "Qwen3.5-Last": "60.45", "Dedicated Mean": "85.30", "Base-Mean": "60.44", "Base-Last": "62.80"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "85.62", "Qwen3-Emb": "84.95", "Gemma3-Mean": "59.90", "Gemma3-Last": "64.88", "Qwen3.5-Mean": "59.94", "Qwen3.5-Last": "60.23", "Dedicated Mean": "85.28", "Base-Mean": "59.92", "Base-Last": "62.55"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Orth. Proj. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "84.31", "Qwen3-Emb": "85.23", "Gemma3-Mean": "42.73", "Gemma3-Last": "46.40", "Qwen3.5-Mean": "43.87", "Qwen3.5-Last": "39.96", "Dedicated Mean": "84.77", "Base-Mean": "43.30", "Base-Last": "43.18"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "84.95", "Qwen3-Emb": "85.27", "Gemma3-Mean": "44.74", "Gemma3-Last": "47.94", "Qwen3.5-Mean": "45.80", "Qwen3.5-Last": "41.50", "Dedicated Mean": "85.11", "Base-Mean": "45.27", "Base-Last": "44.72"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "84.69", "Qwen3-Emb": "85.29", "Gemma3-Mean": "44.74", "Gemma3-Last": "47.93", "Qwen3.5-Mean": "45.79", "Qwen3.5-Last": "41.49", "Dedicated Mean": "84.99", "Base-Mean": "45.27", "Base-Last": "44.71"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "84.62", "Qwen3-Emb": "85.29", "Gemma3-Mean": "57.62", "Gemma3-Last": "64.15", "Qwen3.5-Mean": "58.60", "Qwen3.5-Last": "59.59", "Dedicated Mean": "84.96", "Base-Mean": "58.11", "Base-Last": "61.87"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "85.27", "Qwen3-Emb": "84.90", "Gemma3-Mean": "53.70", "Gemma3-Last": "59.29", "Qwen3.5-Mean": "54.96", "Qwen3.5-Last": "53.90", "Dedicated Mean": "85.09", "Base-Mean": "54.33", "Base-Last": "56.59"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "84.95", "Qwen3-Emb": "85.25", "Gemma3-Mean": "57.62", "Gemma3-Last": "64.18", "Qwen3.5-Mean": "58.62", "Qwen3.5-Last": "59.63", "Dedicated Mean": "85.10", "Base-Mean": "58.12", "Base-Last": "61.91"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "84.67", "Qwen3-Emb": "85.29", "Gemma3-Mean": "57.29", "Gemma3-Last": "63.61", "Qwen3.5-Mean": "58.12", "Qwen3.5-Last": "59.07", "Dedicated Mean": "84.98", "Base-Mean": "57.70", "Base-Last": "61.34"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "84.64", "Qwen3-Emb": "85.22", "Gemma3-Mean": "57.58", "Gemma3-Last": "64.08", "Qwen3.5-Mean": "58.54", "Qwen3.5-Last": "59.62", "Dedicated Mean": "84.93", "Base-Mean": "58.06", "Base-Last": "61.85"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "84.15", "Qwen3-Emb": "84.02", "Gemma3-Mean": "43.27", "Gemma3-Last": "46.36", "Qwen3.5-Mean": "38.10", "Qwen3.5-Last": "36.14", "Dedicated Mean": "84.09", "Base-Mean": "40.69", "Base-Last": "41.25"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "PCA-k", "EmbGemma": "81.35", "Qwen3-Emb": "84.88", "Gemma3-Mean": "39.46", "Gemma3-Last": "43.34", "Qwen3.5-Mean": "41.30", "Qwen3.5-Last": "38.27", "Dedicated Mean": "83.11", "Base-Mean": "40.38", "Base-Last": "40.81"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Whitening-k", "EmbGemma": "83.52", "Qwen3-Emb": "83.71", "Gemma3-Mean": "53.75", "Gemma3-Last": "60.70", "Qwen3.5-Mean": "54.87", "Qwen3.5-Last": "57.04", "Dedicated Mean": "83.61", "Base-Mean": "54.31", "Base-Last": "58.87"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "SpecTemp", "EmbGemma": "83.20", "Qwen3-Emb": "85.20", "Gemma3-Mean": "44.12", "Gemma3-Last": "47.91", "Qwen3.5-Mean": "45.13", "Qwen3.5-Last": "41.80", "Dedicated Mean": "84.20", "Base-Mean": "44.62", "Base-Last": "44.85"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "82.64", "Qwen3-Emb": "85.26", "Gemma3-Mean": "53.76", "Gemma3-Last": "60.69", "Qwen3.5-Mean": "54.83", "Qwen3.5-Last": "57.09", "Dedicated Mean": "83.95", "Base-Mean": "54.30", "Base-Last": "58.89"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "81.53", "Qwen3-Emb": "84.96", "Gemma3-Mean": "39.75", "Gemma3-Last": "43.87", "Qwen3.5-Mean": "41.62", "Qwen3.5-Last": "38.48", "Dedicated Mean": "83.25", "Base-Mean": "40.69", "Base-Last": "41.17"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "83.15", "Qwen3-Emb": "85.24", "Gemma3-Mean": "43.46", "Gemma3-Last": "46.87", "Qwen3.5-Mean": "45.36", "Qwen3.5-Last": "41.84", "Dedicated Mean": "84.19", "Base-Mean": "44.41", "Base-Last": "44.36"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Crowd. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "65.77", "Qwen3-Emb": "67.52", "Gemma3-Mean": "53.11", "Gemma3-Last": "13.80", "Qwen3.5-Mean": "56.98", "Qwen3.5-Last": "15.26", "Dedicated Mean": "66.64", "Base-Mean": "55.05", "Base-Last": "14.53"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.61", "Qwen3-Emb": "67.54", "Gemma3-Mean": "55.69", "Gemma3-Last": "16.24", "Qwen3.5-Mean": "58.31", "Qwen3.5-Last": "21.80", "Dedicated Mean": "67.08", "Base-Mean": "57.00", "Base-Last": "19.02"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "66.41", "Qwen3-Emb": "67.50", "Gemma3-Mean": "56.97", "Gemma3-Last": "17.03", "Qwen3.5-Mean": "60.44", "Qwen3.5-Last": "28.42", "Dedicated Mean": "66.95", "Base-Mean": "58.70", "Base-Last": "22.73"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.61", "Qwen3-Emb": "67.54", "Gemma3-Mean": "60.31", "Gemma3-Last": "17.09", "Qwen3.5-Mean": "62.84", "Qwen3.5-Last": "33.33", "Dedicated Mean": "67.08", "Base-Mean": "61.58", "Base-Last": "25.21"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "66.36", "Qwen3-Emb": "67.57", "Gemma3-Mean": "60.03", "Gemma3-Last": "17.03", "Qwen3.5-Mean": "62.58", "Qwen3.5-Last": "33.08", "Dedicated Mean": "66.97", "Base-Mean": "61.30", "Base-Last": "25.05"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "66.21", "Qwen3-Emb": "67.65", "Gemma3-Mean": "60.16", "Gemma3-Last": "16.30", "Qwen3.5-Mean": "62.84", "Qwen3.5-Last": "33.03", "Dedicated Mean": "66.93", "Base-Mean": "61.50", "Base-Last": "24.66"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "65.79", "Qwen3-Emb": "67.66", "Gemma3-Mean": "58.49", "Gemma3-Last": "17.34", "Qwen3.5-Mean": "55.95", "Qwen3.5-Last": "16.19", "Dedicated Mean": "66.72", "Base-Mean": "57.22", "Base-Last": "16.77"}, {"Dataset": "STS22.v2", "k": "64", "Method": "PCA-k", "EmbGemma": "64.03", "Qwen3-Emb": "67.56", "Gemma3-Mean": "49.69", "Gemma3-Last": "11.44", "Qwen3.5-Mean": "54.88", "Qwen3.5-Last": "10.46", "Dedicated Mean": "65.80", "Base-Mean": "52.28", "Base-Last": "10.95"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Whitening-k", "EmbGemma": "66.34", "Qwen3-Emb": "67.75", "Gemma3-Mean": "54.97", "Gemma3-Last": "19.50", "Qwen3.5-Mean": "59.34", "Qwen3.5-Last": "26.24", "Dedicated Mean": "67.05", "Base-Mean": "57.16", "Base-Last": "22.87"}, {"Dataset": "STS22.v2", "k": "64", "Method": "SpecTemp", "EmbGemma": "66.11", "Qwen3-Emb": "67.75", "Gemma3-Mean": "53.72", "Gemma3-Last": "17.47", "Qwen3.5-Mean": "57.82", "Qwen3.5-Last": "21.53", "Dedicated Mean": "66.93", "Base-Mean": "55.77", "Base-Last": "19.50"}, {"Dataset": "STS22.v2", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "65.57", "Qwen3-Emb": "68.09", "Gemma3-Mean": "55.34", "Gemma3-Last": "18.08", "Qwen3.5-Mean": "59.18", "Qwen3.5-Last": "26.44", "Dedicated Mean": "66.83", "Base-Mean": "57.26", "Base-Last": "22.26"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "64.19", "Qwen3-Emb": "67.73", "Gemma3-Mean": "49.89", "Gemma3-Last": "11.96", "Qwen3.5-Mean": "54.98", "Qwen3.5-Last": "10.66", "Dedicated Mean": "65.96", "Base-Mean": "52.44", "Base-Last": "11.31"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.00", "Qwen3-Emb": "68.05", "Gemma3-Mean": "54.31", "Gemma3-Last": "17.90", "Qwen3.5-Mean": "57.62", "Qwen3.5-Last": "21.80", "Dedicated Mean": "67.03", "Base-Mean": "55.97", "Base-Last": "19.85"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "65.57", "Qwen3-Emb": "68.09", "Gemma3-Mean": "54.31", "Gemma3-Last": "17.85", "Qwen3.5-Mean": "57.61", "Qwen3.5-Last": "21.80", "Dedicated Mean": "66.83", "Base-Mean": "55.96", "Base-Last": "19.83"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "64.32", "Qwen3-Emb": "67.73", "Gemma3-Mean": "55.34", "Gemma3-Last": "18.08", "Qwen3.5-Mean": "59.18", "Qwen3.5-Last": "26.44", "Dedicated Mean": "66.03", "Base-Mean": "57.26", "Base-Last": "22.26"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "65.06", "Qwen3-Emb": "68.04", "Gemma3-Mean": "53.52", "Gemma3-Last": "17.20", "Qwen3.5-Mean": "57.68", "Qwen3.5-Last": "21.69", "Dedicated Mean": "66.55", "Base-Mean": "55.60", "Base-Last": "19.45"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.00", "Qwen3-Emb": "68.05", "Gemma3-Mean": "55.34", "Gemma3-Last": "18.13", "Qwen3.5-Mean": "59.18", "Qwen3.5-Last": "26.44", "Dedicated Mean": "67.03", "Base-Mean": "57.26", "Base-Last": "22.29"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "65.51", "Qwen3-Emb": "68.07", "Gemma3-Mean": "55.30", "Gemma3-Last": "17.79", "Qwen3.5-Mean": "59.14", "Qwen3.5-Last": "26.15", "Dedicated Mean": "66.79", "Base-Mean": "57.22", "Base-Last": "21.97"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "65.43", "Qwen3-Emb": "67.95", "Gemma3-Mean": "54.97", "Gemma3-Last": "17.50", "Qwen3.5-Mean": "59.35", "Qwen3.5-Last": "26.22", "Dedicated Mean": "66.69", "Base-Mean": "57.16", "Base-Last": "21.86"}], "task_comp::Similarity (STS)::Spearman (ρ × 100)::Retention %": [{"Dataset": "STSBenchmark", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "100.2%", "Qwen3-Emb": "100.2%", "Gemma3-Mean": "95.7%", "Gemma3-Last": "101.9%", "Qwen3.5-Mean": "98.1%", "Qwen3.5-Last": "97.7%", "Dedicated Mean": "100.2%", "Base-Mean": "96.9%", "Base-Last": "99.8%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "PCA-k", "EmbGemma": "100.5%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "115.3%", "Gemma3-Last": "114.1%", "Qwen3.5-Mean": "108.8%", "Qwen3.5-Last": "111.5%", "Dedicated Mean": "100.4%", "Base-Mean": "112.1%", "Base-Last": "112.8%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Whitening-k", "EmbGemma": "96.4%", "Qwen3-Emb": "93.7%", "Gemma3-Mean": "157.8%", "Gemma3-Last": "158.3%", "Qwen3.5-Mean": "147.3%", "Qwen3.5-Last": "166.8%", "Dedicated Mean": "95.0%", "Base-Mean": "152.5%", "Base-Last": "162.5%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "SpecTemp", "EmbGemma": "100.7%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "117.9%", "Gemma3-Last": "116.0%", "Qwen3.5-Mean": "110.4%", "Qwen3.5-Last": "112.7%", "Dedicated Mean": "100.5%", "Base-Mean": "114.2%", "Base-Last": "114.3%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "100.9%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "157.6%", "Gemma3-Last": "158.4%", "Qwen3.5-Mean": "146.8%", "Qwen3.5-Last": "167.0%", "Dedicated Mean": "100.7%", "Base-Mean": "152.2%", "Base-Last": "162.7%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.6%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "116.1%", "Gemma3-Last": "115.7%", "Qwen3.5-Mean": "109.5%", "Qwen3.5-Last": "112.0%", "Dedicated Mean": "100.5%", "Base-Mean": "112.8%", "Base-Last": "113.8%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.8%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "118.1%", "Gemma3-Last": "116.8%", "Qwen3.5-Mean": "111.0%", "Qwen3.5-Last": "113.2%", "Dedicated Mean": "100.6%", "Base-Mean": "114.5%", "Base-Last": "115.0%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.7%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "118.0%", "Gemma3-Last": "116.8%", "Qwen3.5-Mean": "111.0%", "Qwen3.5-Last": "113.2%", "Dedicated Mean": "100.6%", "Base-Mean": "114.5%", "Base-Last": "115.0%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.9%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "157.6%", "Gemma3-Last": "158.4%", "Qwen3.5-Mean": "146.8%", "Qwen3.5-Last": "167.0%", "Dedicated Mean": "100.7%", "Base-Mean": "152.2%", "Base-Last": "162.7%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "101.3%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "147.8%", "Gemma3-Last": "148.2%", "Qwen3.5-Mean": "138.6%", "Qwen3.5-Last": "152.7%", "Dedicated Mean": "100.6%", "Base-Mean": "143.2%", "Base-Last": "150.5%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "101.2%", "Qwen3-Emb": "100.2%", "Gemma3-Mean": "157.8%", "Gemma3-Last": "158.3%", "Qwen3.5-Mean": "147.2%", "Qwen3.5-Last": "166.7%", "Dedicated Mean": "100.7%", "Base-Mean": "152.5%", "Base-Last": "162.5%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.9%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "156.6%", "Gemma3-Last": "157.7%", "Qwen3.5-Mean": "145.9%", "Qwen3.5-Last": "166.1%", "Dedicated Mean": "100.7%", "Base-Mean": "151.2%", "Base-Last": "161.9%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.8%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "157.6%", "Gemma3-Last": "158.3%", "Qwen3.5-Mean": "146.9%", "Qwen3.5-Last": "167.0%", "Dedicated Mean": "100.6%", "Base-Mean": "152.2%", "Base-Last": "162.6%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "100.2%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "98.9%", "Gemma3-Last": "100.1%", "Qwen3.5-Mean": "96.4%", "Qwen3.5-Last": "97.2%", "Dedicated Mean": "99.8%", "Base-Mean": "97.7%", "Base-Last": "98.6%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "PCA-k", "EmbGemma": "99.2%", "Qwen3-Emb": "100.7%", "Gemma3-Mean": "111.0%", "Gemma3-Last": "111.3%", "Qwen3.5-Mean": "106.1%", "Qwen3.5-Last": "109.6%", "Dedicated Mean": "99.9%", "Base-Mean": "108.6%", "Base-Last": "110.5%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Whitening-k", "EmbGemma": "97.9%", "Qwen3-Emb": "96.7%", "Gemma3-Mean": "150.6%", "Gemma3-Last": "155.8%", "Qwen3.5-Mean": "142.5%", "Qwen3.5-Last": "164.5%", "Dedicated Mean": "97.3%", "Base-Mean": "146.6%", "Base-Last": "160.2%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "SpecTemp", "EmbGemma": "100.0%", "Qwen3-Emb": "100.7%", "Gemma3-Mean": "117.7%", "Gemma3-Last": "117.1%", "Qwen3.5-Mean": "110.9%", "Qwen3.5-Last": "114.1%", "Dedicated Mean": "100.4%", "Base-Mean": "114.3%", "Base-Last": "115.6%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "99.8%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "150.6%", "Gemma3-Last": "155.9%", "Qwen3.5-Mean": "142.6%", "Qwen3.5-Last": "164.3%", "Dedicated Mean": "100.3%", "Base-Mean": "146.6%", "Base-Last": "160.1%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.3%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "111.7%", "Gemma3-Last": "112.8%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "110.2%", "Dedicated Mean": "100.0%", "Base-Mean": "109.2%", "Base-Last": "111.5%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "117.0%", "Gemma3-Last": "116.5%", "Qwen3.5-Mean": "111.5%", "Qwen3.5-Last": "114.5%", "Dedicated Mean": "100.5%", "Base-Mean": "114.2%", "Base-Last": "115.5%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.8%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "117.0%", "Gemma3-Last": "116.5%", "Qwen3.5-Mean": "111.4%", "Qwen3.5-Last": "114.4%", "Dedicated Mean": "100.3%", "Base-Mean": "114.2%", "Base-Last": "115.5%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.7%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "150.6%", "Gemma3-Last": "155.9%", "Qwen3.5-Mean": "142.6%", "Qwen3.5-Last": "164.3%", "Dedicated Mean": "100.3%", "Base-Mean": "146.6%", "Base-Last": "160.1%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.5%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "140.4%", "Gemma3-Last": "144.1%", "Qwen3.5-Mean": "133.7%", "Qwen3.5-Last": "148.7%", "Dedicated Mean": "100.4%", "Base-Mean": "137.1%", "Base-Last": "146.4%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.1%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "150.7%", "Gemma3-Last": "156.0%", "Qwen3.5-Mean": "142.7%", "Qwen3.5-Last": "164.5%", "Dedicated Mean": "100.5%", "Base-Mean": "146.7%", "Base-Last": "160.2%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.8%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "149.8%", "Gemma3-Last": "154.6%", "Qwen3.5-Mean": "141.4%", "Qwen3.5-Last": "162.9%", "Dedicated Mean": "100.3%", "Base-Mean": "145.6%", "Base-Last": "158.8%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.7%", "Qwen3-Emb": "100.7%", "Gemma3-Mean": "150.6%", "Gemma3-Last": "155.7%", "Qwen3.5-Mean": "142.5%", "Qwen3.5-Last": "164.4%", "Dedicated Mean": "100.2%", "Base-Mean": "146.5%", "Base-Last": "160.1%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "99.2%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "113.1%", "Gemma3-Last": "112.7%", "Qwen3.5-Mean": "92.7%", "Qwen3.5-Last": "99.7%", "Dedicated Mean": "99.2%", "Base-Mean": "102.9%", "Base-Last": "106.2%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "PCA-k", "EmbGemma": "95.9%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "103.2%", "Gemma3-Last": "105.3%", "Qwen3.5-Mean": "100.5%", "Qwen3.5-Last": "105.5%", "Dedicated Mean": "98.1%", "Base-Mean": "101.8%", "Base-Last": "105.4%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Whitening-k", "EmbGemma": "98.4%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "140.5%", "Gemma3-Last": "147.5%", "Qwen3.5-Mean": "133.5%", "Qwen3.5-Last": "157.3%", "Dedicated Mean": "98.7%", "Base-Mean": "137.0%", "Base-Last": "152.4%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "SpecTemp", "EmbGemma": "98.0%", "Qwen3-Emb": "100.7%", "Gemma3-Mean": "115.4%", "Gemma3-Last": "116.4%", "Qwen3.5-Mean": "109.8%", "Qwen3.5-Last": "115.3%", "Dedicated Mean": "99.4%", "Base-Mean": "112.6%", "Base-Last": "115.9%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "97.4%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "140.6%", "Gemma3-Last": "147.5%", "Qwen3.5-Mean": "133.4%", "Qwen3.5-Last": "157.5%", "Dedicated Mean": "99.1%", "Base-Mean": "137.0%", "Base-Last": "152.5%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "96.1%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "103.9%", "Gemma3-Last": "106.6%", "Qwen3.5-Mean": "101.3%", "Qwen3.5-Last": "106.1%", "Dedicated Mean": "98.3%", "Base-Mean": "102.6%", "Base-Last": "106.4%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "98.0%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "113.6%", "Gemma3-Last": "113.9%", "Qwen3.5-Mean": "110.4%", "Qwen3.5-Last": "115.4%", "Dedicated Mean": "99.4%", "Base-Mean": "112.0%", "Base-Last": "114.6%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "93.1%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "114.3%", "Gemma3-Last": "119.8%", "Qwen3.5-Mean": "113.7%", "Qwen3.5-Last": "126.1%", "Dedicated Mean": "96.3%", "Base-Mean": "114.0%", "Base-Last": "123.0%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "93.6%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "124.2%", "Gemma3-Last": "132.3%", "Qwen3.5-Mean": "121.9%", "Qwen3.5-Last": "141.8%", "Dedicated Mean": "96.6%", "Base-Mean": "123.0%", "Base-Last": "137.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "92.5%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "123.8%", "Gemma3-Last": "131.6%", "Qwen3.5-Mean": "121.7%", "Qwen3.5-Last": "140.9%", "Dedicated Mean": "96.1%", "Base-Mean": "122.8%", "Base-Last": "136.2%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Orth. Proj. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "98.0%", "Qwen3-Emb": "95.6%", "Gemma3-Mean": "126.7%", "Gemma3-Last": "113.6%", "Qwen3.5-Mean": "124.5%", "Qwen3.5-Last": "115.0%", "Dedicated Mean": "96.8%", "Base-Mean": "125.6%", "Base-Last": "114.3%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "97.2%", "Qwen3-Emb": "96.1%", "Gemma3-Mean": "127.1%", "Gemma3-Last": "113.8%", "Qwen3.5-Mean": "123.6%", "Qwen3.5-Last": "114.0%", "Dedicated Mean": "96.6%", "Base-Mean": "125.3%", "Base-Last": "113.9%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.2%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "127.4%", "Gemma3-Last": "114.8%", "Qwen3.5-Mean": "124.3%", "Qwen3.5-Last": "115.8%", "Dedicated Mean": "98.5%", "Base-Mean": "125.9%", "Base-Last": "115.3%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Orth. Proj. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.2%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "109.0%", "Gemma3-Last": "104.8%", "Qwen3.5-Mean": "106.4%", "Qwen3.5-Last": "107.0%", "Dedicated Mean": "99.8%", "Base-Mean": "107.7%", "Base-Last": "105.9%"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "111.5%", "Gemma3-Last": "106.5%", "Qwen3.5-Mean": "109.1%", "Qwen3.5-Last": "108.1%", "Dedicated Mean": "99.7%", "Base-Mean": "110.3%", "Base-Last": "107.3%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "98.2%", "Qwen3-Emb": "96.1%", "Gemma3-Mean": "124.5%", "Gemma3-Last": "112.4%", "Qwen3.5-Mean": "122.7%", "Qwen3.5-Last": "114.1%", "Dedicated Mean": "97.2%", "Base-Mean": "123.6%", "Base-Last": "113.2%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "98.5%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "125.4%", "Gemma3-Last": "113.2%", "Qwen3.5-Mean": "122.5%", "Qwen3.5-Last": "114.1%", "Dedicated Mean": "97.9%", "Base-Mean": "124.0%", "Base-Last": "113.7%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.6%", "Qwen3-Emb": "98.5%", "Gemma3-Mean": "125.4%", "Gemma3-Last": "113.7%", "Qwen3.5-Mean": "122.8%", "Qwen3.5-Last": "114.9%", "Dedicated Mean": "99.0%", "Base-Mean": "124.1%", "Base-Last": "114.3%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.2%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "125.4%", "Gemma3-Last": "113.2%", "Qwen3.5-Mean": "122.5%", "Qwen3.5-Last": "114.2%", "Dedicated Mean": "98.7%", "Base-Mean": "123.9%", "Base-Last": "113.7%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "99.2%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "99.7%", "Gemma3-Last": "101.2%", "Qwen3.5-Mean": "96.2%", "Qwen3.5-Last": "101.8%", "Dedicated Mean": "99.5%", "Base-Mean": "97.9%", "Base-Last": "101.5%"}, {"Dataset": "SICK-R", "k": "128", "Method": "PCA-k", "EmbGemma": "97.9%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "106.4%", "Gemma3-Last": "103.5%", "Qwen3.5-Mean": "103.9%", "Qwen3.5-Last": "105.4%", "Dedicated Mean": "99.3%", "Base-Mean": "105.1%", "Base-Last": "104.5%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Whitening-k", "EmbGemma": "94.3%", "Qwen3-Emb": "92.3%", "Gemma3-Mean": "122.2%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "120.2%", "Qwen3.5-Last": "113.9%", "Dedicated Mean": "93.3%", "Base-Mean": "121.2%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "128", "Method": "SpecTemp", "EmbGemma": "99.4%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "112.0%", "Gemma3-Last": "107.9%", "Qwen3.5-Mean": "110.3%", "Qwen3.5-Last": "109.5%", "Dedicated Mean": "99.5%", "Base-Mean": "111.2%", "Base-Last": "108.7%"}, {"Dataset": "SICK-R", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "122.3%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "120.3%", "Qwen3.5-Last": "113.9%", "Dedicated Mean": "99.6%", "Base-Mean": "121.3%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "97.9%", "Qwen3-Emb": "100.9%", "Gemma3-Mean": "106.5%", "Gemma3-Last": "103.8%", "Qwen3.5-Mean": "104.0%", "Qwen3.5-Last": "105.9%", "Dedicated Mean": "99.4%", "Base-Mean": "105.2%", "Base-Last": "104.8%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.5%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "112.1%", "Gemma3-Last": "107.4%", "Qwen3.5-Mean": "110.4%", "Qwen3.5-Last": "108.5%", "Dedicated Mean": "99.5%", "Base-Mean": "111.2%", "Base-Last": "107.9%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.4%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "112.1%", "Gemma3-Last": "107.4%", "Qwen3.5-Mean": "110.4%", "Qwen3.5-Last": "108.5%", "Dedicated Mean": "99.6%", "Base-Mean": "111.2%", "Base-Last": "107.9%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "122.3%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "120.3%", "Qwen3.5-Last": "113.9%", "Dedicated Mean": "99.6%", "Base-Mean": "121.3%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.2%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "121.2%", "Gemma3-Last": "110.9%", "Qwen3.5-Mean": "119.7%", "Qwen3.5-Last": "112.7%", "Dedicated Mean": "98.6%", "Base-Mean": "120.4%", "Base-Last": "111.8%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.5%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "122.3%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "120.3%", "Qwen3.5-Last": "113.9%", "Dedicated Mean": "99.4%", "Base-Mean": "121.3%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.7%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "122.3%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "120.4%", "Qwen3.5-Last": "114.2%", "Dedicated Mean": "99.8%", "Base-Mean": "121.4%", "Base-Last": "113.6%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "99.5%", "Gemma3-Mean": "122.2%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "120.2%", "Qwen3.5-Last": "113.9%", "Dedicated Mean": "99.5%", "Base-Mean": "121.2%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "96.7%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "96.3%", "Gemma3-Last": "98.7%", "Qwen3.5-Mean": "91.3%", "Qwen3.5-Last": "98.3%", "Dedicated Mean": "97.8%", "Base-Mean": "93.8%", "Base-Last": "98.5%"}, {"Dataset": "SICK-R", "k": "64", "Method": "PCA-k", "EmbGemma": "94.7%", "Qwen3-Emb": "100.7%", "Gemma3-Mean": "102.5%", "Gemma3-Last": "101.1%", "Qwen3.5-Mean": "100.7%", "Qwen3.5-Last": "103.2%", "Dedicated Mean": "97.7%", "Base-Mean": "101.6%", "Base-Last": "102.2%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Whitening-k", "EmbGemma": "97.5%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "118.7%", "Gemma3-Last": "111.0%", "Qwen3.5-Mean": "117.8%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "97.1%", "Base-Mean": "118.2%", "Base-Last": "112.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "SpecTemp", "EmbGemma": "98.5%", "Qwen3-Emb": "98.8%", "Gemma3-Mean": "113.0%", "Gemma3-Last": "108.6%", "Qwen3.5-Mean": "113.1%", "Qwen3.5-Last": "110.6%", "Dedicated Mean": "98.7%", "Base-Mean": "113.0%", "Base-Last": "109.6%"}, {"Dataset": "SICK-R", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "98.5%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "118.7%", "Gemma3-Last": "111.1%", "Qwen3.5-Mean": "117.8%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "98.8%", "Base-Mean": "118.2%", "Base-Last": "112.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "94.7%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "102.6%", "Gemma3-Last": "101.5%", "Qwen3.5-Mean": "100.8%", "Qwen3.5-Last": "103.7%", "Dedicated Mean": "97.8%", "Base-Mean": "101.7%", "Base-Last": "102.6%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "98.6%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "113.1%", "Gemma3-Last": "107.8%", "Qwen3.5-Mean": "113.2%", "Qwen3.5-Last": "108.6%", "Dedicated Mean": "98.7%", "Base-Mean": "113.2%", "Base-Last": "108.2%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "98.5%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "113.1%", "Gemma3-Last": "107.8%", "Qwen3.5-Mean": "113.2%", "Qwen3.5-Last": "108.6%", "Dedicated Mean": "98.8%", "Base-Mean": "113.2%", "Base-Last": "108.2%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "98.2%", "Qwen3-Emb": "101.0%", "Gemma3-Mean": "118.7%", "Gemma3-Last": "111.1%", "Qwen3.5-Mean": "117.8%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "99.6%", "Base-Mean": "118.2%", "Base-Last": "112.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "98.7%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "116.2%", "Gemma3-Last": "108.0%", "Qwen3.5-Mean": "115.8%", "Qwen3.5-Last": "110.4%", "Dedicated Mean": "99.5%", "Base-Mean": "116.0%", "Base-Last": "109.2%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "98.6%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "118.7%", "Gemma3-Last": "111.1%", "Qwen3.5-Mean": "117.8%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "98.7%", "Base-Mean": "118.2%", "Base-Last": "112.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "98.2%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "118.7%", "Gemma3-Last": "111.0%", "Qwen3.5-Mean": "117.9%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "98.9%", "Base-Mean": "118.3%", "Base-Last": "112.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "98.5%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "118.6%", "Gemma3-Last": "111.0%", "Qwen3.5-Mean": "117.8%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "98.7%", "Base-Mean": "118.2%", "Base-Last": "112.0%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "99.8%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "100.0%", "Gemma3-Last": "80.0%", "Qwen3.5-Mean": "98.9%", "Qwen3.5-Last": "89.0%", "Dedicated Mean": "99.5%", "Base-Mean": "99.5%", "Base-Last": "84.5%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "PCA-k", "EmbGemma": "99.0%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "94.3%", "Gemma3-Last": "111.0%", "Qwen3.5-Mean": "96.6%", "Qwen3.5-Last": "94.4%", "Dedicated Mean": "98.1%", "Base-Mean": "95.5%", "Base-Last": "102.7%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Whitening-k", "EmbGemma": "102.3%", "Qwen3-Emb": "96.9%", "Gemma3-Mean": "110.6%", "Gemma3-Last": "190.2%", "Qwen3.5-Mean": "106.2%", "Qwen3.5-Last": "213.3%", "Dedicated Mean": "99.6%", "Base-Mean": "108.4%", "Base-Last": "201.8%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "SpecTemp", "EmbGemma": "99.0%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "94.3%", "Gemma3-Last": "111.0%", "Qwen3.5-Mean": "96.6%", "Qwen3.5-Last": "94.4%", "Dedicated Mean": "98.1%", "Base-Mean": "95.5%", "Base-Last": "102.7%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "99.3%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "109.4%", "Gemma3-Last": "172.3%", "Qwen3.5-Mean": "106.3%", "Qwen3.5-Last": "214.8%", "Dedicated Mean": "98.2%", "Base-Mean": "107.9%", "Base-Last": "193.6%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.2%", "Qwen3-Emb": "97.0%", "Gemma3-Mean": "94.2%", "Gemma3-Last": "117.8%", "Qwen3.5-Mean": "96.8%", "Qwen3.5-Last": "97.3%", "Dedicated Mean": "98.1%", "Base-Mean": "95.5%", "Base-Last": "107.5%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.2%", "Qwen3-Emb": "97.0%", "Gemma3-Mean": "94.2%", "Gemma3-Last": "117.8%", "Qwen3.5-Mean": "96.8%", "Qwen3.5-Last": "97.3%", "Dedicated Mean": "98.1%", "Base-Mean": "95.5%", "Base-Last": "107.5%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.2%", "Qwen3-Emb": "97.0%", "Gemma3-Mean": "94.2%", "Gemma3-Last": "117.8%", "Qwen3.5-Mean": "96.8%", "Qwen3.5-Last": "97.3%", "Dedicated Mean": "98.1%", "Base-Mean": "95.5%", "Base-Last": "107.5%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.3%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "109.4%", "Gemma3-Last": "172.3%", "Qwen3.5-Mean": "106.3%", "Qwen3.5-Last": "214.8%", "Dedicated Mean": "98.2%", "Base-Mean": "107.9%", "Base-Last": "193.6%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.2%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "102.8%", "Gemma3-Last": "160.2%", "Qwen3.5-Mean": "102.8%", "Qwen3.5-Last": "175.5%", "Dedicated Mean": "98.7%", "Base-Mean": "102.8%", "Base-Last": "167.8%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.2%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "110.3%", "Gemma3-Last": "168.6%", "Qwen3.5-Mean": "106.0%", "Qwen3.5-Last": "214.6%", "Dedicated Mean": "98.2%", "Base-Mean": "108.2%", "Base-Last": "191.6%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.3%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "109.4%", "Gemma3-Last": "172.3%", "Qwen3.5-Mean": "106.3%", "Qwen3.5-Last": "214.8%", "Dedicated Mean": "98.2%", "Base-Mean": "107.9%", "Base-Last": "193.6%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.0%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "109.4%", "Gemma3-Last": "161.4%", "Qwen3.5-Mean": "106.3%", "Qwen3.5-Last": "212.0%", "Dedicated Mean": "98.1%", "Base-Mean": "107.8%", "Base-Last": "186.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "100.0%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "99.9%", "Gemma3-Last": "55.9%", "Qwen3.5-Mean": "98.8%", "Qwen3.5-Last": "94.3%", "Dedicated Mean": "100.2%", "Base-Mean": "99.3%", "Base-Last": "75.1%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "PCA-k", "EmbGemma": "99.2%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "95.3%", "Gemma3-Last": "111.7%", "Qwen3.5-Mean": "97.0%", "Qwen3.5-Last": "95.9%", "Dedicated Mean": "98.3%", "Base-Mean": "96.2%", "Base-Last": "103.8%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Whitening-k", "EmbGemma": "102.1%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "107.8%", "Gemma3-Last": "154.8%", "Qwen3.5-Mean": "105.5%", "Qwen3.5-Last": "197.6%", "Dedicated Mean": "99.7%", "Base-Mean": "106.7%", "Base-Last": "176.2%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "SpecTemp", "EmbGemma": "99.6%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "96.2%", "Gemma3-Last": "123.5%", "Qwen3.5-Mean": "97.6%", "Qwen3.5-Last": "105.8%", "Dedicated Mean": "98.5%", "Base-Mean": "96.9%", "Base-Last": "114.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "99.6%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "108.1%", "Gemma3-Last": "167.9%", "Qwen3.5-Mean": "105.6%", "Qwen3.5-Last": "206.9%", "Dedicated Mean": "98.5%", "Base-Mean": "106.9%", "Base-Last": "187.4%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "99.3%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "95.2%", "Gemma3-Last": "119.2%", "Qwen3.5-Mean": "97.2%", "Qwen3.5-Last": "100.2%", "Dedicated Mean": "98.3%", "Base-Mean": "96.2%", "Base-Last": "109.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.8%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "96.6%", "Gemma3-Last": "131.0%", "Qwen3.5-Mean": "97.6%", "Qwen3.5-Last": "110.3%", "Dedicated Mean": "98.5%", "Base-Mean": "97.1%", "Base-Last": "120.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.6%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "96.5%", "Gemma3-Last": "130.1%", "Qwen3.5-Mean": "97.6%", "Qwen3.5-Last": "110.0%", "Dedicated Mean": "98.5%", "Base-Mean": "97.1%", "Base-Last": "120.0%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.4%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "108.1%", "Gemma3-Last": "167.9%", "Qwen3.5-Mean": "105.6%", "Qwen3.5-Last": "206.9%", "Dedicated Mean": "98.4%", "Base-Mean": "106.9%", "Base-Last": "187.4%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.3%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "103.8%", "Gemma3-Last": "159.8%", "Qwen3.5-Mean": "103.7%", "Qwen3.5-Last": "182.4%", "Dedicated Mean": "98.7%", "Base-Mean": "103.8%", "Base-Last": "171.1%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.8%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "108.2%", "Gemma3-Last": "165.0%", "Qwen3.5-Mean": "105.1%", "Qwen3.5-Last": "198.4%", "Dedicated Mean": "98.5%", "Base-Mean": "106.7%", "Base-Last": "181.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.6%", "Qwen3-Emb": "97.3%", "Gemma3-Mean": "108.3%", "Gemma3-Last": "165.7%", "Qwen3.5-Mean": "106.1%", "Qwen3.5-Last": "209.7%", "Dedicated Mean": "98.5%", "Base-Mean": "107.2%", "Base-Last": "187.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.5%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "107.8%", "Gemma3-Last": "162.1%", "Qwen3.5-Mean": "105.8%", "Qwen3.5-Last": "205.3%", "Dedicated Mean": "98.4%", "Base-Mean": "106.8%", "Base-Last": "183.7%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "100.5%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "98.6%", "Gemma3-Last": "148.0%", "Qwen3.5-Mean": "95.7%", "Qwen3.5-Last": "105.9%", "Dedicated Mean": "99.4%", "Base-Mean": "97.1%", "Base-Last": "127.0%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "98.8%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "90.2%", "Gemma3-Last": "106.4%", "Qwen3.5-Mean": "94.7%", "Qwen3.5-Last": "92.4%", "Dedicated Mean": "98.0%", "Base-Mean": "92.5%", "Base-Last": "99.4%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "101.3%", "Qwen3-Emb": "96.8%", "Gemma3-Mean": "102.4%", "Gemma3-Last": "139.9%", "Qwen3.5-Mean": "104.4%", "Qwen3.5-Last": "203.2%", "Dedicated Mean": "99.0%", "Base-Mean": "103.4%", "Base-Last": "171.6%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "99.9%", "Qwen3-Emb": "96.9%", "Gemma3-Mean": "94.1%", "Gemma3-Last": "128.5%", "Qwen3.5-Mean": "97.0%", "Qwen3.5-Last": "129.2%", "Dedicated Mean": "98.4%", "Base-Mean": "95.5%", "Base-Last": "128.8%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "99.8%", "Qwen3-Emb": "97.1%", "Gemma3-Mean": "102.6%", "Gemma3-Last": "141.5%", "Qwen3.5-Mean": "104.3%", "Qwen3.5-Last": "205.3%", "Dedicated Mean": "98.4%", "Base-Mean": "103.5%", "Base-Last": "173.4%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. 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ZCA (Σ, γ=1, ε=1e-6)", "EmbGemma": "66.86", "Qwen3-Emb": "65.20", "Gemma3-Mean": "51.89", "Gemma3-Last": "50.01", "Qwen3.5-Mean": "52.26", "Qwen3.5-Last": "48.14", "Dedicated Mean": "66.03", "Base-Mean": "52.08", "Base-Last": "49.08"}, {"Dataset": "SICK-R", "k": "d", "Method": "Centered + ε* (Σ, γ=1, ε*)", "EmbGemma": "78.63", "Qwen3-Emb": "77.41", "Gemma3-Mean": "55.51", "Gemma3-Last": "53.89", "Qwen3.5-Mean": "56.90", "Qwen3.5-Last": "52.11", "Dedicated Mean": "78.02", "Base-Mean": "56.21", "Base-Last": "53.00"}, {"Dataset": "SICK-R", "k": "d", "Method": "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "EmbGemma": "81.66", "Qwen3-Emb": "83.10", "Gemma3-Mean": "58.27", "Gemma3-Last": "53.76", "Qwen3.5-Mean": "58.01", "Qwen3.5-Last": "51.40", "Dedicated Mean": "82.38", "Base-Mean": "58.14", "Base-Last": "52.58"}, {"Dataset": "SICK-R", "k": "d", "Method": "w/o Orth. Proj. 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ZCA (Σ, γ=1, ε=1e-6)", "EmbGemma": "45.07", "Qwen3-Emb": "25.91", "Gemma3-Mean": "46.79", "Gemma3-Last": "10.05", "Qwen3.5-Mean": "41.32", "Qwen3.5-Last": "6.99", "Dedicated Mean": "35.49", "Base-Mean": "44.06", "Base-Last": "8.52"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Centered + ε* (Σ, γ=1, ε*)", "EmbGemma": "70.17", "Qwen3-Emb": "71.10", "Gemma3-Mean": "64.45", "Gemma3-Last": "13.86", "Qwen3.5-Mean": "65.68", "Qwen3.5-Last": "18.88", "Dedicated Mean": "70.64", "Base-Mean": "65.07", "Base-Last": "16.37"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "EmbGemma": "67.29", "Qwen3-Emb": "70.00", "Gemma3-Mean": "65.04", "Gemma3-Last": "13.04", "Qwen3.5-Mean": "65.75", "Qwen3.5-Last": "16.17", "Dedicated Mean": "68.64", "Base-Mean": "65.39", "Base-Last": "14.60"}, {"Dataset": "STS22.v2", "k": "d", "Method": "w/o Orth. Proj. (Σ, γ_crowd, ε*)", "EmbGemma": "67.18", "Qwen3-Emb": "69.92", "Gemma3-Mean": "64.45", "Gemma3-Last": "14.18", "Qwen3.5-Mean": "65.68", "Qwen3.5-Last": "18.88", "Dedicated Mean": "68.55", "Base-Mean": "65.07", "Base-Last": "16.53"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Orth. Soft-ZCA (Σ_⊥, γ=1, 1e-4)", "EmbGemma": "62.29", "Qwen3-Emb": "60.66", "Gemma3-Mean": "65.01", "Gemma3-Last": "11.16", "Qwen3.5-Mean": "65.72", "Qwen3.5-Last": "16.26", "Dedicated Mean": "61.48", "Base-Mean": "65.36", "Base-Last": "13.71"}, {"Dataset": "STS22.v2", "k": "d", "Method": "w/o Crowd. Exp. (Σ_⊥, γ=1, ε*)", "EmbGemma": "70.22", "Qwen3-Emb": "71.12", "Gemma3-Mean": "64.38", "Gemma3-Last": "13.72", "Qwen3.5-Mean": "65.63", "Qwen3.5-Last": "18.79", "Dedicated Mean": "70.67", "Base-Mean": "65.00", "Base-Last": "16.25"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "EmbGemma": "69.60", "Qwen3-Emb": "70.50", "Gemma3-Mean": "61.52", "Gemma3-Last": "13.42", "Qwen3.5-Mean": "62.48", "Qwen3.5-Last": "19.87", "Dedicated Mean": "70.05", "Base-Mean": "62.00", "Base-Last": "16.65"}, {"Dataset": "STS22.v2", "k": "d", "Method": "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)", "EmbGemma": "67.44", "Qwen3-Emb": "69.97", "Gemma3-Mean": "65.01", "Gemma3-Last": "12.95", "Qwen3.5-Mean": "65.72", "Qwen3.5-Last": "16.26", "Dedicated Mean": "68.71", "Base-Mean": "65.36", "Base-Last": "14.60"}], "task_comp::Similarity (STS)::Pearson (r × 100)::Score (Retention %)": [{"Dataset": "STSBenchmark", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "84.44 (100.0%)", "Qwen3-Emb": "84.23 (100.0%)", "Gemma3-Mean": "28.98 (84.2%)", "Gemma3-Last": "24.92 (89.5%)", "Qwen3.5-Mean": "42.67 (98.3%)", "Qwen3.5-Last": "24.01 (93.0%)", "Dedicated Mean": "84.34 (100.0%)", "Base-Mean": "35.83 (91.2%)", "Base-Last": "24.47 (91.3%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "PCA-k", "EmbGemma": "84.55 (100.1%)", "Qwen3-Emb": "84.92 (100.8%)", "Gemma3-Mean": "47.75 (138.7%)", "Gemma3-Last": "43.86 (157.6%)", "Qwen3.5-Mean": "48.18 (111.0%)", "Qwen3.5-Last": "36.61 (141.8%)", "Dedicated Mean": "84.73 (100.5%)", "Base-Mean": "47.97 (124.8%)", "Base-Last": "40.23 (149.7%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Whitening-k", "EmbGemma": "82.01 (97.1%)", "Qwen3-Emb": "79.63 (94.5%)", "Gemma3-Mean": "62.12 (180.4%)", "Gemma3-Last": "64.52 (231.8%)", "Qwen3.5-Mean": "61.51 (141.7%)", "Qwen3.5-Last": "59.92 (232.1%)", "Dedicated Mean": "80.82 (95.8%)", "Base-Mean": "61.81 (161.1%)", "Base-Last": "62.22 (232.0%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "SpecTemp", "EmbGemma": "84.95 (100.6%)", "Qwen3-Emb": "85.06 (101.0%)", "Gemma3-Mean": "48.80 (141.7%)", "Gemma3-Last": "45.15 (162.2%)", "Qwen3.5-Mean": "48.95 (112.8%)", "Qwen3.5-Last": "37.43 (145.0%)", "Dedicated Mean": "85.00 (100.8%)", "Base-Mean": "48.88 (127.3%)", "Base-Last": "41.29 (153.6%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "85.16 (100.8%)", "Qwen3-Emb": "85.38 (101.3%)", "Gemma3-Mean": "62.21 (180.7%)", "Gemma3-Last": "64.86 (233.0%)", "Qwen3.5-Mean": "61.75 (142.3%)", "Qwen3.5-Last": "60.32 (233.7%)", "Dedicated Mean": "85.27 (101.1%)", "Base-Mean": "61.98 (161.5%)", "Base-Last": "62.59 (233.3%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "84.60 (100.2%)", "Qwen3-Emb": "84.98 (100.9%)", "Gemma3-Mean": "48.09 (139.7%)", "Gemma3-Last": "45.64 (164.0%)", "Qwen3.5-Mean": "48.39 (111.5%)", "Qwen3.5-Last": "37.35 (144.7%)", "Dedicated Mean": "84.79 (100.5%)", "Base-Mean": "48.24 (125.6%)", "Base-Last": "41.50 (154.3%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "84.96 (100.6%)", "Qwen3-Emb": "85.12 (101.0%)", "Gemma3-Mean": "48.91 (142.0%)", "Gemma3-Last": "46.43 (166.8%)", "Qwen3.5-Mean": "49.15 (113.3%)", "Qwen3.5-Last": "38.11 (147.6%)", "Dedicated Mean": "85.04 (100.8%)", "Base-Mean": "49.03 (127.7%)", "Base-Last": "42.27 (157.2%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "84.79 (100.4%)", "Qwen3-Emb": "85.08 (101.0%)", "Gemma3-Mean": "48.90 (142.0%)", "Gemma3-Last": "46.42 (166.8%)", "Qwen3.5-Mean": "49.14 (113.2%)", "Qwen3.5-Last": "38.10 (147.6%)", "Dedicated Mean": "84.94 (100.7%)", "Base-Mean": "49.02 (127.6%)", "Base-Last": "42.26 (157.2%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "85.16 (100.8%)", "Qwen3-Emb": "85.38 (101.3%)", "Gemma3-Mean": "62.21 (180.7%)", "Gemma3-Last": "64.86 (233.0%)", "Qwen3.5-Mean": "61.75 (142.3%)", "Qwen3.5-Last": "60.32 (233.7%)", "Dedicated Mean": "85.27 (101.1%)", "Base-Mean": "61.98 (161.5%)", "Base-Last": "62.59 (233.3%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "86.36 (102.2%)", "Qwen3-Emb": "85.48 (101.5%)", "Gemma3-Mean": "60.13 (174.6%)", "Gemma3-Last": "62.32 (223.9%)", "Qwen3.5-Mean": "60.39 (139.2%)", "Qwen3.5-Last": "56.56 (219.1%)", "Dedicated Mean": "85.92 (101.8%)", "Base-Mean": "60.26 (156.9%)", "Base-Last": "59.44 (221.5%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "85.60 (101.3%)", "Qwen3-Emb": "85.49 (101.5%)", "Gemma3-Mean": "62.13 (180.4%)", "Gemma3-Last": "64.56 (231.9%)", "Qwen3.5-Mean": "61.50 (141.7%)", "Qwen3.5-Last": "59.92 (232.1%)", "Dedicated Mean": "85.54 (101.4%)", "Base-Mean": "61.81 (161.1%)", "Base-Last": "62.24 (232.0%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "85.14 (100.8%)", "Qwen3-Emb": "85.37 (101.3%)", "Gemma3-Mean": "62.34 (181.1%)", "Gemma3-Last": "65.23 (234.4%)", "Qwen3.5-Mean": "62.02 (142.9%)", "Qwen3.5-Last": "60.58 (234.6%)", "Dedicated Mean": "85.25 (101.1%)", "Base-Mean": "62.18 (162.0%)", "Base-Last": "62.91 (234.5%)"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "85.12 (100.8%)", "Qwen3-Emb": "85.32 (101.3%)", "Gemma3-Mean": "62.20 (180.7%)", "Gemma3-Last": "64.83 (232.9%)", "Qwen3.5-Mean": "61.76 (142.3%)", "Qwen3.5-Last": "60.34 (233.7%)", "Dedicated Mean": "85.22 (101.0%)", "Base-Mean": "61.98 (161.5%)", "Base-Last": "62.59 (233.3%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "84.01 (99.5%)", "Qwen3-Emb": "83.25 (98.8%)", "Gemma3-Mean": "33.88 (98.4%)", "Gemma3-Last": "19.99 (71.8%)", "Qwen3.5-Mean": "41.14 (94.8%)", "Qwen3.5-Last": "23.43 (90.7%)", "Dedicated Mean": "83.63 (99.1%)", "Base-Mean": "37.51 (96.6%)", "Base-Last": "21.71 (81.3%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "PCA-k", "EmbGemma": "82.78 (98.0%)", "Qwen3-Emb": "84.57 (100.4%)", "Gemma3-Mean": "46.21 (134.2%)", "Gemma3-Last": "42.15 (151.4%)", "Qwen3.5-Mean": "47.11 (108.5%)", "Qwen3.5-Last": "35.38 (137.0%)", "Dedicated Mean": "83.67 (99.2%)", "Base-Mean": "46.66 (121.4%)", "Base-Last": "38.77 (144.2%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Whitening-k", "EmbGemma": "83.56 (98.9%)", "Qwen3-Emb": "82.85 (98.3%)", "Gemma3-Mean": "61.54 (178.7%)", "Gemma3-Last": "65.70 (236.1%)", "Qwen3.5-Mean": "61.67 (142.1%)", "Qwen3.5-Last": "60.63 (234.8%)", "Dedicated Mean": "83.20 (98.6%)", "Base-Mean": "61.61 (160.4%)", "Base-Last": "63.17 (235.4%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "SpecTemp", "EmbGemma": "84.27 (99.8%)", "Qwen3-Emb": "85.21 (101.1%)", "Gemma3-Mean": "49.22 (142.9%)", "Gemma3-Last": "46.46 (166.9%)", "Qwen3.5-Mean": "49.53 (114.1%)", "Qwen3.5-Last": "38.35 (148.6%)", "Dedicated Mean": "84.74 (100.5%)", "Base-Mean": "49.38 (128.5%)", "Base-Last": "42.41 (157.7%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "83.65 (99.0%)", "Qwen3-Emb": "85.18 (101.1%)", "Gemma3-Mean": "61.56 (178.8%)", "Gemma3-Last": "65.77 (236.3%)", "Qwen3.5-Mean": "61.69 (142.2%)", "Qwen3.5-Last": "60.61 (234.8%)", "Dedicated Mean": "84.42 (100.1%)", "Base-Mean": "61.62 (160.5%)", "Base-Last": "63.19 (235.5%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "82.82 (98.0%)", "Qwen3-Emb": "84.65 (100.5%)", "Gemma3-Mean": "46.57 (135.2%)", "Gemma3-Last": "44.00 (158.1%)", "Qwen3.5-Mean": "47.32 (109.0%)", "Qwen3.5-Last": "36.14 (140.0%)", "Dedicated Mean": "83.73 (99.3%)", "Base-Mean": "46.95 (122.1%)", "Base-Last": "40.07 (149.0%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "84.17 (99.7%)", "Qwen3-Emb": "85.27 (101.2%)", "Gemma3-Mean": "48.92 (142.1%)", "Gemma3-Last": "46.66 (167.7%)", "Qwen3.5-Mean": "49.71 (114.5%)", "Qwen3.5-Last": "38.90 (150.7%)", "Dedicated Mean": "84.72 (100.4%)", "Base-Mean": "49.31 (128.3%)", "Base-Last": "42.78 (159.2%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "83.65 (99.0%)", "Qwen3-Emb": "85.11 (101.0%)", "Gemma3-Mean": "48.92 (142.1%)", "Gemma3-Last": "46.66 (167.6%)", "Qwen3.5-Mean": "49.70 (114.5%)", "Qwen3.5-Last": "38.89 (150.6%)", "Dedicated Mean": "84.38 (100.0%)", "Base-Mean": "49.31 (128.3%)", "Base-Last": "42.77 (159.1%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "83.49 (98.8%)", "Qwen3-Emb": "85.18 (101.1%)", "Gemma3-Mean": "61.56 (178.8%)", "Gemma3-Last": "65.77 (236.3%)", "Qwen3.5-Mean": "61.69 (142.2%)", "Qwen3.5-Last": "60.61 (234.8%)", "Dedicated Mean": "84.34 (100.0%)", "Base-Mean": "61.62 (160.5%)", "Base-Last": "63.19 (235.5%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "85.19 (100.9%)", "Qwen3-Emb": "85.55 (101.5%)", "Gemma3-Mean": "58.44 (169.7%)", "Gemma3-Last": "61.40 (220.6%)", "Qwen3.5-Mean": "59.36 (136.8%)", "Qwen3.5-Last": "55.47 (214.8%)", "Dedicated Mean": "85.37 (101.2%)", "Base-Mean": "58.90 (153.2%)", "Base-Last": "58.44 (217.7%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "84.17 (99.7%)", "Qwen3-Emb": "85.34 (101.3%)", "Gemma3-Mean": "61.57 (178.8%)", "Gemma3-Last": "65.78 (236.3%)", "Qwen3.5-Mean": "61.70 (142.2%)", "Qwen3.5-Last": "60.61 (234.8%)", "Dedicated Mean": "84.75 (100.5%)", "Base-Mean": "61.64 (160.5%)", "Base-Last": "63.20 (235.5%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "83.60 (99.0%)", "Qwen3-Emb": "85.13 (101.0%)", "Gemma3-Mean": "61.41 (178.4%)", "Gemma3-Last": "65.50 (235.3%)", "Qwen3.5-Mean": "61.60 (141.9%)", "Qwen3.5-Last": "60.41 (234.0%)", "Dedicated Mean": "84.36 (100.0%)", "Base-Mean": "61.50 (160.2%)", "Base-Last": "62.95 (234.6%)"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "83.75 (99.2%)", "Qwen3-Emb": "85.10 (101.0%)", "Gemma3-Mean": "61.53 (178.7%)", "Gemma3-Last": "65.69 (236.0%)", "Qwen3.5-Mean": "61.66 (142.1%)", "Qwen3.5-Last": "60.63 (234.8%)", "Dedicated Mean": "84.42 (100.1%)", "Base-Mean": "61.59 (160.4%)", "Base-Last": "63.16 (235.4%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "82.63 (97.8%)", "Qwen3-Emb": "82.69 (98.1%)", "Gemma3-Mean": "45.09 (131.0%)", "Gemma3-Last": "42.61 (153.1%)", "Qwen3.5-Mean": "38.57 (88.9%)", "Qwen3.5-Last": "28.89 (111.9%)", "Dedicated Mean": "82.66 (98.0%)", "Base-Mean": "41.83 (109.9%)", "Base-Last": "35.75 (132.5%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "PCA-k", "EmbGemma": "78.94 (93.5%)", "Qwen3-Emb": "83.15 (98.7%)", "Gemma3-Mean": "43.09 (125.2%)", "Gemma3-Last": "38.80 (139.4%)", "Qwen3.5-Mean": "44.72 (103.0%)", "Qwen3.5-Last": "33.17 (128.5%)", "Dedicated Mean": "81.05 (96.1%)", "Base-Mean": "43.91 (114.1%)", "Base-Last": "35.98 (133.9%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Whitening-k", "EmbGemma": "83.41 (98.8%)", "Qwen3-Emb": "84.16 (99.9%)", "Gemma3-Mean": "58.71 (170.5%)", "Gemma3-Last": "63.72 (228.9%)", "Qwen3.5-Mean": "59.45 (137.0%)", "Qwen3.5-Last": "59.24 (229.4%)", "Dedicated Mean": "83.78 (99.3%)", "Base-Mean": "59.08 (153.7%)", "Base-Last": "61.48 (229.2%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "SpecTemp", "EmbGemma": "82.12 (97.2%)", "Qwen3-Emb": "84.86 (100.7%)", "Gemma3-Mean": "48.75 (141.6%)", "Gemma3-Last": "47.49 (170.6%)", "Qwen3.5-Mean": "49.75 (114.6%)", "Qwen3.5-Last": "39.77 (154.0%)", "Dedicated Mean": "83.49 (99.0%)", "Base-Mean": "49.25 (128.1%)", "Base-Last": "43.63 (162.3%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "81.03 (95.9%)", "Qwen3-Emb": "84.66 (100.5%)", "Gemma3-Mean": "58.71 (170.5%)", "Gemma3-Last": "63.74 (229.0%)", "Qwen3.5-Mean": "59.41 (136.9%)", "Qwen3.5-Last": "59.26 (229.5%)", "Dedicated Mean": "82.84 (98.2%)", "Base-Mean": "59.06 (153.7%)", "Base-Last": "61.50 (229.2%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "78.93 (93.5%)", "Qwen3-Emb": "83.24 (98.8%)", "Gemma3-Mean": "43.48 (126.3%)", "Gemma3-Last": "40.68 (146.2%)", "Qwen3.5-Mean": "44.95 (103.6%)", "Qwen3.5-Last": "33.94 (131.5%)", "Dedicated Mean": "81.09 (96.1%)", "Base-Mean": "44.22 (114.9%)", "Base-Last": "37.31 (138.8%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "81.86 (96.9%)", "Qwen3-Emb": "84.90 (100.8%)", "Gemma3-Mean": "47.97 (139.3%)", "Gemma3-Last": "46.17 (165.9%)", "Qwen3.5-Mean": "49.91 (115.0%)", "Qwen3.5-Last": "40.03 (155.0%)", "Dedicated Mean": "83.38 (98.8%)", "Base-Mean": "48.94 (127.2%)", "Base-Last": "43.10 (160.5%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "81.03 (95.9%)", "Qwen3-Emb": "84.66 (100.5%)", "Gemma3-Mean": "47.97 (139.3%)", "Gemma3-Last": "46.17 (165.9%)", "Qwen3.5-Mean": "49.91 (115.0%)", "Qwen3.5-Last": "40.03 (155.0%)", "Dedicated Mean": "82.84 (98.2%)", "Base-Mean": "48.94 (127.2%)", "Base-Last": "43.10 (160.4%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "79.78 (94.5%)", "Qwen3-Emb": "84.00 (99.7%)", "Gemma3-Mean": "58.71 (170.5%)", "Gemma3-Last": "63.74 (229.0%)", "Qwen3.5-Mean": "59.41 (136.9%)", "Qwen3.5-Last": "59.26 (229.5%)", "Dedicated Mean": "81.89 (97.1%)", "Base-Mean": "59.06 (153.7%)", "Base-Last": "61.50 (229.2%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "82.37 (97.5%)", "Qwen3-Emb": "84.97 (100.8%)", "Gemma3-Mean": "54.66 (158.7%)", "Gemma3-Last": "57.90 (208.0%)", "Qwen3.5-Mean": "56.39 (129.9%)", "Qwen3.5-Last": "52.61 (203.8%)", "Dedicated Mean": "83.67 (99.2%)", "Base-Mean": "55.52 (144.3%)", "Base-Last": "55.25 (205.9%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "81.86 (96.9%)", "Qwen3-Emb": "84.90 (100.8%)", "Gemma3-Mean": "58.71 (170.5%)", "Gemma3-Last": "63.74 (229.0%)", "Qwen3.5-Mean": "59.41 (136.9%)", "Qwen3.5-Last": "59.26 (229.5%)", "Dedicated Mean": "83.38 (98.8%)", "Base-Mean": "59.06 (153.7%)", "Base-Last": "61.50 (229.3%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "80.85 (95.7%)", "Qwen3-Emb": "84.53 (100.3%)", "Gemma3-Mean": "58.51 (169.9%)", "Gemma3-Last": "63.29 (227.4%)", "Qwen3.5-Mean": "59.29 (136.6%)", "Qwen3.5-Last": "58.81 (227.8%)", "Dedicated Mean": "82.69 (98.0%)", "Base-Mean": "58.90 (153.3%)", "Base-Last": "61.05 (227.6%)"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "81.30 (96.2%)", "Qwen3-Emb": "84.60 (100.4%)", "Gemma3-Mean": "58.71 (170.5%)", "Gemma3-Last": "63.72 (228.9%)", "Qwen3.5-Mean": "59.45 (137.0%)", "Qwen3.5-Last": "59.23 (229.4%)", "Dedicated Mean": "82.95 (98.3%)", "Base-Mean": "59.08 (153.7%)", "Base-Last": "61.47 (229.2%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "79.47 (94.1%)", "Qwen3-Emb": "80.72 (95.8%)", "Gemma3-Mean": "44.60 (129.5%)", "Gemma3-Last": "39.49 (141.9%)", "Qwen3.5-Mean": "33.67 (77.6%)", "Qwen3.5-Last": "24.15 (93.5%)", "Dedicated Mean": "80.09 (95.0%)", "Base-Mean": "39.14 (103.6%)", "Base-Last": "31.82 (117.7%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "PCA-k", "EmbGemma": "73.06 (86.5%)", "Qwen3-Emb": "79.46 (94.3%)", "Gemma3-Mean": "38.94 (113.1%)", "Gemma3-Last": "34.06 (122.4%)", "Qwen3.5-Mean": "41.41 (95.4%)", "Qwen3.5-Last": "29.89 (115.8%)", "Dedicated Mean": "76.26 (90.4%)", "Base-Mean": "40.17 (104.3%)", "Base-Last": "31.98 (119.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Whitening-k", "EmbGemma": "80.15 (94.9%)", "Qwen3-Emb": "82.86 (98.3%)", "Gemma3-Mean": "53.26 (154.7%)", "Gemma3-Last": "58.29 (209.4%)", "Qwen3.5-Mean": "55.53 (128.0%)", "Qwen3.5-Last": "54.42 (210.8%)", "Dedicated Mean": "81.50 (96.6%)", "Base-Mean": "54.39 (141.3%)", "Base-Last": "56.36 (210.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "SpecTemp", "EmbGemma": "78.38 (92.8%)", "Qwen3-Emb": "82.85 (98.3%)", "Gemma3-Mean": "47.94 (139.2%)", "Gemma3-Last": "48.30 (173.5%)", "Qwen3.5-Mean": "50.27 (115.8%)", "Qwen3.5-Last": "42.16 (163.3%)", "Dedicated Mean": "80.61 (95.6%)", "Base-Mean": "49.11 (127.5%)", "Base-Last": "45.23 (168.4%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "76.96 (91.1%)", "Qwen3-Emb": "82.71 (98.2%)", "Gemma3-Mean": "53.33 (154.9%)", "Gemma3-Last": "58.41 (209.9%)", "Qwen3.5-Mean": "55.53 (128.0%)", "Qwen3.5-Last": "54.36 (210.6%)", "Dedicated Mean": "79.83 (94.6%)", "Base-Mean": "54.43 (141.4%)", "Base-Last": "56.38 (210.2%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "72.98 (86.4%)", "Qwen3-Emb": "79.63 (94.5%)", "Gemma3-Mean": "39.37 (114.3%)", "Gemma3-Last": "35.89 (128.9%)", "Qwen3.5-Mean": "41.62 (95.9%)", "Qwen3.5-Last": "30.64 (118.7%)", "Dedicated Mean": "76.31 (90.5%)", "Base-Mean": "40.49 (105.1%)", "Base-Last": "33.27 (123.8%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "77.94 (92.3%)", "Qwen3-Emb": "82.93 (98.4%)", "Gemma3-Mean": "46.73 (135.7%)", "Gemma3-Last": "45.24 (162.5%)", "Qwen3.5-Mean": "50.32 (116.0%)", "Qwen3.5-Last": "41.76 (161.7%)", "Dedicated Mean": "80.44 (95.4%)", "Base-Mean": "48.52 (125.8%)", "Base-Last": "43.50 (162.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "76.96 (91.1%)", "Qwen3-Emb": "82.71 (98.2%)", "Gemma3-Mean": "46.73 (135.7%)", "Gemma3-Last": "45.24 (162.5%)", "Qwen3.5-Mean": "50.32 (116.0%)", "Qwen3.5-Last": "41.76 (161.7%)", "Dedicated Mean": "79.83 (94.6%)", "Base-Mean": "48.52 (125.8%)", "Base-Last": "43.50 (162.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "73.95 (87.6%)", "Qwen3-Emb": "80.63 (95.7%)", "Gemma3-Mean": "53.33 (154.9%)", "Gemma3-Last": "58.41 (209.9%)", "Qwen3.5-Mean": "55.53 (128.0%)", "Qwen3.5-Last": "54.36 (210.6%)", "Dedicated Mean": "77.29 (91.6%)", "Base-Mean": "54.43 (141.4%)", "Base-Last": "56.38 (210.2%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "77.29 (91.5%)", "Qwen3-Emb": "82.37 (97.8%)", "Gemma3-Mean": "49.18 (142.8%)", "Gemma3-Last": "51.85 (186.3%)", "Qwen3.5-Mean": "52.18 (120.2%)", "Qwen3.5-Last": "47.51 (184.0%)", "Dedicated Mean": "79.83 (94.6%)", "Base-Mean": "50.68 (131.5%)", "Base-Last": "49.68 (185.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "77.94 (92.3%)", "Qwen3-Emb": "82.93 (98.4%)", "Gemma3-Mean": "53.33 (154.9%)", "Gemma3-Last": "58.41 (209.9%)", "Qwen3.5-Mean": "55.53 (128.0%)", "Qwen3.5-Last": "54.36 (210.6%)", "Dedicated Mean": "80.44 (95.4%)", "Base-Mean": "54.43 (141.4%)", "Base-Last": "56.38 (210.2%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "76.60 (90.7%)", "Qwen3-Emb": "82.49 (97.9%)", "Gemma3-Mean": "53.22 (154.6%)", "Gemma3-Last": "58.08 (208.7%)", "Qwen3.5-Mean": "55.44 (127.8%)", "Qwen3.5-Last": "54.12 (209.6%)", "Dedicated Mean": "79.54 (94.3%)", "Base-Mean": "54.33 (141.2%)", "Base-Last": "56.10 (209.1%)"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "77.43 (91.7%)", "Qwen3-Emb": "82.63 (98.1%)", "Gemma3-Mean": "53.26 (154.7%)", "Gemma3-Last": "58.29 (209.4%)", "Qwen3.5-Mean": "55.53 (128.0%)", "Qwen3.5-Last": "54.42 (210.8%)", "Dedicated Mean": "80.03 (94.9%)", "Base-Mean": "54.39 (141.3%)", "Base-Last": "56.36 (210.1%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "83.51 (100.0%)", "Qwen3-Emb": "87.16 (100.4%)", "Gemma3-Mean": "49.04 (98.1%)", "Gemma3-Last": "39.00 (82.6%)", "Qwen3.5-Mean": "52.95 (99.7%)", "Qwen3.5-Last": "50.59 (99.5%)", "Dedicated Mean": "85.34 (100.2%)", "Base-Mean": "51.00 (98.9%)", "Base-Last": "44.80 (91.0%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "PCA-k", "EmbGemma": "83.77 (100.3%)", "Qwen3-Emb": "86.73 (99.9%)", "Gemma3-Mean": "55.84 (111.7%)", "Gemma3-Last": "55.93 (118.5%)", "Qwen3.5-Mean": "56.55 (106.5%)", "Qwen3.5-Last": "55.07 (108.3%)", "Dedicated Mean": "85.25 (100.1%)", "Base-Mean": "56.20 (109.1%)", "Base-Last": "55.50 (113.4%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Whitening-k", "EmbGemma": "69.86 (83.6%)", "Qwen3-Emb": "69.48 (80.0%)", "Gemma3-Mean": "56.88 (113.8%)", "Gemma3-Last": "53.71 (113.8%)", "Qwen3.5-Mean": "56.73 (106.9%)", "Qwen3.5-Last": "51.29 (100.9%)", "Dedicated Mean": "69.67 (81.8%)", "Base-Mean": "56.80 (110.3%)", "Base-Last": "52.50 (107.3%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "SpecTemp", "EmbGemma": "83.84 (100.4%)", "Qwen3-Emb": "86.67 (99.8%)", "Gemma3-Mean": "56.18 (112.4%)", "Gemma3-Last": "56.14 (118.9%)", "Qwen3.5-Mean": "56.97 (107.3%)", "Qwen3.5-Last": "55.20 (108.5%)", "Dedicated Mean": "85.25 (100.1%)", "Base-Mean": "56.58 (109.9%)", "Base-Last": "55.67 (113.7%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "83.46 (99.9%)", "Qwen3-Emb": "84.53 (97.4%)", "Gemma3-Mean": "57.05 (114.2%)", "Gemma3-Last": "54.07 (114.5%)", "Qwen3.5-Mean": "57.30 (107.9%)", "Qwen3.5-Last": "51.88 (102.0%)", "Dedicated Mean": "84.00 (98.6%)", "Base-Mean": "57.17 (111.0%)", "Base-Last": "52.98 (108.3%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "83.80 (100.3%)", "Qwen3-Emb": "86.74 (99.9%)", "Gemma3-Mean": "55.87 (111.8%)", "Gemma3-Last": "56.08 (118.8%)", "Qwen3.5-Mean": "56.59 (106.6%)", "Qwen3.5-Last": "55.30 (108.8%)", "Dedicated Mean": "85.27 (100.1%)", "Base-Mean": "56.23 (109.2%)", "Base-Last": "55.69 (113.8%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "83.87 (100.4%)", "Qwen3-Emb": "86.68 (99.8%)", "Gemma3-Mean": "56.22 (112.5%)", "Gemma3-Last": "56.24 (119.1%)", "Qwen3.5-Mean": "57.01 (107.4%)", "Qwen3.5-Last": "55.37 (108.9%)", "Dedicated Mean": "85.28 (100.1%)", "Base-Mean": "56.61 (109.9%)", "Base-Last": "55.80 (114.0%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "82.47 (98.7%)", "Qwen3-Emb": "82.41 (94.9%)", "Gemma3-Mean": "60.34 (120.7%)", "Gemma3-Last": "56.73 (120.2%)", "Qwen3.5-Mean": "61.43 (115.7%)", "Qwen3.5-Last": "54.87 (107.9%)", "Dedicated Mean": "82.44 (96.8%)", "Base-Mean": "60.89 (118.2%)", "Base-Last": "55.80 (114.0%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "81.48 (97.5%)", "Qwen3-Emb": "83.00 (95.6%)", "Gemma3-Mean": "56.87 (113.8%)", "Gemma3-Last": "53.72 (113.8%)", "Qwen3.5-Mean": "56.73 (106.8%)", "Qwen3.5-Last": "51.29 (100.9%)", "Dedicated Mean": "82.24 (96.6%)", "Base-Mean": "56.80 (110.3%)", "Base-Last": "52.50 (107.3%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "83.65 (100.2%)", "Qwen3-Emb": "84.84 (97.7%)", "Gemma3-Mean": "57.76 (115.6%)", "Gemma3-Last": "54.94 (116.4%)", "Qwen3.5-Mean": "58.34 (109.9%)", "Qwen3.5-Last": "52.83 (103.9%)", "Dedicated Mean": "84.25 (98.9%)", "Base-Mean": "58.05 (112.7%)", "Base-Last": "53.88 (110.1%)"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "83.46 (99.9%)", "Qwen3-Emb": "84.55 (97.4%)", "Gemma3-Mean": "57.06 (114.2%)", "Gemma3-Last": "54.06 (114.5%)", "Qwen3.5-Mean": "57.30 (107.9%)", "Qwen3.5-Last": "51.89 (102.0%)", "Dedicated Mean": "84.00 (98.7%)", "Base-Mean": "57.18 (111.0%)", "Base-Last": "52.98 (108.3%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "82.92 (99.3%)", "Qwen3-Emb": "86.75 (99.9%)", "Gemma3-Mean": "46.00 (92.0%)", "Gemma3-Last": "39.61 (83.9%)", "Qwen3.5-Mean": "52.00 (97.9%)", "Qwen3.5-Last": "51.25 (100.8%)", "Dedicated Mean": "84.84 (99.6%)", "Base-Mean": "49.00 (95.0%)", "Base-Last": "45.43 (92.3%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "PCA-k", "EmbGemma": "83.60 (100.1%)", "Qwen3-Emb": "86.91 (100.1%)", "Gemma3-Mean": "55.41 (110.9%)", "Gemma3-Last": "55.89 (118.4%)", "Qwen3.5-Mean": "56.11 (105.7%)", "Qwen3.5-Last": "55.11 (108.4%)", "Dedicated Mean": "85.25 (100.1%)", "Base-Mean": "55.76 (108.3%)", "Base-Last": "55.50 (113.4%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Whitening-k", "EmbGemma": "74.95 (89.7%)", "Qwen3-Emb": "74.18 (85.4%)", "Gemma3-Mean": "59.40 (118.9%)", "Gemma3-Last": "55.90 (118.4%)", "Qwen3.5-Mean": "59.50 (112.1%)", "Qwen3.5-Last": "53.51 (105.2%)", "Dedicated Mean": "74.56 (87.6%)", "Base-Mean": "59.45 (115.5%)", "Base-Last": "54.70 (111.8%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "SpecTemp", "EmbGemma": "84.09 (100.7%)", "Qwen3-Emb": "86.64 (99.8%)", "Gemma3-Mean": "56.59 (113.2%)", "Gemma3-Last": "56.64 (120.0%)", "Qwen3.5-Mean": "57.54 (108.4%)", "Qwen3.5-Last": "55.60 (109.3%)", "Dedicated Mean": "85.37 (100.2%)", "Base-Mean": "57.06 (110.8%)", "Base-Last": "56.12 (114.7%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "83.88 (100.4%)", "Qwen3-Emb": "85.04 (98.0%)", "Gemma3-Mean": "59.41 (118.9%)", "Gemma3-Last": "55.93 (118.5%)", "Qwen3.5-Mean": "59.54 (112.2%)", "Qwen3.5-Last": "53.56 (105.3%)", "Dedicated Mean": "84.46 (99.2%)", "Base-Mean": "59.47 (115.5%)", "Base-Last": "54.75 (111.9%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "83.63 (100.1%)", "Qwen3-Emb": "86.92 (100.1%)", "Gemma3-Mean": "55.45 (111.0%)", "Gemma3-Last": "56.05 (118.7%)", "Qwen3.5-Mean": "56.15 (105.8%)", "Qwen3.5-Last": "55.35 (108.8%)", "Dedicated Mean": "85.28 (100.1%)", "Base-Mean": "55.80 (108.3%)", "Base-Last": "55.70 (113.8%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "84.11 (100.7%)", "Qwen3-Emb": "86.65 (99.8%)", "Gemma3-Mean": "56.64 (113.3%)", "Gemma3-Last": "56.66 (120.0%)", "Qwen3.5-Mean": "57.59 (108.5%)", "Qwen3.5-Last": "55.65 (109.4%)", "Dedicated Mean": "85.38 (100.3%)", "Base-Mean": "57.12 (110.9%)", "Base-Last": "56.16 (114.7%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "84.08 (100.7%)", "Qwen3-Emb": "86.73 (99.9%)", "Gemma3-Mean": "56.64 (113.3%)", "Gemma3-Last": "56.66 (120.0%)", "Qwen3.5-Mean": "57.59 (108.5%)", "Qwen3.5-Last": "55.65 (109.4%)", "Dedicated Mean": "85.41 (100.3%)", "Base-Mean": "57.12 (110.9%)", "Base-Last": "56.16 (114.7%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "83.88 (100.4%)", "Qwen3-Emb": "85.04 (98.0%)", "Gemma3-Mean": "59.41 (118.9%)", "Gemma3-Last": "55.93 (118.5%)", "Qwen3.5-Mean": "59.54 (112.2%)", "Qwen3.5-Last": "53.56 (105.3%)", "Dedicated Mean": "84.46 (99.2%)", "Base-Mean": "59.47 (115.5%)", "Base-Last": "54.75 (111.9%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "82.94 (99.3%)", "Qwen3-Emb": "83.00 (95.6%)", "Gemma3-Mean": "61.20 (122.5%)", "Gemma3-Last": "57.58 (122.0%)", "Qwen3.5-Mean": "62.37 (117.5%)", "Qwen3.5-Last": "55.75 (109.6%)", "Dedicated Mean": "82.97 (97.5%)", "Base-Mean": "61.78 (120.0%)", "Base-Last": "56.66 (115.8%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "83.12 (99.5%)", "Qwen3-Emb": "84.38 (97.2%)", "Gemma3-Mean": "59.41 (118.9%)", "Gemma3-Last": "55.90 (118.4%)", "Qwen3.5-Mean": "59.51 (112.1%)", "Qwen3.5-Last": "53.51 (105.2%)", "Dedicated Mean": "83.75 (98.3%)", "Base-Mean": "59.46 (115.5%)", "Base-Last": "54.70 (111.8%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "84.22 (100.8%)", "Qwen3-Emb": "85.48 (98.5%)", "Gemma3-Mean": "59.65 (119.4%)", "Gemma3-Last": "56.40 (119.5%)", "Qwen3.5-Mean": "60.10 (113.2%)", "Qwen3.5-Last": "54.18 (106.5%)", "Dedicated Mean": "84.85 (99.7%)", "Base-Mean": "59.88 (116.3%)", "Base-Last": "55.29 (113.0%)"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "83.89 (100.4%)", "Qwen3-Emb": "85.06 (98.0%)", "Gemma3-Mean": "59.40 (118.8%)", "Gemma3-Last": "55.92 (118.5%)", "Qwen3.5-Mean": "59.53 (112.1%)", "Qwen3.5-Last": "53.56 (105.3%)", "Dedicated Mean": "84.47 (99.2%)", "Base-Mean": "59.47 (115.5%)", "Base-Last": "54.74 (111.9%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "82.35 (98.6%)", "Qwen3-Emb": "86.24 (99.3%)", "Gemma3-Mean": "49.15 (98.3%)", "Gemma3-Last": "53.28 (112.8%)", "Qwen3.5-Mean": "51.30 (96.6%)", "Qwen3.5-Last": "50.52 (99.4%)", "Dedicated Mean": "84.29 (99.0%)", "Base-Mean": "50.22 (97.5%)", "Base-Last": "51.90 (106.1%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "PCA-k", "EmbGemma": "82.50 (98.8%)", "Qwen3-Emb": "86.95 (100.1%)", "Gemma3-Mean": "54.40 (108.8%)", "Gemma3-Last": "55.59 (117.7%)", "Qwen3.5-Mean": "55.12 (103.8%)", "Qwen3.5-Last": "54.96 (108.1%)", "Dedicated Mean": "84.72 (99.5%)", "Base-Mean": "54.76 (106.3%)", "Base-Last": "55.28 (112.9%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Whitening-k", "EmbGemma": "79.20 (94.8%)", "Qwen3-Emb": "78.65 (90.6%)", "Gemma3-Mean": "60.29 (120.6%)", "Gemma3-Last": "57.99 (122.8%)", "Qwen3.5-Mean": "61.09 (115.1%)", "Qwen3.5-Last": "55.64 (109.4%)", "Dedicated Mean": "78.93 (92.7%)", "Base-Mean": "60.69 (117.8%)", "Base-Last": "56.81 (116.1%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "SpecTemp", "EmbGemma": "84.19 (100.8%)", "Qwen3-Emb": "86.18 (99.3%)", "Gemma3-Mean": "57.27 (114.6%)", "Gemma3-Last": "57.48 (121.7%)", "Qwen3.5-Mean": "58.63 (110.4%)", "Qwen3.5-Last": "56.29 (110.7%)", "Dedicated Mean": "85.19 (100.0%)", "Base-Mean": "57.95 (112.5%)", "Base-Last": "56.88 (116.2%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "84.44 (101.1%)", "Qwen3-Emb": "86.15 (99.2%)", "Gemma3-Mean": "60.30 (120.7%)", "Gemma3-Last": "57.99 (122.8%)", "Qwen3.5-Mean": "61.12 (115.1%)", "Qwen3.5-Last": "55.64 (109.4%)", "Dedicated Mean": "85.30 (100.2%)", "Base-Mean": "60.71 (117.9%)", "Base-Last": "56.81 (116.1%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "82.55 (98.8%)", "Qwen3-Emb": "86.97 (100.2%)", "Gemma3-Mean": "54.44 (108.9%)", "Gemma3-Last": "55.76 (118.1%)", "Qwen3.5-Mean": "55.16 (103.9%)", "Qwen3.5-Last": "55.24 (108.6%)", "Dedicated Mean": "84.76 (99.5%)", "Base-Mean": "54.80 (106.4%)", "Base-Last": "55.50 (113.4%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "84.22 (100.8%)", "Qwen3-Emb": "86.18 (99.3%)", "Gemma3-Mean": "57.32 (114.7%)", "Gemma3-Last": "57.34 (121.5%)", "Qwen3.5-Mean": "58.67 (110.5%)", "Qwen3.5-Last": "56.10 (110.3%)", "Dedicated Mean": "85.20 (100.0%)", "Base-Mean": "58.00 (112.6%)", "Base-Last": "56.72 (115.9%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "84.17 (100.8%)", "Qwen3-Emb": "86.33 (99.4%)", "Gemma3-Mean": "57.33 (114.7%)", "Gemma3-Last": "57.34 (121.5%)", "Qwen3.5-Mean": "58.67 (110.5%)", "Qwen3.5-Last": "56.10 (110.3%)", "Dedicated Mean": "85.25 (100.1%)", "Base-Mean": "58.00 (112.6%)", "Base-Last": "56.72 (115.9%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "84.44 (101.1%)", "Qwen3-Emb": "86.15 (99.2%)", "Gemma3-Mean": "60.30 (120.7%)", "Gemma3-Last": "57.99 (122.8%)", "Qwen3.5-Mean": "61.12 (115.1%)", "Qwen3.5-Last": "55.64 (109.4%)", "Dedicated Mean": "85.30 (100.2%)", "Base-Mean": "60.71 (117.9%)", "Base-Last": "56.81 (116.1%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "84.00 (100.6%)", "Qwen3-Emb": "84.64 (97.5%)", "Gemma3-Mean": "61.10 (122.3%)", "Gemma3-Last": "58.34 (123.6%)", "Qwen3.5-Mean": "62.61 (117.9%)", "Qwen3.5-Last": "56.77 (111.6%)", "Dedicated Mean": "84.32 (99.0%)", "Base-Mean": "61.86 (120.1%)", "Base-Last": "57.56 (117.6%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "84.32 (101.0%)", "Qwen3-Emb": "85.97 (99.0%)", "Gemma3-Mean": "60.31 (120.7%)", "Gemma3-Last": "57.99 (122.8%)", "Qwen3.5-Mean": "61.12 (115.1%)", "Qwen3.5-Last": "55.64 (109.4%)", "Dedicated Mean": "85.14 (100.0%)", "Base-Mean": "60.72 (117.9%)", "Base-Last": "56.81 (116.1%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "84.52 (101.2%)", "Qwen3-Emb": "86.46 (99.6%)", "Gemma3-Mean": "60.41 (120.9%)", "Gemma3-Last": "58.15 (123.2%)", "Qwen3.5-Mean": "61.35 (115.6%)", "Qwen3.5-Last": "55.92 (110.0%)", "Dedicated Mean": "85.49 (100.4%)", "Base-Mean": "60.88 (118.2%)", "Base-Last": "57.03 (116.6%)"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "84.41 (101.1%)", "Qwen3-Emb": "86.15 (99.2%)", "Gemma3-Mean": "60.28 (120.6%)", "Gemma3-Last": "57.99 (122.8%)", "Qwen3.5-Mean": "61.09 (115.1%)", "Qwen3.5-Last": "55.64 (109.4%)", "Dedicated Mean": "85.28 (100.2%)", "Base-Mean": "60.69 (117.8%)", "Base-Last": "56.81 (116.1%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "79.91 (95.7%)", "Qwen3-Emb": "84.97 (97.9%)", "Gemma3-Mean": "46.30 (92.7%)", "Gemma3-Last": "52.17 (110.5%)", "Qwen3.5-Mean": "49.85 (93.9%)", "Qwen3.5-Last": "46.23 (90.9%)", "Dedicated Mean": "82.44 (96.8%)", "Base-Mean": "48.08 (93.3%)", "Base-Last": "49.20 (100.7%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "PCA-k", "EmbGemma": "79.42 (95.1%)", "Qwen3-Emb": "86.16 (99.2%)", "Gemma3-Mean": "52.64 (105.3%)", "Gemma3-Last": "54.53 (115.5%)", "Qwen3.5-Mean": "53.55 (100.9%)", "Qwen3.5-Last": "54.21 (106.6%)", "Dedicated Mean": "82.79 (97.2%)", "Base-Mean": "53.09 (103.1%)", "Base-Last": "54.37 (111.1%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Whitening-k", "EmbGemma": "82.16 (98.4%)", "Qwen3-Emb": "82.27 (94.8%)", "Gemma3-Mean": "60.36 (120.8%)", "Gemma3-Last": "58.97 (124.9%)", "Qwen3.5-Mean": "61.97 (116.7%)", "Qwen3.5-Last": "57.42 (112.9%)", "Dedicated Mean": "82.22 (96.6%)", "Base-Mean": "61.16 (118.8%)", "Base-Last": "58.20 (118.9%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "SpecTemp", "EmbGemma": "83.62 (100.1%)", "Qwen3-Emb": "84.58 (97.4%)", "Gemma3-Mean": "58.35 (116.8%)", "Gemma3-Last": "58.24 (123.4%)", "Qwen3.5-Mean": "60.72 (114.4%)", "Qwen3.5-Last": "57.13 (112.3%)", "Dedicated Mean": "84.10 (98.8%)", "Base-Mean": "59.53 (115.6%)", "Base-Last": "57.69 (117.8%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "83.60 (100.1%)", "Qwen3-Emb": "84.86 (97.7%)", "Gemma3-Mean": "60.37 (120.8%)", "Gemma3-Last": "59.01 (125.0%)", "Qwen3.5-Mean": "61.97 (116.7%)", "Qwen3.5-Last": "57.39 (112.9%)", "Dedicated Mean": "84.23 (98.9%)", "Base-Mean": "61.17 (118.8%)", "Base-Last": "58.20 (118.9%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "79.48 (95.2%)", "Qwen3-Emb": "86.20 (99.3%)", "Gemma3-Mean": "52.69 (105.4%)", "Gemma3-Last": "54.73 (115.9%)", "Qwen3.5-Mean": "53.60 (101.0%)", "Qwen3.5-Last": "54.52 (107.2%)", "Dedicated Mean": "82.84 (97.2%)", "Base-Mean": "53.14 (103.2%)", "Base-Last": "54.62 (111.6%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "83.66 (100.2%)", "Qwen3-Emb": "84.68 (97.5%)", "Gemma3-Mean": "58.40 (116.9%)", "Gemma3-Last": "57.93 (122.7%)", "Qwen3.5-Mean": "60.77 (114.5%)", "Qwen3.5-Last": "56.55 (111.2%)", "Dedicated Mean": "84.17 (98.8%)", "Base-Mean": "59.59 (115.7%)", "Base-Last": "57.24 (117.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "83.60 (100.1%)", "Qwen3-Emb": "84.86 (97.7%)", "Gemma3-Mean": "58.41 (116.9%)", "Gemma3-Last": "57.93 (122.7%)", "Qwen3.5-Mean": "60.77 (114.5%)", "Qwen3.5-Last": "56.55 (111.2%)", "Dedicated Mean": "84.23 (98.9%)", "Base-Mean": "59.59 (115.7%)", "Base-Last": "57.24 (117.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "83.32 (99.8%)", "Qwen3-Emb": "86.91 (100.1%)", "Gemma3-Mean": "60.37 (120.8%)", "Gemma3-Last": "59.01 (125.0%)", "Qwen3.5-Mean": "61.97 (116.7%)", "Qwen3.5-Last": "57.39 (112.9%)", "Dedicated Mean": "85.11 (99.9%)", "Base-Mean": "61.17 (118.8%)", "Base-Last": "58.20 (118.9%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "83.78 (100.3%)", "Qwen3-Emb": "86.23 (99.3%)", "Gemma3-Mean": "59.87 (119.8%)", "Gemma3-Last": "58.01 (122.9%)", "Qwen3.5-Mean": "61.99 (116.8%)", "Qwen3.5-Last": "57.11 (112.3%)", "Dedicated Mean": "85.00 (99.8%)", "Base-Mean": "60.93 (118.3%)", "Base-Last": "57.56 (117.6%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "83.66 (100.2%)", "Qwen3-Emb": "84.68 (97.5%)", "Gemma3-Mean": "60.37 (120.8%)", "Gemma3-Last": "59.01 (125.0%)", "Qwen3.5-Mean": "61.97 (116.7%)", "Qwen3.5-Last": "57.39 (112.9%)", "Dedicated Mean": "84.17 (98.8%)", "Base-Mean": "61.17 (118.8%)", "Base-Last": "58.20 (118.9%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "83.33 (99.8%)", "Qwen3-Emb": "85.48 (98.5%)", "Gemma3-Mean": "60.42 (120.9%)", "Gemma3-Last": "59.02 (125.0%)", "Qwen3.5-Mean": "62.07 (116.9%)", "Qwen3.5-Last": "57.44 (113.0%)", "Dedicated Mean": "84.41 (99.1%)", "Base-Mean": "61.25 (118.9%)", "Base-Last": "58.23 (119.0%)"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "83.56 (100.0%)", "Qwen3-Emb": "84.76 (97.6%)", "Gemma3-Mean": "60.36 (120.8%)", "Gemma3-Last": "58.97 (124.9%)", "Qwen3.5-Mean": "61.97 (116.7%)", "Qwen3.5-Last": "57.42 (112.9%)", "Dedicated Mean": "84.16 (98.8%)", "Base-Mean": "61.16 (118.8%)", "Base-Last": "58.20 (118.9%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "67.08 (100.3%)", "Qwen3-Emb": "69.76 (98.9%)", "Gemma3-Mean": "44.10 (91.1%)", "Gemma3-Last": "9.43 (75.2%)", "Qwen3.5-Mean": "49.27 (98.5%)", "Qwen3.5-Last": "11.83 (85.0%)", "Dedicated Mean": "68.42 (99.6%)", "Base-Mean": "46.69 (94.8%)", "Base-Last": "10.63 (80.1%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "PCA-k", "EmbGemma": "67.03 (100.3%)", "Qwen3-Emb": "69.76 (98.9%)", "Gemma3-Mean": "53.87 (111.3%)", "Gemma3-Last": "12.56 (100.2%)", "Qwen3.5-Mean": "53.42 (106.8%)", "Qwen3.5-Last": "12.40 (89.0%)", "Dedicated Mean": "68.40 (99.6%)", "Base-Mean": "53.64 (109.1%)", "Base-Last": "12.48 (94.6%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Whitening-k", "EmbGemma": "45.07 (67.4%)", "Qwen3-Emb": "25.91 (36.7%)", "Gemma3-Mean": "46.79 (96.7%)", "Gemma3-Last": "10.05 (80.2%)", "Qwen3.5-Mean": "41.32 (82.6%)", "Qwen3.5-Last": "6.99 (50.2%)", "Dedicated Mean": "35.49 (52.1%)", "Base-Mean": "44.05 (89.7%)", "Base-Last": "8.52 (65.2%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "SpecTemp", "EmbGemma": "67.03 (100.3%)", "Qwen3-Emb": "69.76 (98.9%)", "Gemma3-Mean": "53.87 (111.3%)", "Gemma3-Last": "12.56 (100.2%)", "Qwen3.5-Mean": "53.42 (106.8%)", "Qwen3.5-Last": "12.40 (89.0%)", "Dedicated Mean": "68.40 (99.6%)", "Base-Mean": "53.64 (109.1%)", "Base-Last": "12.48 (94.6%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "67.34 (100.7%)", "Qwen3-Emb": "69.87 (99.0%)", "Gemma3-Mean": "64.38 (133.0%)", "Gemma3-Last": "14.14 (112.8%)", "Qwen3.5-Mean": "65.63 (131.2%)", "Qwen3.5-Last": "18.79 (134.9%)", "Dedicated Mean": "68.61 (99.9%)", "Base-Mean": "65.00 (132.1%)", "Base-Last": "16.46 (123.9%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "67.19 (100.5%)", "Qwen3-Emb": "69.74 (98.8%)", "Gemma3-Mean": "54.01 (111.6%)", "Gemma3-Last": "12.97 (103.5%)", "Qwen3.5-Mean": "53.43 (106.8%)", "Qwen3.5-Last": "12.93 (92.8%)", "Dedicated Mean": "68.47 (99.7%)", "Base-Mean": "53.72 (109.2%)", "Base-Last": "12.95 (98.2%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "67.19 (100.5%)", "Qwen3-Emb": "69.74 (98.8%)", "Gemma3-Mean": "54.01 (111.6%)", "Gemma3-Last": "12.97 (103.5%)", "Qwen3.5-Mean": "53.43 (106.8%)", "Qwen3.5-Last": "12.93 (92.8%)", "Dedicated Mean": "68.47 (99.7%)", "Base-Mean": "53.72 (109.2%)", "Base-Last": "12.95 (98.2%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "67.19 (100.5%)", "Qwen3-Emb": "69.74 (98.8%)", "Gemma3-Mean": "54.01 (111.6%)", "Gemma3-Last": "12.97 (103.5%)", "Qwen3.5-Mean": "53.43 (106.8%)", "Qwen3.5-Last": "12.93 (92.8%)", "Dedicated Mean": "68.47 (99.7%)", "Base-Mean": "53.72 (109.2%)", "Base-Last": "12.95 (98.2%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "67.34 (100.7%)", "Qwen3-Emb": "69.87 (99.0%)", "Gemma3-Mean": "64.38 (133.0%)", "Gemma3-Last": "14.14 (112.8%)", "Qwen3.5-Mean": "65.63 (131.2%)", "Qwen3.5-Last": "18.79 (134.9%)", "Dedicated Mean": "68.61 (99.9%)", "Base-Mean": "65.00 (132.1%)", "Base-Last": "16.46 (123.9%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "69.07 (103.3%)", "Qwen3-Emb": "70.71 (100.2%)", "Gemma3-Mean": "61.75 (127.6%)", "Gemma3-Last": "14.17 (113.0%)", "Qwen3.5-Mean": "62.53 (125.0%)", "Qwen3.5-Last": "20.23 (145.2%)", "Dedicated Mean": "69.89 (101.8%)", "Base-Mean": "62.14 (126.3%)", "Base-Last": "17.20 (129.1%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "67.44 (100.9%)", "Qwen3-Emb": "69.97 (99.2%)", "Gemma3-Mean": "46.73 (96.5%)", "Gemma3-Last": "12.49 (99.7%)", "Qwen3.5-Mean": "41.36 (82.7%)", "Qwen3.5-Last": "7.04 (50.5%)", "Dedicated Mean": "68.70 (100.0%)", "Base-Mean": "44.05 (89.6%)", "Base-Last": "9.77 (75.1%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "67.34 (100.7%)", "Qwen3-Emb": "69.87 (99.0%)", "Gemma3-Mean": "64.38 (133.0%)", "Gemma3-Last": "14.14 (112.8%)", "Qwen3.5-Mean": "65.63 (131.2%)", "Qwen3.5-Last": "18.79 (134.9%)", "Dedicated Mean": "68.61 (99.9%)", "Base-Mean": "65.00 (132.1%)", "Base-Last": "16.46 (123.9%)"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "67.18 (100.5%)", "Qwen3-Emb": "69.92 (99.1%)", "Gemma3-Mean": "64.45 (133.2%)", "Gemma3-Last": "14.18 (113.2%)", "Qwen3.5-Mean": "65.68 (131.3%)", "Qwen3.5-Last": "18.88 (135.6%)", "Dedicated Mean": "68.55 (99.8%)", "Base-Mean": "65.06 (132.2%)", "Base-Last": "16.53 (124.4%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "66.76 (99.9%)", "Qwen3-Emb": "69.59 (98.6%)", "Gemma3-Mean": "40.76 (84.2%)", "Gemma3-Last": "4.77 (38.1%)", "Qwen3.5-Mean": "48.27 (96.5%)", "Qwen3.5-Last": "12.23 (87.8%)", "Dedicated Mean": "68.18 (99.2%)", "Base-Mean": "44.52 (90.4%)", "Base-Last": "8.50 (62.9%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "PCA-k", "EmbGemma": "67.11 (100.4%)", "Qwen3-Emb": "69.80 (98.9%)", "Gemma3-Mean": "54.13 (111.8%)", "Gemma3-Last": "13.23 (105.6%)", "Qwen3.5-Mean": "53.56 (107.1%)", "Qwen3.5-Last": "12.99 (93.3%)", "Dedicated Mean": "68.45 (99.7%)", "Base-Mean": "53.84 (109.5%)", "Base-Last": "13.11 (99.4%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Whitening-k", "EmbGemma": "71.10 (106.4%)", "Qwen3-Emb": "69.97 (99.2%)", "Gemma3-Mean": "66.36 (137.1%)", "Gemma3-Last": "15.53 (123.9%)", "Qwen3.5-Mean": "66.73 (133.4%)", "Qwen3.5-Last": "20.12 (144.5%)", "Dedicated Mean": "70.53 (102.8%)", "Base-Mean": "66.55 (135.3%)", "Base-Last": "17.82 (134.2%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "SpecTemp", "EmbGemma": "67.96 (101.7%)", "Qwen3-Emb": "70.37 (99.7%)", "Gemma3-Mean": "55.00 (113.6%)", "Gemma3-Last": "13.91 (111.0%)", "Qwen3.5-Mean": "54.26 (108.5%)", "Qwen3.5-Last": "14.37 (103.2%)", "Dedicated Mean": "69.16 (100.7%)", "Base-Mean": "54.63 (111.1%)", "Base-Last": "14.14 (107.1%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "67.74 (101.3%)", "Qwen3-Emb": "69.98 (99.2%)", "Gemma3-Mean": "66.34 (137.1%)", "Gemma3-Last": "15.89 (126.8%)", "Qwen3.5-Mean": "66.96 (133.9%)", "Qwen3.5-Last": "21.52 (154.6%)", "Dedicated Mean": "68.86 (100.2%)", "Base-Mean": "66.65 (135.5%)", "Base-Last": "18.70 (140.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "67.27 (100.6%)", "Qwen3-Emb": "69.78 (98.9%)", "Gemma3-Mean": "54.27 (112.1%)", "Gemma3-Last": "13.65 (108.9%)", "Qwen3.5-Mean": "53.58 (107.1%)", "Qwen3.5-Last": "13.52 (97.1%)", "Dedicated Mean": "68.53 (99.8%)", "Base-Mean": "53.92 (109.6%)", "Base-Last": "13.59 (103.0%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "68.13 (101.9%)", "Qwen3-Emb": "70.16 (99.4%)", "Gemma3-Mean": "55.36 (114.4%)", "Gemma3-Last": "14.22 (113.5%)", "Qwen3.5-Mean": "54.28 (108.5%)", "Qwen3.5-Last": "14.86 (106.7%)", "Dedicated Mean": "69.14 (100.7%)", "Base-Mean": "54.82 (111.5%)", "Base-Last": "14.54 (110.1%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "67.74 (101.3%)", "Qwen3-Emb": "69.98 (99.2%)", "Gemma3-Mean": "55.34 (114.3%)", "Gemma3-Last": "14.20 (113.3%)", "Qwen3.5-Mean": "54.26 (108.5%)", "Qwen3.5-Last": "14.85 (106.6%)", "Dedicated Mean": "68.86 (100.2%)", "Base-Mean": "54.80 (111.4%)", "Base-Last": "14.52 (110.0%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "67.42 (100.8%)", "Qwen3-Emb": "69.92 (99.1%)", "Gemma3-Mean": "66.34 (137.1%)", "Gemma3-Last": "15.89 (126.8%)", "Qwen3.5-Mean": "66.96 (133.9%)", "Qwen3.5-Last": "21.52 (154.6%)", "Dedicated Mean": "68.67 (100.0%)", "Base-Mean": "66.65 (135.5%)", "Base-Last": "18.70 (140.7%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "69.21 (103.5%)", "Qwen3-Emb": "70.86 (100.4%)", "Gemma3-Mean": "62.72 (129.6%)", "Gemma3-Last": "15.66 (125.0%)", "Qwen3.5-Mean": "63.29 (126.6%)", "Qwen3.5-Last": "21.67 (155.7%)", "Dedicated Mean": "70.03 (102.0%)", "Base-Mean": "63.00 (128.1%)", "Base-Last": "18.66 (140.3%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "68.13 (101.9%)", "Qwen3-Emb": "70.16 (99.4%)", "Gemma3-Mean": "66.39 (137.2%)", "Gemma3-Last": "15.70 (125.3%)", "Qwen3.5-Mean": "66.69 (133.4%)", "Qwen3.5-Last": "20.26 (145.5%)", "Dedicated Mean": "69.14 (100.7%)", "Base-Mean": "66.54 (135.3%)", "Base-Last": "17.98 (135.4%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "67.73 (101.3%)", "Qwen3-Emb": "69.97 (99.2%)", "Gemma3-Mean": "66.18 (136.7%)", "Gemma3-Last": "15.91 (127.0%)", "Qwen3.5-Mean": "66.87 (133.7%)", "Qwen3.5-Last": "22.52 (161.8%)", "Dedicated Mean": "68.85 (100.2%)", "Base-Mean": "66.53 (135.2%)", "Base-Last": "19.21 (144.4%)"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "67.57 (101.1%)", "Qwen3-Emb": "70.15 (99.4%)", "Gemma3-Mean": "66.32 (137.0%)", "Gemma3-Last": "15.85 (126.5%)", "Qwen3.5-Mean": "66.98 (133.9%)", "Qwen3.5-Last": "21.43 (153.9%)", "Dedicated Mean": "68.86 (100.2%)", "Base-Mean": "66.65 (135.5%)", "Base-Last": "18.64 (140.2%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "66.27 (99.1%)", "Qwen3-Emb": "67.24 (95.3%)", "Gemma3-Mean": "57.53 (118.9%)", "Gemma3-Last": "18.22 (145.4%)", "Qwen3.5-Mean": "43.94 (87.9%)", "Qwen3.5-Last": "17.09 (122.7%)", "Dedicated Mean": "66.75 (97.2%)", "Base-Mean": "50.73 (103.4%)", "Base-Last": "17.66 (134.1%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "63.67 (95.2%)", "Qwen3-Emb": "67.71 (96.0%)", "Gemma3-Mean": "51.55 (106.5%)", "Gemma3-Last": "12.83 (102.4%)", "Qwen3.5-Mean": "52.09 (104.2%)", "Qwen3.5-Last": "12.94 (93.0%)", "Dedicated Mean": "65.69 (95.6%)", "Base-Mean": "51.82 (105.3%)", "Base-Last": "12.88 (97.7%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "67.86 (101.5%)", "Qwen3-Emb": "70.07 (99.3%)", "Gemma3-Mean": "60.73 (125.5%)", "Gemma3-Last": "16.51 (131.8%)", "Qwen3.5-Mean": "64.21 (128.4%)", "Qwen3.5-Last": "28.26 (202.9%)", "Dedicated Mean": "68.97 (100.4%)", "Base-Mean": "62.47 (126.9%)", "Base-Last": "22.39 (167.3%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "65.97 (98.7%)", "Qwen3-Emb": "69.31 (98.2%)", "Gemma3-Mean": "54.67 (112.9%)", "Gemma3-Last": "14.92 (119.0%)", "Qwen3.5-Mean": "55.08 (110.2%)", "Qwen3.5-Last": "18.56 (133.3%)", "Dedicated Mean": "67.64 (98.5%)", "Base-Mean": "54.88 (111.5%)", "Base-Last": "16.74 (126.1%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "65.47 (97.9%)", "Qwen3-Emb": "68.36 (96.9%)", "Gemma3-Mean": "60.82 (125.7%)", "Gemma3-Last": "16.14 (128.8%)", "Qwen3.5-Mean": "64.03 (128.0%)", "Qwen3.5-Last": "28.42 (204.1%)", "Dedicated Mean": "66.91 (97.4%)", "Base-Mean": "62.42 (126.8%)", "Base-Last": "22.28 (166.4%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "63.88 (95.6%)", "Qwen3-Emb": "67.65 (95.9%)", "Gemma3-Mean": "51.73 (106.9%)", "Gemma3-Last": "13.34 (106.5%)", "Qwen3.5-Mean": "52.07 (104.1%)", "Qwen3.5-Last": "13.45 (96.6%)", "Dedicated Mean": "65.77 (95.7%)", "Base-Mean": "51.90 (105.5%)", "Base-Last": "13.39 (101.5%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.18 (99.0%)", "Qwen3-Emb": "68.76 (97.4%)", "Gemma3-Mean": "55.57 (114.8%)", "Gemma3-Last": "15.15 (120.9%)", "Qwen3.5-Mean": "55.06 (110.1%)", "Qwen3.5-Last": "18.95 (136.1%)", "Dedicated Mean": "67.47 (98.2%)", "Base-Mean": "55.31 (112.5%)", "Base-Last": "17.05 (128.5%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "65.61 (98.1%)", "Qwen3-Emb": "68.66 (97.3%)", "Gemma3-Mean": "57.79 (119.4%)", "Gemma3-Last": "15.77 (125.8%)", "Qwen3.5-Mean": "60.05 (120.1%)", "Qwen3.5-Last": "23.86 (171.3%)", "Dedicated Mean": "67.13 (97.7%)", "Base-Mean": "58.92 (119.7%)", "Base-Last": "19.81 (148.6%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.18 (99.0%)", "Qwen3-Emb": "68.76 (97.4%)", "Gemma3-Mean": "60.83 (125.7%)", "Gemma3-Last": "16.17 (129.0%)", "Qwen3.5-Mean": "64.06 (128.1%)", "Qwen3.5-Last": "28.45 (204.3%)", "Dedicated Mean": "67.47 (98.2%)", "Base-Mean": "62.45 (126.9%)", "Base-Last": "22.31 (166.7%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "65.44 (97.9%)", "Qwen3-Emb": "68.34 (96.8%)", "Gemma3-Mean": "60.67 (125.3%)", "Gemma3-Last": "16.04 (128.0%)", "Qwen3.5-Mean": "63.74 (127.5%)", "Qwen3.5-Last": "28.20 (202.5%)", "Dedicated Mean": "66.89 (97.4%)", "Base-Mean": "62.20 (126.4%)", "Base-Last": "22.12 (165.2%)"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Orth. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "59.84 (89.5%)", "Qwen3-Emb": "64.86 (91.9%)", "Gemma3-Mean": "48.82 (100.9%)", "Gemma3-Last": "12.29 (98.0%)", "Qwen3.5-Mean": "49.71 (99.4%)", "Qwen3.5-Last": "9.76 (70.1%)", "Dedicated Mean": "62.35 (90.7%)", "Base-Mean": "49.27 (100.1%)", "Base-Last": "11.02 (84.1%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "63.50 (95.0%)", "Qwen3-Emb": "66.25 (93.9%)", "Gemma3-Mean": "55.12 (113.9%)", "Gemma3-Last": "15.81 (126.2%)", "Qwen3.5-Mean": "55.50 (111.0%)", "Qwen3.5-Last": "18.67 (134.1%)", "Dedicated Mean": "64.88 (94.4%)", "Base-Mean": "55.31 (112.4%)", "Base-Last": "17.24 (130.1%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "61.53 (92.0%)", "Qwen3-Emb": "65.67 (93.1%)", "Gemma3-Mean": "53.73 (111.0%)", "Gemma3-Last": "15.35 (122.5%)", "Qwen3.5-Mean": "55.65 (111.3%)", "Qwen3.5-Last": "18.46 (132.5%)", "Dedicated Mean": "63.60 (92.5%)", "Base-Mean": "54.69 (111.2%)", "Base-Last": "16.91 (127.5%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "63.50 (95.0%)", "Qwen3-Emb": "66.25 (93.9%)", "Gemma3-Mean": "56.16 (116.0%)", "Gemma3-Last": "15.97 (127.4%)", "Qwen3.5-Mean": "58.61 (117.2%)", "Qwen3.5-Last": "23.15 (166.2%)", "Dedicated Mean": "64.88 (94.4%)", "Base-Mean": "57.38 (116.6%)", "Base-Last": "19.56 (146.8%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "62.62 (93.7%)", "Qwen3-Emb": "65.92 (93.4%)", "Gemma3-Mean": "56.12 (116.0%)", "Gemma3-Last": "15.76 (125.8%)", "Qwen3.5-Mean": "58.54 (117.1%)", "Qwen3.5-Last": "22.94 (164.8%)", "Dedicated Mean": "64.27 (93.5%)", "Base-Mean": "57.33 (116.5%)", "Base-Last": "19.35 (145.2%)"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "62.60 (93.6%)", "Qwen3-Emb": "66.34 (94.0%)", "Gemma3-Mean": "56.10 (115.9%)", "Gemma3-Last": "15.72 (125.4%)", "Qwen3.5-Mean": "58.95 (117.9%)", "Qwen3.5-Last": "22.98 (165.0%)", "Dedicated Mean": "64.47 (93.8%)", "Base-Mean": "57.53 (116.9%)", "Base-Last": "19.35 (145.2%)"}], "task_comp::Similarity (STS)::Pearson (r × 100)::Absolute Score": [{"Dataset": "STSBenchmark", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "84.44", "Qwen3-Emb": "84.23", "Gemma3-Mean": "28.98", "Gemma3-Last": "24.92", "Qwen3.5-Mean": "42.67", "Qwen3.5-Last": "24.01", "Dedicated Mean": "84.34", "Base-Mean": "35.83", "Base-Last": "24.47"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "PCA-k", "EmbGemma": "84.55", "Qwen3-Emb": "84.92", "Gemma3-Mean": "47.75", "Gemma3-Last": "43.86", "Qwen3.5-Mean": "48.18", "Qwen3.5-Last": "36.61", "Dedicated Mean": "84.73", "Base-Mean": "47.97", "Base-Last": "40.23"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Whitening-k", "EmbGemma": "82.01", "Qwen3-Emb": "79.63", "Gemma3-Mean": "62.12", "Gemma3-Last": "64.52", "Qwen3.5-Mean": "61.51", "Qwen3.5-Last": "59.92", "Dedicated Mean": "80.82", "Base-Mean": "61.81", "Base-Last": "62.22"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "SpecTemp", "EmbGemma": "84.95", "Qwen3-Emb": "85.06", "Gemma3-Mean": "48.80", "Gemma3-Last": "45.15", "Qwen3.5-Mean": "48.95", "Qwen3.5-Last": "37.43", "Dedicated Mean": "85.00", "Base-Mean": "48.88", "Base-Last": "41.29"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "85.16", "Qwen3-Emb": "85.38", "Gemma3-Mean": "62.21", "Gemma3-Last": "64.86", "Qwen3.5-Mean": "61.75", "Qwen3.5-Last": "60.32", "Dedicated Mean": "85.27", "Base-Mean": "61.98", "Base-Last": "62.59"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "69.07", "Qwen3-Emb": "70.71", "Gemma3-Mean": "61.75", "Gemma3-Last": "14.17", "Qwen3.5-Mean": "62.53", "Qwen3.5-Last": "20.23", "Dedicated Mean": "69.89", "Base-Mean": "62.14", "Base-Last": "17.20"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "67.44", "Qwen3-Emb": "69.97", "Gemma3-Mean": "46.73", "Gemma3-Last": "12.49", "Qwen3.5-Mean": "41.36", "Qwen3.5-Last": "7.04", "Dedicated Mean": "68.70", "Base-Mean": "44.05", "Base-Last": "9.77"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "67.34", "Qwen3-Emb": "69.87", "Gemma3-Mean": "64.38", "Gemma3-Last": "14.14", "Qwen3.5-Mean": "65.63", "Qwen3.5-Last": "18.79", "Dedicated Mean": "68.61", "Base-Mean": "65.00", "Base-Last": "16.46"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "67.18", "Qwen3-Emb": "69.92", "Gemma3-Mean": "64.45", "Gemma3-Last": "14.18", "Qwen3.5-Mean": "65.68", "Qwen3.5-Last": "18.88", "Dedicated Mean": "68.55", "Base-Mean": "65.06", "Base-Last": "16.53"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "66.76", "Qwen3-Emb": "69.59", "Gemma3-Mean": "40.76", "Gemma3-Last": "4.77", "Qwen3.5-Mean": "48.27", "Qwen3.5-Last": "12.23", "Dedicated Mean": "68.18", "Base-Mean": "44.52", "Base-Last": "8.50"}, {"Dataset": "STS22.v2", "k": "256", "Method": "PCA-k", "EmbGemma": "67.11", "Qwen3-Emb": "69.80", "Gemma3-Mean": "54.13", "Gemma3-Last": "13.23", "Qwen3.5-Mean": "53.56", "Qwen3.5-Last": "12.99", "Dedicated Mean": "68.45", "Base-Mean": "53.84", "Base-Last": "13.11"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Whitening-k", "EmbGemma": "71.10", "Qwen3-Emb": "69.97", "Gemma3-Mean": "66.36", "Gemma3-Last": "15.53", "Qwen3.5-Mean": "66.73", "Qwen3.5-Last": "20.12", "Dedicated Mean": "70.53", "Base-Mean": "66.55", "Base-Last": "17.82"}, {"Dataset": "STS22.v2", "k": "256", "Method": "SpecTemp", "EmbGemma": "67.96", "Qwen3-Emb": "70.37", "Gemma3-Mean": "55.00", "Gemma3-Last": "13.91", "Qwen3.5-Mean": "54.26", "Qwen3.5-Last": "14.37", "Dedicated Mean": "69.16", "Base-Mean": "54.63", "Base-Last": "14.14"}, {"Dataset": "STS22.v2", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "67.74", "Qwen3-Emb": "69.98", "Gemma3-Mean": "66.34", "Gemma3-Last": "15.89", "Qwen3.5-Mean": "66.96", "Qwen3.5-Last": "21.52", "Dedicated Mean": "68.86", "Base-Mean": "66.65", "Base-Last": "18.70"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "67.27", "Qwen3-Emb": "69.78", "Gemma3-Mean": "54.27", "Gemma3-Last": "13.65", "Qwen3.5-Mean": "53.58", "Qwen3.5-Last": "13.52", "Dedicated Mean": "68.53", "Base-Mean": "53.92", "Base-Last": "13.59"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "68.13", "Qwen3-Emb": "70.16", "Gemma3-Mean": "55.36", "Gemma3-Last": "14.22", "Qwen3.5-Mean": "54.28", "Qwen3.5-Last": "14.86", "Dedicated Mean": "69.14", "Base-Mean": "54.82", "Base-Last": "14.54"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "67.74", "Qwen3-Emb": "69.98", "Gemma3-Mean": "55.34", "Gemma3-Last": "14.20", "Qwen3.5-Mean": "54.26", "Qwen3.5-Last": "14.85", "Dedicated Mean": "68.86", "Base-Mean": "54.80", "Base-Last": "14.52"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "67.42", "Qwen3-Emb": "69.92", "Gemma3-Mean": "66.34", "Gemma3-Last": "15.89", "Qwen3.5-Mean": "66.96", "Qwen3.5-Last": "21.52", "Dedicated Mean": "68.67", "Base-Mean": "66.65", "Base-Last": "18.70"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "69.21", "Qwen3-Emb": "70.86", "Gemma3-Mean": "62.72", "Gemma3-Last": "15.66", "Qwen3.5-Mean": "63.29", "Qwen3.5-Last": "21.67", "Dedicated Mean": "70.03", "Base-Mean": "63.00", "Base-Last": "18.66"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "68.13", "Qwen3-Emb": "70.16", "Gemma3-Mean": "66.39", "Gemma3-Last": "15.70", "Qwen3.5-Mean": "66.69", "Qwen3.5-Last": "20.26", "Dedicated Mean": "69.14", "Base-Mean": "66.54", "Base-Last": "17.98"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "67.73", "Qwen3-Emb": "69.97", "Gemma3-Mean": "66.18", "Gemma3-Last": "15.91", "Qwen3.5-Mean": "66.87", "Qwen3.5-Last": "22.52", "Dedicated Mean": "68.85", "Base-Mean": "66.53", "Base-Last": "19.21"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "67.57", "Qwen3-Emb": "70.15", "Gemma3-Mean": "66.32", "Gemma3-Last": "15.85", "Qwen3.5-Mean": "66.98", "Qwen3.5-Last": "21.43", "Dedicated Mean": "68.86", "Base-Mean": "66.65", "Base-Last": "18.64"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "66.27", "Qwen3-Emb": "67.24", "Gemma3-Mean": "57.53", "Gemma3-Last": "18.22", "Qwen3.5-Mean": "43.94", "Qwen3.5-Last": "17.09", "Dedicated Mean": "66.75", "Base-Mean": "50.73", "Base-Last": "17.66"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "63.67", "Qwen3-Emb": "67.71", "Gemma3-Mean": "51.55", "Gemma3-Last": "12.83", "Qwen3.5-Mean": "52.09", "Qwen3.5-Last": "12.94", "Dedicated Mean": "65.69", "Base-Mean": "51.82", "Base-Last": "12.88"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "67.86", "Qwen3-Emb": "70.07", "Gemma3-Mean": "60.73", "Gemma3-Last": "16.51", "Qwen3.5-Mean": "64.21", "Qwen3.5-Last": "28.26", "Dedicated Mean": "68.97", "Base-Mean": "62.47", "Base-Last": "22.39"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "65.97", "Qwen3-Emb": "69.31", "Gemma3-Mean": "54.67", "Gemma3-Last": "14.92", "Qwen3.5-Mean": "55.08", "Qwen3.5-Last": "18.56", "Dedicated Mean": "67.64", "Base-Mean": "54.88", "Base-Last": "16.74"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "65.47", "Qwen3-Emb": "68.36", "Gemma3-Mean": "60.82", "Gemma3-Last": "16.14", "Qwen3.5-Mean": "64.03", "Qwen3.5-Last": "28.42", "Dedicated Mean": "66.91", "Base-Mean": "62.42", "Base-Last": "22.28"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "63.88", "Qwen3-Emb": "67.65", "Gemma3-Mean": "51.73", "Gemma3-Last": "13.34", "Qwen3.5-Mean": "52.07", "Qwen3.5-Last": "13.45", "Dedicated Mean": "65.77", "Base-Mean": "51.90", "Base-Last": "13.39"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "66.18", "Qwen3-Emb": "68.76", "Gemma3-Mean": "55.57", "Gemma3-Last": "15.15", "Qwen3.5-Mean": "55.06", "Qwen3.5-Last": "18.95", "Dedicated Mean": "67.47", "Base-Mean": "55.31", "Base-Last": "17.05"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "65.47", "Qwen3-Emb": "68.36", "Gemma3-Mean": "55.56", "Gemma3-Last": "15.12", "Qwen3.5-Mean": "55.04", "Qwen3.5-Last": "18.93", "Dedicated Mean": "66.91", "Base-Mean": "55.30", "Base-Last": "17.02"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "64.02", "Qwen3-Emb": "67.77", "Gemma3-Mean": "60.82", "Gemma3-Last": "16.14", "Qwen3.5-Mean": "64.03", "Qwen3.5-Last": "28.42", "Dedicated Mean": "65.89", "Base-Mean": "62.42", "Base-Last": "22.28"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "65.61", "Qwen3-Emb": "68.66", "Gemma3-Mean": "57.79", "Gemma3-Last": "15.77", "Qwen3.5-Mean": "60.05", "Qwen3.5-Last": "23.86", "Dedicated Mean": "67.13", "Base-Mean": "58.92", "Base-Last": "19.81"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "66.18", "Qwen3-Emb": "68.76", "Gemma3-Mean": "60.83", "Gemma3-Last": "16.17", "Qwen3.5-Mean": "64.06", "Qwen3.5-Last": "28.45", "Dedicated Mean": "67.47", "Base-Mean": "62.45", "Base-Last": "22.31"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "65.44", "Qwen3-Emb": "68.34", "Gemma3-Mean": "60.67", "Gemma3-Last": "16.04", "Qwen3.5-Mean": "63.74", "Qwen3.5-Last": "28.20", "Dedicated Mean": "66.89", "Base-Mean": "62.20", "Base-Last": "22.12"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "65.24", "Qwen3-Emb": "68.90", "Gemma3-Mean": "60.71", "Gemma3-Last": "15.94", "Qwen3.5-Mean": "64.18", "Qwen3.5-Last": "28.23", "Dedicated Mean": "67.07", "Base-Mean": "62.45", "Base-Last": "22.09"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "63.13", "Qwen3-Emb": "65.63", "Gemma3-Mean": "54.38", "Gemma3-Last": "18.86", "Qwen3.5-Mean": "39.73", "Qwen3.5-Last": "15.62", "Dedicated Mean": "64.38", "Base-Mean": "47.05", "Base-Last": "17.24"}, {"Dataset": "STS22.v2", "k": "64", "Method": "PCA-k", "EmbGemma": "59.66", "Qwen3-Emb": "64.85", "Gemma3-Mean": "48.65", "Gemma3-Last": "11.69", "Qwen3.5-Mean": "49.74", "Qwen3.5-Last": "9.31", "Dedicated Mean": "62.25", "Base-Mean": "49.20", "Base-Last": "10.50"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Whitening-k", "EmbGemma": "63.83", "Qwen3-Emb": "66.56", "Gemma3-Mean": "56.11", "Gemma3-Last": "16.94", "Qwen3.5-Mean": "58.95", "Qwen3.5-Last": "22.98", "Dedicated Mean": "65.19", "Base-Mean": "57.53", "Base-Last": "19.96"}, {"Dataset": "STS22.v2", "k": "64", "Method": "SpecTemp", "EmbGemma": "63.50", "Qwen3-Emb": "66.56", "Gemma3-Mean": "54.14", "Gemma3-Last": "15.72", "Qwen3.5-Mean": "55.66", "Qwen3.5-Last": "18.41", "Dedicated Mean": "65.03", "Base-Mean": "54.90", "Base-Last": "17.07"}, {"Dataset": "STS22.v2", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "62.69", "Qwen3-Emb": "65.96", "Gemma3-Mean": "56.16", "Gemma3-Last": "15.94", "Qwen3.5-Mean": "58.61", "Qwen3.5-Last": "23.15", "Dedicated Mean": "64.32", "Base-Mean": "57.38", "Base-Last": "19.54"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "59.84", "Qwen3-Emb": "64.86", "Gemma3-Mean": "48.82", "Gemma3-Last": "12.29", "Qwen3.5-Mean": "49.71", "Qwen3.5-Last": "9.76", "Dedicated Mean": "62.35", "Base-Mean": "49.27", "Base-Last": "11.02"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "63.50", "Qwen3-Emb": "66.25", "Gemma3-Mean": "55.12", "Gemma3-Last": "15.81", "Qwen3.5-Mean": "55.50", "Qwen3.5-Last": "18.67", "Dedicated Mean": "64.88", "Base-Mean": "55.31", "Base-Last": "17.24"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "62.69", "Qwen3-Emb": "65.96", "Gemma3-Mean": "55.12", "Gemma3-Last": "15.79", "Qwen3.5-Mean": "55.50", "Qwen3.5-Last": "18.67", "Dedicated Mean": "64.32", "Base-Mean": "55.31", "Base-Last": "17.23"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "59.97", "Qwen3-Emb": "64.96", "Gemma3-Mean": "56.16", "Gemma3-Last": "15.94", "Qwen3.5-Mean": "58.61", "Qwen3.5-Last": "23.15", "Dedicated Mean": "62.46", "Base-Mean": "57.38", "Base-Last": "19.54"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "61.53", "Qwen3-Emb": "65.67", "Gemma3-Mean": "53.73", "Gemma3-Last": "15.35", "Qwen3.5-Mean": "55.65", "Qwen3.5-Last": "18.46", "Dedicated Mean": "63.60", "Base-Mean": "54.69", "Base-Last": "16.91"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "63.50", "Qwen3-Emb": "66.25", "Gemma3-Mean": "56.16", "Gemma3-Last": "15.97", "Qwen3.5-Mean": "58.61", "Qwen3.5-Last": "23.15", "Dedicated Mean": "64.88", "Base-Mean": "57.38", "Base-Last": "19.56"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "62.62", "Qwen3-Emb": "65.92", "Gemma3-Mean": "56.12", "Gemma3-Last": "15.76", "Qwen3.5-Mean": "58.54", "Qwen3.5-Last": "22.94", "Dedicated Mean": "64.27", "Base-Mean": "57.33", "Base-Last": "19.35"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "62.60", "Qwen3-Emb": "66.34", "Gemma3-Mean": "56.10", "Gemma3-Last": "15.72", "Qwen3.5-Mean": "58.95", "Qwen3.5-Last": "22.98", "Dedicated Mean": "64.47", "Base-Mean": "57.53", "Base-Last": "19.35"}], "task_comp::Similarity (STS)::Pearson (r × 100)::Retention %": [{"Dataset": "STSBenchmark", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "100.0%", "Qwen3-Emb": "100.0%", "Gemma3-Mean": "84.2%", "Gemma3-Last": "89.5%", "Qwen3.5-Mean": "98.3%", "Qwen3.5-Last": "93.0%", "Dedicated Mean": "100.0%", "Base-Mean": "91.2%", "Base-Last": "91.3%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "PCA-k", "EmbGemma": "100.1%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "138.7%", "Gemma3-Last": "157.6%", "Qwen3.5-Mean": "111.0%", "Qwen3.5-Last": "141.8%", "Dedicated Mean": "100.5%", "Base-Mean": "124.8%", "Base-Last": "149.7%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Whitening-k", "EmbGemma": "97.1%", "Qwen3-Emb": "94.5%", "Gemma3-Mean": "180.4%", "Gemma3-Last": "231.8%", "Qwen3.5-Mean": "141.7%", "Qwen3.5-Last": "232.1%", "Dedicated Mean": "95.8%", "Base-Mean": "161.1%", "Base-Last": "232.0%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "SpecTemp", "EmbGemma": "100.6%", "Qwen3-Emb": "101.0%", "Gemma3-Mean": "141.7%", "Gemma3-Last": "162.2%", "Qwen3.5-Mean": "112.8%", "Qwen3.5-Last": "145.0%", "Dedicated Mean": "100.8%", "Base-Mean": "127.3%", "Base-Last": "153.6%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "100.8%", "Qwen3-Emb": "101.3%", "Gemma3-Mean": "180.7%", "Gemma3-Last": "233.0%", "Qwen3.5-Mean": "142.3%", "Qwen3.5-Last": "233.7%", "Dedicated Mean": "101.1%", "Base-Mean": "161.5%", "Base-Last": "233.3%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.2%", "Qwen3-Emb": "100.9%", "Gemma3-Mean": "139.7%", "Gemma3-Last": "164.0%", "Qwen3.5-Mean": "111.5%", "Qwen3.5-Last": "144.7%", "Dedicated Mean": "100.5%", "Base-Mean": "125.6%", "Base-Last": "154.3%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.6%", "Qwen3-Emb": "101.0%", "Gemma3-Mean": "142.0%", "Gemma3-Last": "166.8%", "Qwen3.5-Mean": "113.3%", "Qwen3.5-Last": "147.6%", "Dedicated Mean": "100.8%", "Base-Mean": "127.7%", "Base-Last": "157.2%"}, {"Dataset": "STSBenchmark", "k": "512", "Method": "w/o Crowd. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "98.0%", "Qwen3-Emb": "100.5%", "Gemma3-Mean": "135.2%", "Gemma3-Last": "158.1%", "Qwen3.5-Mean": "109.0%", "Qwen3.5-Last": "140.0%", "Dedicated Mean": "99.3%", "Base-Mean": "122.1%", "Base-Last": "149.0%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.7%", "Qwen3-Emb": "101.2%", "Gemma3-Mean": "142.1%", "Gemma3-Last": "167.7%", "Qwen3.5-Mean": "114.5%", "Qwen3.5-Last": "150.7%", "Dedicated Mean": "100.4%", "Base-Mean": "128.3%", "Base-Last": "159.2%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "99.0%", "Qwen3-Emb": "101.0%", "Gemma3-Mean": "142.1%", "Gemma3-Last": "167.6%", "Qwen3.5-Mean": "114.5%", "Qwen3.5-Last": "150.6%", "Dedicated Mean": "100.0%", "Base-Mean": "128.3%", "Base-Last": "159.1%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "98.8%", "Qwen3-Emb": "101.1%", "Gemma3-Mean": "178.8%", "Gemma3-Last": "236.3%", "Qwen3.5-Mean": "142.2%", "Qwen3.5-Last": "234.8%", "Dedicated Mean": "100.0%", "Base-Mean": "160.5%", "Base-Last": "235.5%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.9%", "Qwen3-Emb": "101.5%", "Gemma3-Mean": "169.7%", "Gemma3-Last": "220.6%", "Qwen3.5-Mean": "136.8%", "Qwen3.5-Last": "214.8%", "Dedicated Mean": "101.2%", "Base-Mean": "153.2%", "Base-Last": "217.7%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.7%", "Qwen3-Emb": "101.3%", "Gemma3-Mean": "178.8%", "Gemma3-Last": "236.3%", "Qwen3.5-Mean": "142.2%", "Qwen3.5-Last": "234.8%", "Dedicated Mean": "100.5%", "Base-Mean": "160.5%", "Base-Last": "235.5%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.0%", "Qwen3-Emb": "101.0%", "Gemma3-Mean": "178.4%", "Gemma3-Last": "235.3%", "Qwen3.5-Mean": "141.9%", "Qwen3.5-Last": "234.0%", "Dedicated Mean": "100.0%", "Base-Mean": "160.2%", "Base-Last": "234.6%"}, {"Dataset": "STSBenchmark", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.2%", "Qwen3-Emb": "101.0%", "Gemma3-Mean": "178.7%", "Gemma3-Last": "236.0%", "Qwen3.5-Mean": "142.1%", "Qwen3.5-Last": "234.8%", "Dedicated Mean": "100.1%", "Base-Mean": "160.4%", "Base-Last": "235.4%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "97.8%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "131.0%", "Gemma3-Last": "153.1%", "Qwen3.5-Mean": "88.9%", "Qwen3.5-Last": "111.9%", "Dedicated Mean": "98.0%", "Base-Mean": "109.9%", "Base-Last": "132.5%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "PCA-k", "EmbGemma": "93.5%", "Qwen3-Emb": "98.7%", "Gemma3-Mean": "125.2%", "Gemma3-Last": "139.4%", "Qwen3.5-Mean": "103.0%", "Qwen3.5-Last": "128.5%", "Dedicated Mean": "96.1%", "Base-Mean": "114.1%", "Base-Last": "133.9%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Whitening-k", "EmbGemma": "98.8%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "170.5%", "Gemma3-Last": "228.9%", "Qwen3.5-Mean": "137.0%", "Qwen3.5-Last": "229.4%", "Dedicated Mean": "99.3%", "Base-Mean": "153.7%", "Base-Last": "229.2%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "SpecTemp", "EmbGemma": "97.2%", "Qwen3-Emb": "100.7%", "Gemma3-Mean": "141.6%", "Gemma3-Last": "170.6%", "Qwen3.5-Mean": "114.6%", "Qwen3.5-Last": "154.0%", "Dedicated Mean": "99.0%", "Base-Mean": "128.1%", "Base-Last": "162.3%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "95.9%", "Qwen3-Emb": "100.5%", "Gemma3-Mean": "170.5%", "Gemma3-Last": "229.0%", "Qwen3.5-Mean": "136.9%", "Qwen3.5-Last": "229.5%", "Dedicated Mean": "98.2%", "Base-Mean": "153.7%", "Base-Last": "229.2%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "93.5%", "Qwen3-Emb": "98.8%", "Gemma3-Mean": "126.3%", "Gemma3-Last": "146.2%", "Qwen3.5-Mean": "103.6%", "Qwen3.5-Last": "131.5%", "Dedicated Mean": "96.1%", "Base-Mean": "114.9%", "Base-Last": "138.8%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "96.9%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "139.3%", "Gemma3-Last": "165.9%", "Qwen3.5-Mean": "115.0%", "Qwen3.5-Last": "155.0%", "Dedicated Mean": "98.8%", "Base-Mean": "127.2%", "Base-Last": "160.5%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "95.9%", "Qwen3-Emb": "100.5%", "Gemma3-Mean": "139.3%", "Gemma3-Last": "165.9%", "Qwen3.5-Mean": "115.0%", "Qwen3.5-Last": "155.0%", "Dedicated Mean": "98.2%", "Base-Mean": "127.2%", "Base-Last": "160.4%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "94.5%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "170.5%", "Gemma3-Last": "229.0%", "Qwen3.5-Mean": "136.9%", "Qwen3.5-Last": "229.5%", "Dedicated Mean": "97.1%", "Base-Mean": "153.7%", "Base-Last": "229.2%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "97.5%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "158.7%", "Gemma3-Last": "208.0%", "Qwen3.5-Mean": "129.9%", "Qwen3.5-Last": "203.8%", "Dedicated Mean": "99.2%", "Base-Mean": "144.3%", "Base-Last": "205.9%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "96.9%", "Qwen3-Emb": "100.8%", "Gemma3-Mean": "170.5%", "Gemma3-Last": "229.0%", "Qwen3.5-Mean": "136.9%", "Qwen3.5-Last": "229.5%", "Dedicated Mean": "98.8%", "Base-Mean": "153.7%", "Base-Last": "229.3%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "95.7%", "Qwen3-Emb": "100.3%", "Gemma3-Mean": "169.9%", "Gemma3-Last": "227.4%", "Qwen3.5-Mean": "136.6%", "Qwen3.5-Last": "227.8%", "Dedicated Mean": "98.0%", "Base-Mean": "153.3%", "Base-Last": "227.6%"}, {"Dataset": "STSBenchmark", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "96.2%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "170.5%", "Gemma3-Last": "228.9%", "Qwen3.5-Mean": "137.0%", "Qwen3.5-Last": "229.4%", "Dedicated Mean": "98.3%", "Base-Mean": "153.7%", "Base-Last": "229.2%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "94.1%", "Qwen3-Emb": "95.8%", "Gemma3-Mean": "129.5%", "Gemma3-Last": "141.9%", "Qwen3.5-Mean": "77.6%", "Qwen3.5-Last": "93.5%", "Dedicated Mean": "95.0%", "Base-Mean": "103.6%", "Base-Last": "117.7%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "PCA-k", "EmbGemma": "86.5%", "Qwen3-Emb": "94.3%", "Gemma3-Mean": "113.1%", "Gemma3-Last": "122.4%", "Qwen3.5-Mean": "95.4%", "Qwen3.5-Last": "115.8%", "Dedicated Mean": "90.4%", "Base-Mean": "104.3%", "Base-Last": "119.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Whitening-k", "EmbGemma": "94.9%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "154.7%", "Gemma3-Last": "209.4%", "Qwen3.5-Mean": "128.0%", "Qwen3.5-Last": "210.8%", "Dedicated Mean": "96.6%", "Base-Mean": "141.3%", "Base-Last": "210.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "SpecTemp", "EmbGemma": "92.8%", "Qwen3-Emb": "98.3%", "Gemma3-Mean": "139.2%", "Gemma3-Last": "173.5%", "Qwen3.5-Mean": "115.8%", "Qwen3.5-Last": "163.3%", "Dedicated Mean": "95.6%", "Base-Mean": "127.5%", "Base-Last": "168.4%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "91.1%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "154.9%", "Gemma3-Last": "209.9%", "Qwen3.5-Mean": "128.0%", "Qwen3.5-Last": "210.6%", "Dedicated Mean": "94.6%", "Base-Mean": "141.4%", "Base-Last": "210.2%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "86.4%", "Qwen3-Emb": "94.5%", "Gemma3-Mean": "114.3%", "Gemma3-Last": "128.9%", "Qwen3.5-Mean": "95.9%", "Qwen3.5-Last": "118.7%", "Dedicated Mean": "90.5%", "Base-Mean": "105.1%", "Base-Last": "123.8%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "92.3%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "135.7%", "Gemma3-Last": "162.5%", "Qwen3.5-Mean": "116.0%", "Qwen3.5-Last": "161.7%", "Dedicated Mean": "95.4%", "Base-Mean": "125.8%", "Base-Last": "162.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "91.1%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "135.7%", "Gemma3-Last": "162.5%", "Qwen3.5-Mean": "116.0%", "Qwen3.5-Last": "161.7%", "Dedicated Mean": "94.6%", "Base-Mean": "125.8%", "Base-Last": "162.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "87.6%", "Qwen3-Emb": "95.7%", "Gemma3-Mean": "154.9%", "Gemma3-Last": "209.9%", "Qwen3.5-Mean": "128.0%", "Qwen3.5-Last": "210.6%", "Dedicated Mean": "91.6%", "Base-Mean": "141.4%", "Base-Last": "210.2%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "91.5%", "Qwen3-Emb": "97.8%", "Gemma3-Mean": "142.8%", "Gemma3-Last": "186.3%", "Qwen3.5-Mean": "120.2%", "Qwen3.5-Last": "184.0%", "Dedicated Mean": "94.6%", "Base-Mean": "131.5%", "Base-Last": "185.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "92.3%", "Qwen3-Emb": "98.4%", "Gemma3-Mean": "154.9%", "Gemma3-Last": "209.9%", "Qwen3.5-Mean": "128.0%", "Qwen3.5-Last": "210.6%", "Dedicated Mean": "95.4%", "Base-Mean": "141.4%", "Base-Last": "210.2%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "90.7%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "154.6%", "Gemma3-Last": "208.7%", "Qwen3.5-Mean": "127.8%", "Qwen3.5-Last": "209.6%", "Dedicated Mean": "94.3%", "Base-Mean": "141.2%", "Base-Last": "209.1%"}, {"Dataset": "STSBenchmark", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "91.7%", "Qwen3-Emb": "98.1%", "Gemma3-Mean": "154.7%", "Gemma3-Last": "209.4%", "Qwen3.5-Mean": "128.0%", "Qwen3.5-Last": "210.8%", "Dedicated Mean": "94.9%", "Base-Mean": "141.3%", "Base-Last": "210.1%"}, {"Dataset": "SICK-R", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "100.0%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "98.1%", "Gemma3-Last": "82.6%", "Qwen3.5-Mean": "99.7%", "Qwen3.5-Last": "99.5%", "Dedicated Mean": "100.2%", "Base-Mean": "98.9%", "Base-Last": "91.0%"}, {"Dataset": "SICK-R", "k": "512", "Method": "PCA-k", "EmbGemma": "100.3%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "111.7%", "Gemma3-Last": "118.5%", "Qwen3.5-Mean": "106.5%", "Qwen3.5-Last": "108.3%", "Dedicated Mean": "100.1%", "Base-Mean": "109.1%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "512", "Method": "Whitening-k", "EmbGemma": "83.6%", "Qwen3-Emb": "80.0%", "Gemma3-Mean": "113.8%", "Gemma3-Last": "113.8%", "Qwen3.5-Mean": "106.9%", "Qwen3.5-Last": "100.9%", "Dedicated Mean": "81.8%", "Base-Mean": "110.3%", "Base-Last": "107.3%"}, {"Dataset": "SICK-R", "k": "512", "Method": "SpecTemp", "EmbGemma": "100.4%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "112.4%", "Gemma3-Last": "118.9%", "Qwen3.5-Mean": "107.3%", "Qwen3.5-Last": "108.5%", "Dedicated Mean": "100.1%", "Base-Mean": "109.9%", "Base-Last": "113.7%"}, {"Dataset": "SICK-R", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "99.9%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "114.2%", "Gemma3-Last": "114.5%", "Qwen3.5-Mean": "107.9%", "Qwen3.5-Last": "102.0%", "Dedicated Mean": "98.6%", "Base-Mean": "111.0%", "Base-Last": "108.3%"}, {"Dataset": "SICK-R", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.3%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "111.8%", "Gemma3-Last": "118.8%", "Qwen3.5-Mean": "106.6%", "Qwen3.5-Last": "108.8%", "Dedicated Mean": "100.1%", "Base-Mean": "109.2%", "Base-Last": "113.8%"}, {"Dataset": "SICK-R", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.4%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "112.5%", "Gemma3-Last": "119.1%", "Qwen3.5-Mean": "107.4%", "Qwen3.5-Last": "108.9%", "Dedicated Mean": "100.1%", "Base-Mean": "109.9%", "Base-Last": "114.0%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.4%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "112.5%", "Gemma3-Last": "119.1%", "Qwen3.5-Mean": "107.4%", "Qwen3.5-Last": "108.9%", "Dedicated Mean": "100.1%", "Base-Mean": "109.9%", "Base-Last": "114.0%"}, {"Dataset": "SICK-R", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.9%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "114.2%", "Gemma3-Last": "114.5%", "Qwen3.5-Mean": "107.9%", "Qwen3.5-Last": "102.0%", "Dedicated Mean": "98.6%", "Base-Mean": "111.0%", "Base-Last": "108.3%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "98.7%", "Qwen3-Emb": "94.9%", "Gemma3-Mean": "120.7%", "Gemma3-Last": "120.2%", "Qwen3.5-Mean": "115.7%", "Qwen3.5-Last": "107.9%", "Dedicated Mean": "96.8%", "Base-Mean": "118.2%", "Base-Last": "114.0%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "97.5%", "Qwen3-Emb": "95.6%", "Gemma3-Mean": "113.8%", "Gemma3-Last": "113.8%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "100.9%", "Dedicated Mean": "96.6%", "Base-Mean": "110.3%", "Base-Last": "107.3%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.2%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "115.6%", "Gemma3-Last": "116.4%", "Qwen3.5-Mean": "109.9%", "Qwen3.5-Last": "103.9%", "Dedicated Mean": "98.9%", "Base-Mean": "112.7%", "Base-Last": "110.1%"}, {"Dataset": "SICK-R", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "99.9%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "114.2%", "Gemma3-Last": "114.5%", "Qwen3.5-Mean": "107.9%", "Qwen3.5-Last": "102.0%", "Dedicated Mean": "98.7%", "Base-Mean": "111.0%", "Base-Last": "108.3%"}, {"Dataset": "SICK-R", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "99.3%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "92.0%", "Gemma3-Last": "83.9%", "Qwen3.5-Mean": "97.9%", "Qwen3.5-Last": "100.8%", "Dedicated Mean": "99.6%", "Base-Mean": "95.0%", "Base-Last": "92.3%"}, {"Dataset": "SICK-R", "k": "256", "Method": "PCA-k", "EmbGemma": "100.1%", "Qwen3-Emb": "100.1%", "Gemma3-Mean": "110.9%", "Gemma3-Last": "118.4%", "Qwen3.5-Mean": "105.7%", "Qwen3.5-Last": "108.4%", "Dedicated Mean": "100.1%", "Base-Mean": "108.3%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "256", "Method": "Whitening-k", "EmbGemma": "89.7%", "Qwen3-Emb": "85.4%", "Gemma3-Mean": "118.9%", "Gemma3-Last": "118.4%", "Qwen3.5-Mean": "112.1%", "Qwen3.5-Last": "105.2%", "Dedicated Mean": "87.6%", "Base-Mean": "115.5%", "Base-Last": "111.8%"}, {"Dataset": "SICK-R", "k": "256", "Method": "SpecTemp", "EmbGemma": "100.7%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "113.2%", "Gemma3-Last": "120.0%", "Qwen3.5-Mean": "108.4%", "Qwen3.5-Last": "109.3%", "Dedicated Mean": "100.2%", "Base-Mean": "110.8%", "Base-Last": "114.7%"}, {"Dataset": "SICK-R", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "100.4%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "118.9%", "Gemma3-Last": "118.5%", "Qwen3.5-Mean": "112.2%", "Qwen3.5-Last": "105.3%", "Dedicated Mean": "99.2%", "Base-Mean": "115.5%", "Base-Last": "111.9%"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.1%", "Qwen3-Emb": "100.1%", "Gemma3-Mean": "111.0%", "Gemma3-Last": "118.7%", "Qwen3.5-Mean": "105.8%", "Qwen3.5-Last": "108.8%", "Dedicated Mean": "100.1%", "Base-Mean": "108.3%", "Base-Last": "113.8%"}, {"Dataset": "SICK-R", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.7%", "Qwen3-Emb": "99.8%", "Gemma3-Mean": "113.3%", "Gemma3-Last": "120.0%", "Qwen3.5-Mean": "108.5%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "100.3%", "Base-Mean": "110.9%", "Base-Last": "114.7%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.7%", "Qwen3-Emb": "99.9%", "Gemma3-Mean": "113.3%", "Gemma3-Last": "120.0%", "Qwen3.5-Mean": "108.5%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "100.3%", "Base-Mean": "110.9%", "Base-Last": "114.7%"}, {"Dataset": "SICK-R", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.4%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "118.9%", "Gemma3-Last": "118.5%", "Qwen3.5-Mean": "112.2%", "Qwen3.5-Last": "105.3%", "Dedicated Mean": "99.2%", "Base-Mean": "115.5%", "Base-Last": "111.9%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "99.3%", "Qwen3-Emb": "95.6%", "Gemma3-Mean": "122.5%", "Gemma3-Last": "122.0%", "Qwen3.5-Mean": "117.5%", "Qwen3.5-Last": "109.6%", "Dedicated Mean": "97.5%", "Base-Mean": "120.0%", "Base-Last": "115.8%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "99.5%", "Qwen3-Emb": "97.2%", "Gemma3-Mean": "118.9%", "Gemma3-Last": "118.4%", "Qwen3.5-Mean": "112.1%", "Qwen3.5-Last": "105.2%", "Dedicated Mean": "98.3%", "Base-Mean": "115.5%", "Base-Last": "111.8%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.8%", "Qwen3-Emb": "98.5%", "Gemma3-Mean": "119.4%", "Gemma3-Last": "119.5%", "Qwen3.5-Mean": "113.2%", "Qwen3.5-Last": "106.5%", "Dedicated Mean": "99.7%", "Base-Mean": "116.3%", "Base-Last": "113.0%"}, {"Dataset": "SICK-R", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.4%", "Qwen3-Emb": "98.0%", "Gemma3-Mean": "118.8%", "Gemma3-Last": "118.5%", "Qwen3.5-Mean": "112.1%", "Qwen3.5-Last": "105.3%", "Dedicated Mean": "99.2%", "Base-Mean": "115.5%", "Base-Last": "111.9%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "98.6%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "98.3%", "Gemma3-Last": "112.8%", "Qwen3.5-Mean": "96.6%", "Qwen3.5-Last": "99.4%", "Dedicated Mean": "99.0%", "Base-Mean": "97.5%", "Base-Last": "106.1%"}, {"Dataset": "SICK-R", "k": "128", "Method": "PCA-k", "EmbGemma": "98.8%", "Qwen3-Emb": "100.1%", "Gemma3-Mean": "108.8%", "Gemma3-Last": "117.7%", "Qwen3.5-Mean": "103.8%", "Qwen3.5-Last": "108.1%", "Dedicated Mean": "99.5%", "Base-Mean": "106.3%", "Base-Last": "112.9%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Whitening-k", "EmbGemma": "94.8%", "Qwen3-Emb": "90.6%", "Gemma3-Mean": "120.6%", "Gemma3-Last": "122.8%", "Qwen3.5-Mean": "115.1%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "92.7%", "Base-Mean": "117.8%", "Base-Last": "116.1%"}, {"Dataset": "SICK-R", "k": "128", "Method": "SpecTemp", "EmbGemma": "100.8%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "114.6%", "Gemma3-Last": "121.7%", "Qwen3.5-Mean": "110.4%", "Qwen3.5-Last": "110.7%", "Dedicated Mean": "100.0%", "Base-Mean": "112.5%", "Base-Last": "116.2%"}, {"Dataset": "SICK-R", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "101.1%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "120.7%", "Gemma3-Last": "122.8%", "Qwen3.5-Mean": "115.1%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "100.2%", "Base-Mean": "117.9%", "Base-Last": "116.1%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "98.8%", "Qwen3-Emb": "100.2%", "Gemma3-Mean": "108.9%", "Gemma3-Last": "118.1%", "Qwen3.5-Mean": "103.9%", "Qwen3.5-Last": "108.6%", "Dedicated Mean": "99.5%", "Base-Mean": "106.4%", "Base-Last": "113.4%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.8%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "114.7%", "Gemma3-Last": "121.5%", "Qwen3.5-Mean": "110.5%", "Qwen3.5-Last": "110.3%", "Dedicated Mean": "100.0%", "Base-Mean": "112.6%", "Base-Last": "115.9%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.8%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "114.7%", "Gemma3-Last": "121.5%", "Qwen3.5-Mean": "110.5%", "Qwen3.5-Last": "110.3%", "Dedicated Mean": "100.1%", "Base-Mean": "112.6%", "Base-Last": "115.9%"}, {"Dataset": "SICK-R", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "101.1%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "120.7%", "Gemma3-Last": "122.8%", "Qwen3.5-Mean": "115.1%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "100.2%", "Base-Mean": "117.9%", "Base-Last": "116.1%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.6%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "122.3%", "Gemma3-Last": "123.6%", "Qwen3.5-Mean": "117.9%", "Qwen3.5-Last": "111.6%", "Dedicated Mean": "99.0%", "Base-Mean": "120.1%", "Base-Last": "117.6%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "101.0%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "120.7%", "Gemma3-Last": "122.8%", "Qwen3.5-Mean": "115.1%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "100.0%", "Base-Mean": "117.9%", "Base-Last": "116.1%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "101.2%", "Qwen3-Emb": "99.6%", "Gemma3-Mean": "120.9%", "Gemma3-Last": "123.2%", "Qwen3.5-Mean": "115.6%", "Qwen3.5-Last": "110.0%", "Dedicated Mean": "100.4%", "Base-Mean": "118.2%", "Base-Last": "116.6%"}, {"Dataset": "SICK-R", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "101.1%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "120.6%", "Gemma3-Last": "122.8%", "Qwen3.5-Mean": "115.1%", "Qwen3.5-Last": "109.4%", "Dedicated Mean": "100.2%", "Base-Mean": "117.8%", "Base-Last": "116.1%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "95.7%", "Qwen3-Emb": "97.9%", "Gemma3-Mean": "92.7%", "Gemma3-Last": "110.5%", "Qwen3.5-Mean": "93.9%", "Qwen3.5-Last": "90.9%", "Dedicated Mean": "96.8%", "Base-Mean": "93.3%", "Base-Last": "100.7%"}, {"Dataset": "SICK-R", "k": "64", "Method": "PCA-k", "EmbGemma": "95.1%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "105.3%", "Gemma3-Last": "115.5%", "Qwen3.5-Mean": "100.9%", "Qwen3.5-Last": "106.6%", "Dedicated Mean": "97.2%", "Base-Mean": "103.1%", "Base-Last": "111.1%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Whitening-k", "EmbGemma": "98.4%", "Qwen3-Emb": "94.8%", "Gemma3-Mean": "120.8%", "Gemma3-Last": "124.9%", "Qwen3.5-Mean": "116.7%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "96.6%", "Base-Mean": "118.8%", "Base-Last": "118.9%"}, {"Dataset": "SICK-R", "k": "64", "Method": "SpecTemp", "EmbGemma": "100.1%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "116.8%", "Gemma3-Last": "123.4%", "Qwen3.5-Mean": "114.4%", "Qwen3.5-Last": "112.3%", "Dedicated Mean": "98.8%", "Base-Mean": "115.6%", "Base-Last": "117.8%"}, {"Dataset": "SICK-R", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "100.1%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "120.8%", "Gemma3-Last": "125.0%", "Qwen3.5-Mean": "116.7%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "98.9%", "Base-Mean": "118.8%", "Base-Last": "118.9%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "95.2%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "105.4%", "Gemma3-Last": "115.9%", "Qwen3.5-Mean": "101.0%", "Qwen3.5-Last": "107.2%", "Dedicated Mean": "97.2%", "Base-Mean": "103.2%", "Base-Last": "111.6%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.2%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "116.9%", "Gemma3-Last": "122.7%", "Qwen3.5-Mean": "114.5%", "Qwen3.5-Last": "111.2%", "Dedicated Mean": "98.8%", "Base-Mean": "115.7%", "Base-Last": "117.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.1%", "Qwen3-Emb": "97.7%", "Gemma3-Mean": "116.9%", "Gemma3-Last": "122.7%", "Qwen3.5-Mean": "114.5%", "Qwen3.5-Last": "111.2%", "Dedicated Mean": "98.9%", "Base-Mean": "115.7%", "Base-Last": "117.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "99.8%", "Qwen3-Emb": "100.1%", "Gemma3-Mean": "120.8%", "Gemma3-Last": "125.0%", "Qwen3.5-Mean": "116.7%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "99.9%", "Base-Mean": "118.8%", "Base-Last": "118.9%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "100.3%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "119.8%", "Gemma3-Last": "122.9%", "Qwen3.5-Mean": "116.8%", "Qwen3.5-Last": "112.3%", "Dedicated Mean": "99.8%", "Base-Mean": "118.3%", "Base-Last": "117.6%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.2%", "Qwen3-Emb": "97.5%", "Gemma3-Mean": "120.8%", "Gemma3-Last": "125.0%", "Qwen3.5-Mean": "116.7%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "98.8%", "Base-Mean": "118.8%", "Base-Last": "118.9%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "99.8%", "Qwen3-Emb": "98.5%", "Gemma3-Mean": "120.9%", "Gemma3-Last": "125.0%", "Qwen3.5-Mean": "116.9%", "Qwen3.5-Last": "113.0%", "Dedicated Mean": "99.1%", "Base-Mean": "118.9%", "Base-Last": "119.0%"}, {"Dataset": "SICK-R", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.0%", "Qwen3-Emb": "97.6%", "Gemma3-Mean": "120.8%", "Gemma3-Last": "124.9%", "Qwen3.5-Mean": "116.7%", "Qwen3.5-Last": "112.9%", "Dedicated Mean": "98.8%", "Base-Mean": "118.8%", "Base-Last": "118.9%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "100.3%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "91.1%", "Gemma3-Last": "75.2%", "Qwen3.5-Mean": "98.5%", "Qwen3.5-Last": "85.0%", "Dedicated Mean": "99.6%", "Base-Mean": "94.8%", "Base-Last": "80.1%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "PCA-k", "EmbGemma": "100.3%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "111.3%", "Gemma3-Last": "100.2%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "89.0%", "Dedicated Mean": "99.6%", "Base-Mean": "109.1%", "Base-Last": "94.6%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Whitening-k", "EmbGemma": "67.4%", "Qwen3-Emb": "36.7%", "Gemma3-Mean": "96.7%", "Gemma3-Last": "80.2%", "Qwen3.5-Mean": "82.6%", "Qwen3.5-Last": "50.2%", "Dedicated Mean": "52.1%", "Base-Mean": "89.7%", "Base-Last": "65.2%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "SpecTemp", "EmbGemma": "100.3%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "111.3%", "Gemma3-Last": "100.2%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "89.0%", "Dedicated Mean": "99.6%", "Base-Mean": "109.1%", "Base-Last": "94.6%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "100.7%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "133.0%", "Gemma3-Last": "112.8%", "Qwen3.5-Mean": "131.2%", "Qwen3.5-Last": "134.9%", "Dedicated Mean": "99.9%", "Base-Mean": "132.1%", "Base-Last": "123.9%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.5%", "Qwen3-Emb": "98.8%", "Gemma3-Mean": "111.6%", "Gemma3-Last": "103.5%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "92.8%", "Dedicated Mean": "99.7%", "Base-Mean": "109.2%", "Base-Last": "98.2%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "100.5%", "Qwen3-Emb": "98.8%", "Gemma3-Mean": "111.6%", "Gemma3-Last": "103.5%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "92.8%", "Dedicated Mean": "99.7%", "Base-Mean": "109.2%", "Base-Last": "98.2%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "100.5%", "Qwen3-Emb": "98.8%", "Gemma3-Mean": "111.6%", "Gemma3-Last": "103.5%", "Qwen3.5-Mean": "106.8%", "Qwen3.5-Last": "92.8%", "Dedicated Mean": "99.7%", "Base-Mean": "109.2%", "Base-Last": "98.2%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.7%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "133.0%", "Gemma3-Last": "112.8%", "Qwen3.5-Mean": "131.2%", "Qwen3.5-Last": "134.9%", "Dedicated Mean": "99.9%", "Base-Mean": "132.1%", "Base-Last": "123.9%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "103.3%", "Qwen3-Emb": "100.2%", "Gemma3-Mean": "127.6%", "Gemma3-Last": "113.0%", "Qwen3.5-Mean": "125.0%", "Qwen3.5-Last": "145.2%", "Dedicated Mean": "101.8%", "Base-Mean": "126.3%", "Base-Last": "129.1%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "100.9%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "96.5%", "Gemma3-Last": "99.7%", "Qwen3.5-Mean": "82.7%", "Qwen3.5-Last": "50.5%", "Dedicated Mean": "100.0%", "Base-Mean": "89.6%", "Base-Last": "75.1%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "100.7%", "Qwen3-Emb": "99.0%", "Gemma3-Mean": "133.0%", "Gemma3-Last": "112.8%", "Qwen3.5-Mean": "131.2%", "Qwen3.5-Last": "134.9%", "Dedicated Mean": "99.9%", "Base-Mean": "132.1%", "Base-Last": "123.9%"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "100.5%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "133.2%", "Gemma3-Last": "113.2%", "Qwen3.5-Mean": "131.3%", "Qwen3.5-Last": "135.6%", "Dedicated Mean": "99.8%", "Base-Mean": "132.2%", "Base-Last": "124.4%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "99.9%", "Qwen3-Emb": "98.6%", "Gemma3-Mean": "84.2%", "Gemma3-Last": "38.1%", "Qwen3.5-Mean": "96.5%", "Qwen3.5-Last": "87.8%", "Dedicated Mean": "99.2%", "Base-Mean": "90.4%", "Base-Last": "62.9%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "PCA-k", "EmbGemma": "100.4%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "111.8%", "Gemma3-Last": "105.6%", "Qwen3.5-Mean": "107.1%", "Qwen3.5-Last": "93.3%", "Dedicated Mean": "99.7%", "Base-Mean": "109.5%", "Base-Last": "99.4%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Whitening-k", "EmbGemma": "106.4%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "137.1%", "Gemma3-Last": "123.9%", "Qwen3.5-Mean": "133.4%", "Qwen3.5-Last": "144.5%", "Dedicated Mean": "102.8%", "Base-Mean": "135.3%", "Base-Last": "134.2%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "SpecTemp", "EmbGemma": "101.7%", "Qwen3-Emb": "99.7%", "Gemma3-Mean": "113.6%", "Gemma3-Last": "111.0%", "Qwen3.5-Mean": "108.5%", "Qwen3.5-Last": "103.2%", "Dedicated Mean": "100.7%", "Base-Mean": "111.1%", "Base-Last": "107.1%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "101.3%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "137.1%", "Gemma3-Last": "126.8%", "Qwen3.5-Mean": "133.9%", "Qwen3.5-Last": "154.6%", "Dedicated Mean": "100.2%", "Base-Mean": "135.5%", "Base-Last": "140.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "100.6%", "Qwen3-Emb": "98.9%", "Gemma3-Mean": "112.1%", "Gemma3-Last": "108.9%", "Qwen3.5-Mean": "107.1%", "Qwen3.5-Last": "97.1%", "Dedicated Mean": "99.8%", "Base-Mean": "109.6%", "Base-Last": "103.0%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "101.9%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "114.4%", "Gemma3-Last": "113.5%", "Qwen3.5-Mean": "108.5%", "Qwen3.5-Last": "106.7%", "Dedicated Mean": "100.7%", "Base-Mean": "111.5%", "Base-Last": "110.1%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "101.3%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "114.3%", "Gemma3-Last": "113.3%", "Qwen3.5-Mean": "108.5%", "Qwen3.5-Last": "106.6%", "Dedicated Mean": "100.2%", "Base-Mean": "111.4%", "Base-Last": "110.0%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "100.8%", "Qwen3-Emb": "99.1%", "Gemma3-Mean": "137.1%", "Gemma3-Last": "126.8%", "Qwen3.5-Mean": "133.9%", "Qwen3.5-Last": "154.6%", "Dedicated Mean": "100.0%", "Base-Mean": "135.5%", "Base-Last": "140.7%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "103.5%", "Qwen3-Emb": "100.4%", "Gemma3-Mean": "129.6%", "Gemma3-Last": "125.0%", "Qwen3.5-Mean": "126.6%", "Qwen3.5-Last": "155.7%", "Dedicated Mean": "102.0%", "Base-Mean": "128.1%", "Base-Last": "140.3%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "101.9%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "137.2%", "Gemma3-Last": "125.3%", "Qwen3.5-Mean": "133.4%", "Qwen3.5-Last": "145.5%", "Dedicated Mean": "100.7%", "Base-Mean": "135.3%", "Base-Last": "135.4%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "101.3%", "Qwen3-Emb": "99.2%", "Gemma3-Mean": "136.7%", "Gemma3-Last": "127.0%", "Qwen3.5-Mean": "133.7%", "Qwen3.5-Last": "161.8%", "Dedicated Mean": "100.2%", "Base-Mean": "135.2%", "Base-Last": "144.4%"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "101.1%", "Qwen3-Emb": "99.4%", "Gemma3-Mean": "137.0%", "Gemma3-Last": "126.5%", "Qwen3.5-Mean": "133.9%", "Qwen3.5-Last": "153.9%", "Dedicated Mean": "100.2%", "Base-Mean": "135.5%", "Base-Last": "140.2%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "99.1%", "Qwen3-Emb": "95.3%", "Gemma3-Mean": "118.9%", "Gemma3-Last": "145.4%", "Qwen3.5-Mean": "87.9%", "Qwen3.5-Last": "122.7%", "Dedicated Mean": "97.2%", "Base-Mean": "103.4%", "Base-Last": "134.1%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "95.2%", "Qwen3-Emb": "96.0%", "Gemma3-Mean": "106.5%", "Gemma3-Last": "102.4%", "Qwen3.5-Mean": "104.2%", "Qwen3.5-Last": "93.0%", "Dedicated Mean": "95.6%", "Base-Mean": "105.3%", "Base-Last": "97.7%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "101.5%", "Qwen3-Emb": "99.3%", "Gemma3-Mean": "125.5%", "Gemma3-Last": "131.8%", "Qwen3.5-Mean": "128.4%", "Qwen3.5-Last": "202.9%", "Dedicated Mean": "100.4%", "Base-Mean": "126.9%", "Base-Last": "167.3%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "98.7%", "Qwen3-Emb": "98.2%", "Gemma3-Mean": "112.9%", "Gemma3-Last": "119.0%", "Qwen3.5-Mean": "110.2%", "Qwen3.5-Last": "133.3%", "Dedicated Mean": "98.5%", "Base-Mean": "111.5%", "Base-Last": "126.1%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "97.9%", "Qwen3-Emb": "96.9%", "Gemma3-Mean": "125.7%", "Gemma3-Last": "128.8%", "Qwen3.5-Mean": "128.0%", "Qwen3.5-Last": "204.1%", "Dedicated Mean": "97.4%", "Base-Mean": "126.8%", "Base-Last": "166.4%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "95.6%", "Qwen3-Emb": "95.9%", "Gemma3-Mean": "106.9%", "Gemma3-Last": "106.5%", "Qwen3.5-Mean": "104.1%", "Qwen3.5-Last": "96.6%", "Dedicated Mean": "95.7%", "Base-Mean": "105.5%", "Base-Last": "101.5%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "99.0%", "Qwen3-Emb": "97.4%", "Gemma3-Mean": "114.8%", "Gemma3-Last": "120.9%", "Qwen3.5-Mean": "110.1%", "Qwen3.5-Last": "136.1%", "Dedicated Mean": "98.2%", "Base-Mean": "112.5%", "Base-Last": "128.5%"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Crowd. 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(Σ, γ*, ε*)", "EmbGemma": "0.0050", "Qwen3-Emb": "0.0055", "Gemma3-Mean": "0.0081", "Gemma3-Last": "0.0163", "Qwen3.5-Mean": "0.0074", "Qwen3.5-Last": "0.0106", "Dedicated Mean": "0.0052", "Base-Mean": "0.0077", "Base-Last": "0.0135"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "0.4987", "Qwen3-Emb": "0.4556", "Gemma3-Mean": "0.4259", "Gemma3-Last": "0.5265", "Qwen3.5-Mean": "0.8323", "Qwen3.5-Last": "0.7247", "Dedicated Mean": "0.4771", "Base-Mean": "0.6291", "Base-Last": "0.6256"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "0.0061", "Qwen3-Emb": "0.0059", "Gemma3-Mean": "0.0371", "Gemma3-Last": "0.0398", "Qwen3.5-Mean": "0.0217", "Qwen3.5-Last": "0.0380", "Dedicated Mean": "0.0060", "Base-Mean": "0.0294", "Base-Last": "0.0389"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "0.0060", "Qwen3-Emb": "0.0061", "Gemma3-Mean": "0.0155", "Gemma3-Last": "0.0173", "Qwen3.5-Mean": "0.0133", "Qwen3.5-Last": "0.0189", "Dedicated Mean": "0.0060", "Base-Mean": "0.0144", "Base-Last": "0.0181"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "0.0062", "Qwen3-Emb": "0.0064", "Gemma3-Mean": "0.0308", "Gemma3-Last": "0.0315", "Qwen3.5-Mean": "0.0209", "Qwen3.5-Last": "0.0329", "Dedicated Mean": "0.0063", "Base-Mean": "0.0258", "Base-Last": "0.0322"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "0.0056", "Qwen3-Emb": "0.0051", "Gemma3-Mean": "0.0153", "Gemma3-Last": "0.0209", "Qwen3.5-Mean": "0.0128", "Qwen3.5-Last": "0.0182", "Dedicated Mean": "0.0054", "Base-Mean": "0.0140", "Base-Last": "0.0195"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. 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(Σ, γ*, ε*)", "EmbGemma": "0.0284", "Qwen3-Emb": "0.0385", "Gemma3-Mean": "0.0100", "Gemma3-Last": "0.0138", "Qwen3.5-Mean": "0.0097", "Qwen3.5-Last": "0.0165", "Dedicated Mean": "0.0335", "Base-Mean": "0.0099", "Base-Last": "0.0152"}, {"Dataset": "ArguAna", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.0504", "Qwen3-Emb": "0.0821", "Gemma3-Mean": "0.2273", "Gemma3-Last": "0.3611", "Qwen3.5-Mean": "0.1793", "Qwen3.5-Last": "0.4048", "Dedicated Mean": "0.0663", "Base-Mean": "0.2033", "Base-Last": "0.3830"}, {"Dataset": "ArguAna", "k": "64", "Method": "PCA-k", "EmbGemma": "0.0634", "Qwen3-Emb": "0.0678", "Gemma3-Mean": "0.1236", "Gemma3-Last": "0.3250", "Qwen3.5-Mean": "0.1326", "Qwen3.5-Last": "0.3330", "Dedicated Mean": "0.0656", "Base-Mean": "0.1281", "Base-Last": "0.3290"}, {"Dataset": "ArguAna", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.0170", "Qwen3-Emb": "0.0171", "Gemma3-Mean": "0.0189", "Gemma3-Last": "0.0242", "Qwen3.5-Mean": "0.0186", "Qwen3.5-Last": "0.0290", "Dedicated Mean": "0.0171", "Base-Mean": "0.0187", "Base-Last": "0.0266"}, {"Dataset": "ArguAna", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.0202", "Qwen3-Emb": "0.0326", "Gemma3-Mean": "0.0509", "Gemma3-Last": "0.1818", "Qwen3.5-Mean": "0.0605", "Qwen3.5-Last": "0.1725", "Dedicated Mean": "0.0264", "Base-Mean": "0.0557", "Base-Last": "0.1771"}, {"Dataset": "ArguAna", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.0417", "Qwen3-Emb": "0.0425", "Gemma3-Mean": "0.0189", "Gemma3-Last": "0.0240", "Qwen3.5-Mean": "0.0186", "Qwen3.5-Last": "0.0288", "Dedicated Mean": "0.0421", "Base-Mean": "0.0187", "Base-Last": "0.0264"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.0638", "Qwen3-Emb": "0.0682", "Gemma3-Mean": "0.1239", "Gemma3-Last": "0.3262", "Qwen3.5-Mean": "0.1330", "Qwen3.5-Last": "0.3345", "Dedicated Mean": "0.0660", "Base-Mean": "0.1285", "Base-Last": "0.3304"}, {"Dataset": "ArguAna", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.0358", "Qwen3-Emb": "0.0369", "Gemma3-Mean": "0.0508", "Gemma3-Last": "0.1816", "Qwen3.5-Mean": "0.0606", "Qwen3.5-Last": "0.2530", "Dedicated Mean": "0.0364", "Base-Mean": "0.0557", "Base-Last": "0.2173"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.0417", "Qwen3-Emb": "0.0425", "Gemma3-Mean": "0.0508", "Gemma3-Last": "0.1816", "Qwen3.5-Mean": "0.0606", "Qwen3.5-Last": "0.2530", "Dedicated Mean": "0.0421", "Base-Mean": "0.0557", "Base-Last": "0.2173"}, {"Dataset": "ArguAna", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.0599", "Qwen3-Emb": "0.0630", "Gemma3-Mean": "0.0189", "Gemma3-Last": "0.0240", "Qwen3.5-Mean": "0.0186", "Qwen3.5-Last": "0.0288", "Dedicated Mean": "0.0615", "Base-Mean": "0.0187", "Base-Last": "0.0264"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.0400", "Qwen3-Emb": "0.0409", "Gemma3-Mean": "0.0525", "Gemma3-Last": "0.1001", "Qwen3.5-Mean": "0.0560", "Qwen3.5-Last": "0.1066", "Dedicated Mean": "0.0404", "Base-Mean": "0.0542", "Base-Last": "0.1033"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.0358", "Qwen3-Emb": "0.0369", "Gemma3-Mean": "0.0189", "Gemma3-Last": "0.0240", "Qwen3.5-Mean": "0.0187", "Qwen3.5-Last": "0.0288", "Dedicated Mean": "0.0364", "Base-Mean": "0.0188", "Base-Last": "0.0264"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.0434", "Qwen3-Emb": "0.0447", "Gemma3-Mean": "0.0191", "Gemma3-Last": "0.0251", "Qwen3.5-Mean": "0.0191", "Qwen3.5-Last": "0.0301", "Dedicated Mean": "0.0440", "Base-Mean": "0.0191", "Base-Last": "0.0276"}, {"Dataset": "ArguAna", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.0249", "Qwen3-Emb": "0.0380", "Gemma3-Mean": "0.0189", "Gemma3-Last": "0.0242", "Qwen3.5-Mean": "0.0186", "Qwen3.5-Last": "0.0289", "Dedicated Mean": "0.0314", "Base-Mean": "0.0187", "Base-Last": "0.0265"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.0421", "Qwen3-Emb": "0.0502", "Gemma3-Mean": "0.1744", "Gemma3-Last": "0.1111", "Qwen3.5-Mean": "0.1236", "Qwen3.5-Last": "0.1088", "Dedicated Mean": "0.0461", "Base-Mean": "0.1490", "Base-Last": "0.1099"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "PCA-k", "EmbGemma": "0.0443", "Qwen3-Emb": "0.0437", "Gemma3-Mean": "0.1192", "Gemma3-Last": "0.1188", "Qwen3.5-Mean": "0.0982", "Qwen3.5-Last": "0.1061", "Dedicated Mean": "0.0440", "Base-Mean": "0.1087", "Base-Last": "0.1124"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.0025", "Qwen3-Emb": "0.0025", "Gemma3-Mean": "0.0034", "Gemma3-Last": "0.0042", "Qwen3.5-Mean": "0.0030", "Qwen3.5-Last": "0.0039", "Dedicated Mean": "0.0025", "Base-Mean": "0.0032", "Base-Last": "0.0040"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.0384", "Qwen3-Emb": "0.0403", "Gemma3-Mean": "0.1151", "Gemma3-Last": "0.1081", "Qwen3.5-Mean": "0.0950", "Qwen3.5-Last": "0.0977", "Dedicated Mean": "0.0393", "Base-Mean": "0.1051", "Base-Last": "0.1029"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.0297", "Qwen3-Emb": "0.0366", "Gemma3-Mean": "0.0036", "Gemma3-Last": "0.0046", "Qwen3.5-Mean": "0.0034", "Qwen3.5-Last": "0.0044", "Dedicated Mean": "0.0331", "Base-Mean": "0.0035", "Base-Last": "0.0045"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.0417", "Qwen3-Emb": "0.0413", "Gemma3-Mean": "0.1202", "Gemma3-Last": "0.1114", "Qwen3.5-Mean": "0.0984", "Qwen3.5-Last": "0.1002", "Dedicated Mean": "0.0415", "Base-Mean": "0.1093", "Base-Last": "0.1058"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.0366", "Qwen3-Emb": "0.0390", "Gemma3-Mean": "0.1160", "Gemma3-Last": "0.1058", "Qwen3.5-Mean": "0.0940", "Qwen3.5-Last": "0.0919", "Dedicated Mean": "0.0378", "Base-Mean": "0.1050", "Base-Last": "0.0988"}, {"Dataset": "SCIDOCS", "k": "512", "Method": "w/o Crowd. 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(Σ, γ*, ε*)", "EmbGemma": "0.0313", "Qwen3-Emb": "0.0382", "Gemma3-Mean": "0.0036", "Gemma3-Last": "0.0047", "Qwen3.5-Mean": "0.0034", "Qwen3.5-Last": "0.0044", "Dedicated Mean": "0.0348", "Base-Mean": "0.0035", "Base-Last": "0.0046"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "0.0489", "Qwen3-Emb": "0.0608", "Gemma3-Mean": "0.2331", "Gemma3-Last": "0.1340", "Qwen3.5-Mean": "0.1448", "Qwen3.5-Last": "0.1126", "Dedicated Mean": "0.0548", "Base-Mean": "0.1890", "Base-Last": "0.1233"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "PCA-k", "EmbGemma": "0.0516", "Qwen3-Emb": "0.0497", "Gemma3-Mean": "0.1255", "Gemma3-Last": "0.1276", "Qwen3.5-Mean": "0.1040", "Qwen3.5-Last": "0.1142", "Dedicated Mean": "0.0507", "Base-Mean": "0.1147", "Base-Last": "0.1209"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Whitening-k", "EmbGemma": "0.0047", "Qwen3-Emb": "0.0046", "Gemma3-Mean": "0.0061", "Gemma3-Last": "0.0075", "Qwen3.5-Mean": "0.0057", "Qwen3.5-Last": "0.0071", "Dedicated Mean": "0.0046", "Base-Mean": "0.0059", "Base-Last": "0.0073"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "SpecTemp", "EmbGemma": "0.0347", "Qwen3-Emb": "0.0377", "Gemma3-Mean": "0.1111", "Gemma3-Last": "0.0951", "Qwen3.5-Mean": "0.0933", "Qwen3.5-Last": "0.0901", "Dedicated Mean": "0.0362", "Base-Mean": "0.1022", "Base-Last": "0.0926"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "0.0350", "Qwen3-Emb": "0.0416", "Gemma3-Mean": "0.0061", "Gemma3-Last": "0.0075", "Qwen3.5-Mean": "0.0058", "Qwen3.5-Last": "0.0072", "Dedicated Mean": "0.0383", "Base-Mean": "0.0060", "Base-Last": "0.0073"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.0487", "Qwen3-Emb": "0.0469", "Gemma3-Mean": "0.1266", "Gemma3-Last": "0.1196", "Qwen3.5-Mean": "0.1042", "Qwen3.5-Last": "0.1078", "Dedicated Mean": "0.0478", "Base-Mean": "0.1154", "Base-Last": "0.1137"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.0339", "Qwen3-Emb": "0.0389", "Gemma3-Mean": "0.1120", "Gemma3-Last": "0.1023", "Qwen3.5-Mean": "0.0892", "Qwen3.5-Last": "0.0839", "Dedicated Mean": "0.0364", "Base-Mean": "0.1006", "Base-Last": "0.0931"}, {"Dataset": "SCIDOCS", "k": "256", "Method": "w/o Crowd. 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(Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.0176", "Qwen3-Emb": "0.0214", "Gemma3-Mean": "0.0264", "Gemma3-Last": "0.0222", "Qwen3.5-Mean": "0.0346", "Qwen3.5-Last": "0.0306", "Dedicated Mean": "0.0195", "Base-Mean": "0.0305", "Base-Last": "0.0264"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.0293", "Qwen3-Emb": "0.0353", "Gemma3-Mean": "0.0051", "Gemma3-Last": "0.0103", "Qwen3.5-Mean": "0.0051", "Qwen3.5-Last": "0.0051", "Dedicated Mean": "0.0323", "Base-Mean": "0.0051", "Base-Last": "0.0077"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.0299", "Qwen3-Emb": "0.0365", "Gemma3-Mean": "0.0056", "Gemma3-Last": "0.0152", "Qwen3.5-Mean": "0.0063", "Qwen3.5-Last": "0.0083", "Dedicated Mean": "0.0332", "Base-Mean": "0.0060", "Base-Last": "0.0118"}, {"Dataset": "STS22.v2", "k": "512", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.0301", "Qwen3-Emb": "0.0367", "Gemma3-Mean": "0.0056", "Gemma3-Last": "0.0175", "Qwen3.5-Mean": "0.0063", "Qwen3.5-Last": "0.0084", "Dedicated Mean": "0.0334", "Base-Mean": "0.0060", "Base-Last": "0.0129"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Prefix (MRL)", "EmbGemma": "0.0362", "Qwen3-Emb": "0.0484", "Gemma3-Mean": "0.2224", "Gemma3-Last": "0.1250", "Qwen3.5-Mean": "0.1271", "Qwen3.5-Last": "0.1408", "Dedicated Mean": "0.0423", "Base-Mean": "0.1747", "Base-Last": "0.1329"}, {"Dataset": "STS22.v2", "k": "256", "Method": "PCA-k", "EmbGemma": "0.0322", "Qwen3-Emb": "0.0403", "Gemma3-Mean": "0.0942", "Gemma3-Last": "0.0809", "Qwen3.5-Mean": "0.1184", "Qwen3.5-Last": "0.1235", "Dedicated Mean": "0.0363", "Base-Mean": "0.1063", "Base-Last": "0.1022"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Whitening-k", "EmbGemma": "0.0056", "Qwen3-Emb": "0.0058", "Gemma3-Mean": "0.0066", "Gemma3-Last": "0.0105", "Qwen3.5-Mean": "0.0061", "Qwen3.5-Last": "0.0097", "Dedicated Mean": "0.0057", "Base-Mean": "0.0063", "Base-Last": "0.0101"}, {"Dataset": "STS22.v2", "k": "256", "Method": "SpecTemp", "EmbGemma": "0.0274", "Qwen3-Emb": "0.0331", "Gemma3-Mean": "0.0868", "Gemma3-Last": "0.0652", "Qwen3.5-Mean": "0.1118", "Qwen3.5-Last": "0.1082", "Dedicated Mean": "0.0302", "Base-Mean": "0.0993", "Base-Last": "0.0867"}, {"Dataset": "STS22.v2", "k": "256", "Method": "COAST (Ours)", "EmbGemma": "0.0286", "Qwen3-Emb": "0.0367", "Gemma3-Mean": "0.0068", "Gemma3-Last": "0.0164", "Qwen3.5-Mean": "0.0066", "Qwen3.5-Last": "0.0100", "Dedicated Mean": "0.0326", "Base-Mean": "0.0067", "Base-Last": "0.0132"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.0320", "Qwen3-Emb": "0.0399", "Gemma3-Mean": "0.0942", "Gemma3-Last": "0.0733", "Qwen3.5-Mean": "0.1190", "Qwen3.5-Last": "0.1242", "Dedicated Mean": "0.0359", "Base-Mean": "0.1066", "Base-Last": "0.0988"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.0270", "Qwen3-Emb": "0.0352", "Gemma3-Mean": "0.0849", "Gemma3-Last": "0.0597", "Qwen3.5-Mean": "0.1123", "Qwen3.5-Last": "0.1088", "Dedicated Mean": "0.0311", "Base-Mean": "0.0986", "Base-Last": "0.0842"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.0286", "Qwen3-Emb": "0.0367", "Gemma3-Mean": "0.0850", "Gemma3-Last": "0.0606", "Qwen3.5-Mean": "0.1124", "Qwen3.5-Last": "0.1091", "Dedicated Mean": "0.0326", "Base-Mean": "0.0987", "Base-Last": "0.0849"}, {"Dataset": "STS22.v2", "k": "256", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.0309", "Qwen3-Emb": "0.0376", "Gemma3-Mean": "0.0068", "Gemma3-Last": "0.0164", "Qwen3.5-Mean": "0.0066", "Qwen3.5-Last": "0.0100", "Dedicated Mean": "0.0343", "Base-Mean": "0.0067", "Base-Last": "0.0132"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.0184", "Qwen3-Emb": "0.0222", "Gemma3-Mean": "0.0279", "Gemma3-Last": "0.0234", "Qwen3.5-Mean": "0.0349", "Qwen3.5-Last": "0.0327", "Dedicated Mean": "0.0203", "Base-Mean": "0.0314", "Base-Last": "0.0280"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.0270", "Qwen3-Emb": "0.0352", "Gemma3-Mean": "0.0066", "Gemma3-Last": "0.0142", "Qwen3.5-Mean": "0.0061", "Qwen3.5-Last": "0.0097", "Dedicated Mean": "0.0311", "Base-Mean": "0.0063", "Base-Last": "0.0120"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.0287", "Qwen3-Emb": "0.0367", "Gemma3-Mean": "0.0072", "Gemma3-Last": "0.0177", "Qwen3.5-Mean": "0.0074", "Qwen3.5-Last": "0.0104", "Dedicated Mean": "0.0327", "Base-Mean": "0.0073", "Base-Last": "0.0140"}, {"Dataset": "STS22.v2", "k": "256", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.0290", "Qwen3-Emb": "0.0349", "Gemma3-Mean": "0.0069", "Gemma3-Last": "0.0185", "Qwen3.5-Mean": "0.0066", "Qwen3.5-Last": "0.0100", "Dedicated Mean": "0.0319", "Base-Mean": "0.0067", "Base-Last": "0.0142"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Prefix (MRL)", "EmbGemma": "0.0417", "Qwen3-Emb": "0.0561", "Gemma3-Mean": "0.1670", "Gemma3-Last": "0.1054", "Qwen3.5-Mean": "0.1472", "Qwen3.5-Last": "0.1570", "Dedicated Mean": "0.0489", "Base-Mean": "0.1571", "Base-Last": "0.1312"}, {"Dataset": "STS22.v2", "k": "128", "Method": "PCA-k", "EmbGemma": "0.0386", "Qwen3-Emb": "0.0465", "Gemma3-Mean": "0.1025", "Gemma3-Last": "0.0958", "Qwen3.5-Mean": "0.1249", "Qwen3.5-Last": "0.1383", "Dedicated Mean": "0.0426", "Base-Mean": "0.1137", "Base-Last": "0.1171"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Whitening-k", "EmbGemma": "0.0103", "Qwen3-Emb": "0.0098", "Gemma3-Mean": "0.0141", "Gemma3-Last": "0.0141", "Qwen3.5-Mean": "0.0127", "Qwen3.5-Last": "0.0155", "Dedicated Mean": "0.0100", "Base-Mean": "0.0134", "Base-Last": "0.0148"}, {"Dataset": "STS22.v2", "k": "128", "Method": "SpecTemp", "EmbGemma": "0.0215", "Qwen3-Emb": "0.0211", "Gemma3-Mean": "0.0690", "Gemma3-Last": "0.0500", "Qwen3.5-Mean": "0.0931", "Qwen3.5-Last": "0.0857", "Dedicated Mean": "0.0213", "Base-Mean": "0.0811", "Base-Last": "0.0678"}, {"Dataset": "STS22.v2", "k": "128", "Method": "COAST (Ours)", "EmbGemma": "0.0249", "Qwen3-Emb": "0.0325", "Gemma3-Mean": "0.0141", "Gemma3-Last": "0.0242", "Qwen3.5-Mean": "0.0129", "Qwen3.5-Last": "0.0156", "Dedicated Mean": "0.0287", "Base-Mean": "0.0135", "Base-Last": "0.0199"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.0385", "Qwen3-Emb": "0.0459", "Gemma3-Mean": "0.1026", "Gemma3-Last": "0.0877", "Qwen3.5-Mean": "0.1255", "Qwen3.5-Last": "0.1393", "Dedicated Mean": "0.0422", "Base-Mean": "0.1140", "Base-Last": "0.1135"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.0208", "Qwen3-Emb": "0.0282", "Gemma3-Mean": "0.0609", "Gemma3-Last": "0.0477", "Qwen3.5-Mean": "0.0934", "Qwen3.5-Last": "0.0864", "Dedicated Mean": "0.0245", "Base-Mean": "0.0771", "Base-Last": "0.0670"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.0249", "Qwen3-Emb": "0.0325", "Gemma3-Mean": "0.0610", "Gemma3-Last": "0.0484", "Qwen3.5-Mean": "0.0935", "Qwen3.5-Last": "0.0866", "Dedicated Mean": "0.0287", "Base-Mean": "0.0772", "Base-Last": "0.0675"}, {"Dataset": "STS22.v2", "k": "128", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.0374", "Qwen3-Emb": "0.0436", "Gemma3-Mean": "0.0141", "Gemma3-Last": "0.0242", "Qwen3.5-Mean": "0.0129", "Qwen3.5-Last": "0.0156", "Dedicated Mean": "0.0405", "Base-Mean": "0.0135", "Base-Last": "0.0199"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.0237", "Qwen3-Emb": "0.0271", "Gemma3-Mean": "0.0376", "Gemma3-Last": "0.0330", "Qwen3.5-Mean": "0.0440", "Qwen3.5-Last": "0.0459", "Dedicated Mean": "0.0254", "Base-Mean": "0.0408", "Base-Last": "0.0394"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.0208", "Qwen3-Emb": "0.0282", "Gemma3-Mean": "0.0141", "Gemma3-Last": "0.0234", "Qwen3.5-Mean": "0.0128", "Qwen3.5-Last": "0.0155", "Dedicated Mean": "0.0245", "Base-Mean": "0.0135", "Base-Last": "0.0195"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.0251", "Qwen3-Emb": "0.0329", "Gemma3-Mean": "0.0144", "Gemma3-Last": "0.0265", "Qwen3.5-Mean": "0.0136", "Qwen3.5-Last": "0.0164", "Dedicated Mean": "0.0290", "Base-Mean": "0.0140", "Base-Last": "0.0215"}, {"Dataset": "STS22.v2", "k": "128", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.0257", "Qwen3-Emb": "0.0252", "Gemma3-Mean": "0.0141", "Gemma3-Last": "0.0263", "Qwen3.5-Mean": "0.0128", "Qwen3.5-Last": "0.0156", "Dedicated Mean": "0.0255", "Base-Mean": "0.0135", "Base-Last": "0.0209"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Prefix (MRL)", "EmbGemma": "0.0543", "Qwen3-Emb": "0.0738", "Gemma3-Mean": "0.2530", "Gemma3-Last": "0.1434", "Qwen3.5-Mean": "0.1750", "Qwen3.5-Last": "0.1944", "Dedicated Mean": "0.0640", "Base-Mean": "0.2140", "Base-Last": "0.1689"}, {"Dataset": "STS22.v2", "k": "64", "Method": "PCA-k", "EmbGemma": "0.0520", "Qwen3-Emb": "0.0600", "Gemma3-Mean": "0.1179", "Gemma3-Last": "0.1204", "Qwen3.5-Mean": "0.1371", "Qwen3.5-Last": "0.1627", "Dedicated Mean": "0.0560", "Base-Mean": "0.1275", "Base-Last": "0.1416"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Whitening-k", "EmbGemma": "0.0192", "Qwen3-Emb": "0.0190", "Gemma3-Mean": "0.0254", "Gemma3-Last": "0.0249", "Qwen3.5-Mean": "0.0233", "Qwen3.5-Last": "0.0266", "Dedicated Mean": "0.0191", "Base-Mean": "0.0244", "Base-Last": "0.0257"}, {"Dataset": "STS22.v2", "k": "64", "Method": "SpecTemp", "EmbGemma": "0.0208", "Qwen3-Emb": "0.0190", "Gemma3-Mean": "0.0480", "Gemma3-Last": "0.0415", "Qwen3.5-Mean": "0.0615", "Qwen3.5-Last": "0.0639", "Dedicated Mean": "0.0199", "Base-Mean": "0.0548", "Base-Last": "0.0527"}, {"Dataset": "STS22.v2", "k": "64", "Method": "COAST (Ours)", "EmbGemma": "0.0247", "Qwen3-Emb": "0.0303", "Gemma3-Mean": "0.0255", "Gemma3-Last": "0.0389", "Qwen3.5-Mean": "0.0235", "Qwen3.5-Last": "0.0266", "Dedicated Mean": "0.0275", "Base-Mean": "0.0245", "Base-Last": "0.0328"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.0519", "Qwen3-Emb": "0.0593", "Gemma3-Mean": "0.1181", "Gemma3-Last": "0.1106", "Qwen3.5-Mean": "0.1377", "Qwen3.5-Last": "0.1637", "Dedicated Mean": "0.0556", "Base-Mean": "0.1279", "Base-Last": "0.1371"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.0200", "Qwen3-Emb": "0.0246", "Gemma3-Mean": "0.0361", "Gemma3-Last": "0.0414", "Qwen3.5-Mean": "0.0619", "Qwen3.5-Last": "0.0642", "Dedicated Mean": "0.0223", "Base-Mean": "0.0490", "Base-Last": "0.0528"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Crowd. 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PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.9656", "Qwen3-Emb": "0.9626", "Gemma3-Mean": "0.8579", "Gemma3-Last": "0.8971", "Qwen3.5-Mean": "0.8291", "Qwen3.5-Last": "0.8500", "Dedicated Mean": "0.9641", "Base-Mean": "0.8435", "Base-Last": "0.8736"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.9987", "Qwen3-Emb": "0.9969", "Gemma3-Mean": "0.9817", "Gemma3-Last": "0.9780", "Qwen3.5-Mean": "0.9502", "Qwen3.5-Last": "0.9574", "Dedicated Mean": "0.9978", "Base-Mean": "0.9660", "Base-Last": "0.9677"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Crowd. Floor (Σ_⊥, γ_SNR, ε*)", "EmbGemma": "0.9954", "Qwen3-Emb": "0.9917", "Gemma3-Mean": "0.9817", "Gemma3-Last": "0.9776", "Qwen3.5-Mean": "0.9502", "Qwen3.5-Last": "0.9573", "Dedicated Mean": "0.9935", "Base-Mean": "0.9660", "Base-Last": "0.9675"}, {"Dataset": "STS22.v2", "k": "64", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, ε*)", "EmbGemma": "0.9672", "Qwen3-Emb": "0.9655", "Gemma3-Mean": "0.9914", "Gemma3-Last": "0.9802", "Qwen3.5-Mean": "0.9943", "Qwen3.5-Last": "0.9867", "Dedicated Mean": "0.9664", "Base-Mean": "0.9929", "Base-Last": "0.9834"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o SNR Sched. (Σ_⊥, γ_crowd, ε*)", "EmbGemma": "0.9858", "Qwen3-Emb": "0.9847", "Gemma3-Mean": "0.9594", "Gemma3-Last": "0.9694", "Qwen3.5-Mean": "0.9530", "Qwen3.5-Last": "0.9554", "Dedicated Mean": "0.9852", "Base-Mean": "0.9562", "Base-Last": "0.9624"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Adaptive ε* (Σ_⊥, γ*, 1e-6)", "EmbGemma": "0.9987", "Qwen3-Emb": "0.9969", "Gemma3-Mean": "0.9914", "Gemma3-Last": "0.9806", "Qwen3.5-Mean": "0.9943", "Qwen3.5-Last": "0.9867", "Dedicated Mean": "0.9978", "Base-Mean": "0.9929", "Base-Last": "0.9837"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Rank Scale τ² (Σ_⊥, γ*, ε*(d))", "EmbGemma": "0.9950", "Qwen3-Emb": "0.9908", "Gemma3-Mean": "0.9913", "Gemma3-Last": "0.9768", "Qwen3.5-Mean": "0.9940", "Qwen3.5-Last": "0.9861", "Dedicated Mean": "0.9929", "Base-Mean": "0.9927", "Base-Last": "0.9814"}, {"Dataset": "STS22.v2", "k": "64", "Method": "w/o Orth. Proj. (Σ, γ*, ε*)", "EmbGemma": "0.9943", "Qwen3-Emb": "0.9973", "Gemma3-Mean": "0.9914", "Gemma3-Last": "0.9778", "Qwen3.5-Mean": "0.9943", "Qwen3.5-Last": "0.9866", "Dedicated Mean": "0.9958", "Base-Mean": "0.9929", "Base-Last": "0.9822"}], "geom_full::IsoScore": [{"Dataset": "FiQA-2018", "k": "d", "Method": "Baseline", "EmbGemma": "0.1640", "Qwen3-Emb": "0.1226", "Gemma3-Mean": "0.0239", "Gemma3-Last": "0.0190", "Qwen3.5-Mean": "0.0335", "Qwen3.5-Last": "0.0137", "Dedicated Mean": "0.1433", "Base-Mean": "0.0287", "Base-Last": "0.0163"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Standardization", "EmbGemma": "0.1744", "Qwen3-Emb": "0.1371", "Gemma3-Mean": "0.0554", "Gemma3-Last": "0.0271", "Qwen3.5-Mean": "0.0453", "Qwen3.5-Last": "0.0234", "Dedicated Mean": "0.1557", "Base-Mean": "0.0503", "Base-Last": "0.0253"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "R1", "EmbGemma": "0.1581", "Qwen3-Emb": "0.1213", "Gemma3-Mean": "0.0301", "Gemma3-Last": "0.0186", "Qwen3.5-Mean": "0.0334", "Qwen3.5-Last": "0.0148", "Dedicated Mean": "0.1397", "Base-Mean": "0.0318", "Base-Last": "0.0167"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "R2", "EmbGemma": "0.1616", "Qwen3-Emb": "0.1213", "Gemma3-Mean": "0.0303", "Gemma3-Last": "0.0189", "Qwen3.5-Mean": "0.0334", "Qwen3.5-Last": "0.0150", "Dedicated Mean": "0.1414", "Base-Mean": "0.0319", "Base-Last": "0.0169"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Soft-ZCA", "EmbGemma": "0.8761", "Qwen3-Emb": "0.8158", "Gemma3-Mean": "0.4962", "Gemma3-Last": "0.6440", "Qwen3.5-Mean": "0.5275", "Qwen3.5-Last": "0.6194", "Dedicated Mean": "0.8459", "Base-Mean": "0.5118", "Base-Last": "0.6317"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "COAST (Ours)", "EmbGemma": "0.1878", "Qwen3-Emb": "0.1404", "Gemma3-Mean": "0.7213", "Gemma3-Last": "0.6065", "Qwen3.5-Mean": "0.6719", "Qwen3.5-Last": "0.6127", "Dedicated Mean": "0.1641", "Base-Mean": "0.6966", "Base-Last": "0.6096"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "ABTT (D=1)", "EmbGemma": "0.1917", "Qwen3-Emb": "0.1400", "Gemma3-Mean": "0.0319", "Gemma3-Last": "0.0535", "Qwen3.5-Mean": "0.0470", "Qwen3.5-Last": "0.0573", "Dedicated Mean": "0.1658", "Base-Mean": "0.0394", "Base-Last": "0.0554"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "ABTT (D=2)", "EmbGemma": "0.2107", "Qwen3-Emb": "0.1528", "Gemma3-Mean": "0.0490", "Gemma3-Last": "0.0591", "Qwen3.5-Mean": "0.0505", "Qwen3.5-Last": "0.0626", "Dedicated Mean": "0.1817", "Base-Mean": "0.0498", "Base-Last": "0.0609"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "ABTT (D=3)", "EmbGemma": "0.2292", "Qwen3-Emb": "0.1633", "Gemma3-Mean": "0.0564", "Gemma3-Last": "0.0779", "Qwen3.5-Mean": "0.0564", "Qwen3.5-Last": "0.0744", "Dedicated Mean": "0.1962", "Base-Mean": "0.0564", "Base-Last": "0.0761"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Unreg. ZCA (Σ, γ=1, ε=1e-6)", "EmbGemma": "0.9616", "Qwen3-Emb": "0.9933", "Gemma3-Mean": "0.9384", "Gemma3-Last": "0.9253", "Qwen3.5-Mean": "0.9415", "Qwen3.5-Last": "0.9246", "Dedicated Mean": "0.9774", "Base-Mean": "0.9400", "Base-Last": "0.9249"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Centered + ε* (Σ, γ=1, ε*)", "EmbGemma": "0.4673", "Qwen3-Emb": "0.3795", "Gemma3-Mean": "0.7111", "Gemma3-Last": "0.5997", "Qwen3.5-Mean": "0.6661", "Qwen3.5-Last": "0.6056", "Dedicated Mean": "0.4234", "Base-Mean": "0.6886", "Base-Last": "0.6027"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "EmbGemma": "0.2051", "Qwen3-Emb": "0.1559", "Gemma3-Mean": "0.4962", "Gemma3-Last": "0.6440", "Qwen3.5-Mean": "0.5275", "Qwen3.5-Last": "0.6194", "Dedicated Mean": "0.1805", "Base-Mean": "0.5118", "Base-Last": "0.6317"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "w/o Orth. Proj. 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(Σ_⊥, γ=1, ε*)", "EmbGemma": "0.4861", "Qwen3-Emb": "0.3718", "Gemma3-Mean": "0.7213", "Gemma3-Last": "0.6065", "Qwen3.5-Mean": "0.6719", "Qwen3.5-Last": "0.6127", "Dedicated Mean": "0.4289", "Base-Mean": "0.6966", "Base-Last": "0.6096"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "EmbGemma": "0.5362", "Qwen3-Emb": "0.4227", "Gemma3-Mean": "0.1735", "Gemma3-Last": "0.2021", "Qwen3.5-Mean": "0.1820", "Qwen3.5-Last": "0.1844", "Dedicated Mean": "0.4795", "Base-Mean": "0.1777", "Base-Last": "0.1933"}, {"Dataset": "FiQA-2018", "k": "d", "Method": "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)", "EmbGemma": "0.2102", "Qwen3-Emb": "0.1564", "Gemma3-Mean": "0.4958", "Gemma3-Last": "0.6436", "Qwen3.5-Mean": "0.5268", "Qwen3.5-Last": "0.6191", "Dedicated Mean": "0.1833", "Base-Mean": "0.5113", "Base-Last": "0.6313"}, {"Dataset": "ArguAna", "k": "d", "Method": "Baseline", "EmbGemma": "0.1679", "Qwen3-Emb": "0.1135", "Gemma3-Mean": "0.0342", "Gemma3-Last": "0.0128", "Qwen3.5-Mean": "0.0309", "Qwen3.5-Last": "0.0108", "Dedicated Mean": "0.1407", "Base-Mean": "0.0326", "Base-Last": "0.0118"}, {"Dataset": "ArguAna", "k": "d", "Method": "Standardization", "EmbGemma": "0.1720", "Qwen3-Emb": "0.1265", "Gemma3-Mean": "0.0649", "Gemma3-Last": "0.0239", "Qwen3.5-Mean": "0.0404", "Qwen3.5-Last": "0.0173", "Dedicated Mean": "0.1492", "Base-Mean": "0.0527", "Base-Last": "0.0206"}, {"Dataset": "ArguAna", "k": "d", "Method": "R1", "EmbGemma": "0.1661", "Qwen3-Emb": "0.1128", "Gemma3-Mean": "0.0347", "Gemma3-Last": "0.0126", "Qwen3.5-Mean": "0.0314", "Qwen3.5-Last": "0.0107", "Dedicated Mean": "0.1394", "Base-Mean": "0.0330", "Base-Last": "0.0117"}, {"Dataset": "ArguAna", "k": "d", "Method": "R2", "EmbGemma": "0.1670", "Qwen3-Emb": "0.1127", "Gemma3-Mean": "0.0347", "Gemma3-Last": "0.0125", "Qwen3.5-Mean": "0.0313", "Qwen3.5-Last": "0.0107", "Dedicated Mean": "0.1399", "Base-Mean": "0.0330", "Base-Last": "0.0116"}, {"Dataset": "ArguAna", "k": "d", "Method": "Soft-ZCA", "EmbGemma": "0.8573", "Qwen3-Emb": "0.7712", "Gemma3-Mean": "0.4458", "Gemma3-Last": "0.6290", "Qwen3.5-Mean": "0.4733", "Qwen3.5-Last": "0.5813", "Dedicated Mean": "0.8142", "Base-Mean": "0.4596", "Base-Last": "0.6052"}, {"Dataset": "ArguAna", "k": "d", "Method": "COAST (Ours)", "EmbGemma": "0.1802", "Qwen3-Emb": "0.1239", "Gemma3-Mean": "0.7307", "Gemma3-Last": "0.5921", "Qwen3.5-Mean": "0.6336", "Qwen3.5-Last": "0.5664", "Dedicated Mean": "0.1520", "Base-Mean": "0.6822", "Base-Last": "0.5793"}, {"Dataset": "ArguAna", "k": "d", "Method": "ABTT (D=1)", "EmbGemma": "0.1839", "Qwen3-Emb": "0.1273", "Gemma3-Mean": "0.0451", "Gemma3-Last": "0.0610", "Qwen3.5-Mean": "0.0412", "Qwen3.5-Last": "0.0376", "Dedicated Mean": "0.1556", "Base-Mean": "0.0432", "Base-Last": "0.0493"}, {"Dataset": "ArguAna", "k": "d", "Method": "ABTT (D=2)", "EmbGemma": "0.2005", "Qwen3-Emb": "0.1394", "Gemma3-Mean": "0.0532", "Gemma3-Last": "0.0778", "Qwen3.5-Mean": "0.0495", "Qwen3.5-Last": "0.0596", "Dedicated Mean": "0.1699", "Base-Mean": "0.0513", "Base-Last": "0.0687"}, {"Dataset": "ArguAna", "k": "d", "Method": "ABTT (D=3)", "EmbGemma": "0.2088", "Qwen3-Emb": "0.1478", "Gemma3-Mean": "0.0611", "Gemma3-Last": "0.0854", "Qwen3.5-Mean": "0.0552", "Qwen3.5-Last": "0.0765", "Dedicated Mean": "0.1783", "Base-Mean": "0.0582", "Base-Last": "0.0809"}, {"Dataset": "ArguAna", "k": "d", "Method": "Unreg. 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(Σ, γ_crowd, ε*)", "EmbGemma": "0.1397", "Qwen3-Emb": "0.0912", "Gemma3-Mean": "0.6022", "Gemma3-Last": "0.5254", "Qwen3.5-Mean": "0.5433", "Qwen3.5-Last": "0.5060", "Dedicated Mean": "0.1154", "Base-Mean": "0.5727", "Base-Last": "0.5157"}, {"Dataset": "SICK-R", "k": "d", "Method": "Orth. Soft-ZCA (Σ_⊥, γ=1, 1e-4)", "EmbGemma": "0.6720", "Qwen3-Emb": "0.5713", "Gemma3-Mean": "0.3687", "Gemma3-Last": "0.5381", "Qwen3.5-Mean": "0.4490", "Qwen3.5-Last": "0.5815", "Dedicated Mean": "0.6217", "Base-Mean": "0.4089", "Base-Last": "0.5598"}, {"Dataset": "SICK-R", "k": "d", "Method": "w/o Crowd. Exp. (Σ_⊥, γ=1, ε*)", "EmbGemma": "0.3250", "Qwen3-Emb": "0.2608", "Gemma3-Mean": "0.6024", "Gemma3-Last": "0.5293", "Qwen3.5-Mean": "0.5441", "Qwen3.5-Last": "0.5099", "Dedicated Mean": "0.2929", "Base-Mean": "0.5733", "Base-Last": "0.5196"}, {"Dataset": "SICK-R", "k": "d", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "EmbGemma": "0.2992", "Qwen3-Emb": "0.2136", "Gemma3-Mean": "0.1268", "Gemma3-Last": "0.2059", "Qwen3.5-Mean": "0.1419", "Qwen3.5-Last": "0.2217", "Dedicated Mean": "0.2564", "Base-Mean": "0.1343", "Base-Last": "0.2138"}, {"Dataset": "SICK-R", "k": "d", "Method": "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)", "EmbGemma": "0.2046", "Qwen3-Emb": "0.1223", "Gemma3-Mean": "0.3687", "Gemma3-Last": "0.5381", "Qwen3.5-Mean": "0.4490", "Qwen3.5-Last": "0.5815", "Dedicated Mean": "0.1635", "Base-Mean": "0.4089", "Base-Last": "0.5598"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Baseline", "EmbGemma": "0.1477", "Qwen3-Emb": "0.0986", "Gemma3-Mean": "0.0285", "Gemma3-Last": "0.0495", "Qwen3.5-Mean": "0.0241", "Qwen3.5-Last": "0.0328", "Dedicated Mean": "0.1231", "Base-Mean": "0.0263", "Base-Last": "0.0412"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Standardization", "EmbGemma": "0.1510", "Qwen3-Emb": "0.1073", "Gemma3-Mean": "0.0618", "Gemma3-Last": "0.0810", "Qwen3.5-Mean": "0.0304", "Qwen3.5-Last": "0.0418", "Dedicated Mean": "0.1291", "Base-Mean": "0.0461", "Base-Last": "0.0614"}, {"Dataset": "STS22.v2", "k": "d", "Method": "R1", "EmbGemma": "0.1464", "Qwen3-Emb": "0.0974", "Gemma3-Mean": "0.0294", "Gemma3-Last": "0.0493", "Qwen3.5-Mean": "0.0240", "Qwen3.5-Last": "0.0315", "Dedicated Mean": "0.1219", "Base-Mean": "0.0267", "Base-Last": "0.0404"}, {"Dataset": "STS22.v2", "k": "d", "Method": "R2", "EmbGemma": "0.1478", "Qwen3-Emb": "0.0979", "Gemma3-Mean": "0.0295", "Gemma3-Last": "0.0527", "Qwen3.5-Mean": "0.0239", "Qwen3.5-Last": "0.0318", "Dedicated Mean": "0.1228", "Base-Mean": "0.0267", "Base-Last": "0.0422"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Soft-ZCA", "EmbGemma": "0.4724", "Qwen3-Emb": "0.3517", "Gemma3-Mean": "0.2497", "Gemma3-Last": "0.3169", "Qwen3.5-Mean": "0.2755", "Qwen3.5-Last": "0.3366", "Dedicated Mean": "0.4121", "Base-Mean": "0.2626", "Base-Last": "0.3267"}, {"Dataset": "STS22.v2", "k": "d", "Method": "COAST (Ours)", "EmbGemma": "0.1522", "Qwen3-Emb": "0.1027", "Gemma3-Mean": "0.2810", "Gemma3-Last": "0.1916", "Qwen3.5-Mean": "0.2804", "Qwen3.5-Last": "0.3091", "Dedicated Mean": "0.1275", "Base-Mean": "0.2807", "Base-Last": "0.2503"}, {"Dataset": "STS22.v2", "k": "d", "Method": "ABTT (D=1)", "EmbGemma": "0.1544", "Qwen3-Emb": "0.1066", "Gemma3-Mean": "0.0352", "Gemma3-Last": "0.0658", "Qwen3.5-Mean": "0.0297", "Qwen3.5-Last": "0.0494", "Dedicated Mean": "0.1305", "Base-Mean": "0.0324", "Base-Last": "0.0576"}, {"Dataset": "STS22.v2", "k": "d", "Method": "ABTT (D=2)", "EmbGemma": "0.1627", "Qwen3-Emb": "0.1120", "Gemma3-Mean": "0.0412", "Gemma3-Last": "0.0773", "Qwen3.5-Mean": "0.0334", "Qwen3.5-Last": "0.0636", "Dedicated Mean": "0.1373", "Base-Mean": "0.0373", "Base-Last": "0.0704"}, {"Dataset": "STS22.v2", "k": "d", "Method": "ABTT (D=3)", "EmbGemma": "0.1689", "Qwen3-Emb": "0.1170", "Gemma3-Mean": "0.0454", "Gemma3-Last": "0.0879", "Qwen3.5-Mean": "0.0401", "Qwen3.5-Last": "0.0737", "Dedicated Mean": "0.1429", "Base-Mean": "0.0427", "Base-Last": "0.0808"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Unreg. ZCA (Σ, γ=1, ε=1e-6)", "EmbGemma": "0.5059", "Qwen3-Emb": "0.3793", "Gemma3-Mean": "0.3365", "Gemma3-Last": "0.3371", "Qwen3.5-Mean": "0.3785", "Qwen3.5-Last": "0.3793", "Dedicated Mean": "0.4426", "Base-Mean": "0.3575", "Base-Last": "0.3582"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Centered + ε* (Σ, γ=1, ε*)", "EmbGemma": "0.2792", "Qwen3-Emb": "0.2140", "Gemma3-Mean": "0.2805", "Gemma3-Last": "0.2510", "Qwen3.5-Mean": "0.2799", "Qwen3.5-Last": "0.3067", "Dedicated Mean": "0.2466", "Base-Mean": "0.2802", "Base-Last": "0.2788"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Centered + γ_crowd (Σ, γ_crowd, 1e-4)", "EmbGemma": "0.1541", "Qwen3-Emb": "0.1062", "Gemma3-Mean": "0.2497", "Gemma3-Last": "0.2281", "Qwen3.5-Mean": "0.2755", "Qwen3.5-Last": "0.3366", "Dedicated Mean": "0.1301", "Base-Mean": "0.2626", "Base-Last": "0.2823"}, {"Dataset": "STS22.v2", "k": "d", "Method": "w/o Orth. Proj. (Σ, γ_crowd, ε*)", "EmbGemma": "0.1507", "Qwen3-Emb": "0.1029", "Gemma3-Mean": "0.2805", "Gemma3-Last": "0.1799", "Qwen3.5-Mean": "0.2799", "Qwen3.5-Last": "0.3067", "Dedicated Mean": "0.1268", "Base-Mean": "0.2802", "Base-Last": "0.2433"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Orth. Soft-ZCA (Σ_⊥, γ=1, 1e-4)", "EmbGemma": "0.4723", "Qwen3-Emb": "0.3516", "Gemma3-Mean": "0.2496", "Gemma3-Last": "0.3168", "Qwen3.5-Mean": "0.2754", "Qwen3.5-Last": "0.3365", "Dedicated Mean": "0.4120", "Base-Mean": "0.2625", "Base-Last": "0.3266"}, {"Dataset": "STS22.v2", "k": "d", "Method": "w/o Crowd. Exp. (Σ_⊥, γ=1, ε*)", "EmbGemma": "0.2827", "Qwen3-Emb": "0.1952", "Gemma3-Mean": "0.2810", "Gemma3-Last": "0.2558", "Qwen3.5-Mean": "0.2804", "Qwen3.5-Last": "0.3091", "Dedicated Mean": "0.2389", "Base-Mean": "0.2807", "Base-Last": "0.2824"}, {"Dataset": "STS22.v2", "k": "d", "Method": "Fixed γ=0.5 (Σ_⊥, γ=0.5, 1e-4)", "EmbGemma": "0.3046", "Qwen3-Emb": "0.2165", "Gemma3-Mean": "0.1188", "Gemma3-Last": "0.1894", "Qwen3.5-Mean": "0.1082", "Qwen3.5-Last": "0.1668", "Dedicated Mean": "0.2606", "Base-Mean": "0.1135", "Base-Last": "0.1781"}, {"Dataset": "STS22.v2", "k": "d", "Method": "w/o Adaptive ε* (Σ_⊥, γ_crowd, 1e-4)", "EmbGemma": "0.1556", "Qwen3-Emb": "0.1068", "Gemma3-Mean": "0.2496", "Gemma3-Last": "0.2393", "Qwen3.5-Mean": "0.2754", "Qwen3.5-Last": "0.3365", "Dedicated Mean": "0.1312", "Base-Mean": "0.2625", "Base-Last": "0.2879"}], "geom_comp::IsoScore": [{"Dataset": "FiQA-2018", "k": "512", "Method": "Prefix (MRL)", "EmbGemma": "0.2271", "Qwen3-Emb": "0.1820", "Gemma3-Mean": "0.0331", "Gemma3-Last": "0.0385", "Qwen3.5-Mean": "0.0549", "Qwen3.5-Last": "0.0264", "Dedicated Mean": "0.2046", "Base-Mean": "0.0440", "Base-Last": "0.0324"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "PCA-k", "EmbGemma": "0.2200", "Qwen3-Emb": "0.2219", "Gemma3-Mean": "0.0623", "Gemma3-Last": "0.0386", "Qwen3.5-Mean": "0.0634", "Qwen3.5-Last": "0.0280", "Dedicated Mean": "0.2209", "Base-Mean": "0.0629", "Base-Last": "0.0333"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "Whitening-k", "EmbGemma": "0.9916", "Qwen3-Emb": "0.9964", "Gemma3-Mean": "0.9486", "Gemma3-Last": "0.9487", "Qwen3.5-Mean": "0.9643", "Qwen3.5-Last": "0.9564", "Dedicated Mean": "0.9940", "Base-Mean": "0.9565", "Base-Last": "0.9526"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "SpecTemp", "EmbGemma": "0.2577", "Qwen3-Emb": "0.2544", "Gemma3-Mean": "0.0678", "Gemma3-Last": "0.0407", "Qwen3.5-Mean": "0.0682", "Qwen3.5-Last": "0.0311", "Dedicated Mean": "0.2560", "Base-Mean": "0.0680", "Base-Last": "0.0359"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "COAST (Ours)", "EmbGemma": "0.2610", "Qwen3-Emb": "0.2564", "Gemma3-Mean": "0.9429", "Gemma3-Last": "0.9331", "Qwen3.5-Mean": "0.9523", "Qwen3.5-Last": "0.9334", "Dedicated Mean": "0.2587", "Base-Mean": "0.9476", "Base-Last": "0.9333"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "Orth. PCA (Σ_⊥, γ=0, ε=0)", "EmbGemma": "0.2250", "Qwen3-Emb": "0.2218", "Gemma3-Mean": "0.0626", "Gemma3-Last": "0.0392", "Qwen3.5-Mean": "0.0633", "Qwen3.5-Last": "0.0284", "Dedicated Mean": "0.2234", "Base-Mean": "0.0630", "Base-Last": "0.0338"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "Orth. SpecTemp (Σ_⊥, γ_SNR, 1e-6)", "EmbGemma": "0.2689", "Qwen3-Emb": "0.2519", "Gemma3-Mean": "0.0669", "Gemma3-Last": "0.0421", "Qwen3.5-Mean": "0.0674", "Qwen3.5-Last": "0.0307", "Dedicated Mean": "0.2604", "Base-Mean": "0.0672", "Base-Last": "0.0364"}, {"Dataset": "FiQA-2018", "k": "512", "Method": "w/o Crowd. 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