{ "math_check": { "m": [ 4, 8, 16, 32, 64 ], "uniform_fill_distance": [ 0.16666666666666663, 0.0714285714285714, 0.033333333333333326, 0.016129032258064502, 0.007936507936507908 ], "random_fill_distance": [ 0.23397415250196385, 0.1277494556085682, 0.28570086584640264, 0.05971168753329348, 0.038909038705860266 ], "uniform_theory": [ 0.16666666666666666, 0.07142857142857142, 0.03333333333333333, 0.016129032258064516, 0.007936507936507936 ], "loglog_slope": -1.0931476233886805, "max_uniform_theory_error": 2.7755575615628914e-17 }, "records": [ { "m": 16, "kappa": 0.5, "N": 4, "oracle_error": 0.2040305789000492, "learned_error": 0.9853597366377419, "learned_oracle_gap": 0.7813291577376927, "feature_fill_proxy": 3.472172940430821, "kernel_solve_flops_proxy": 64, "wall_seconds": 0.17418547600004786 }, { "m": 16, "kappa": 1.0, "N": 16, "oracle_error": 0.2040305789000492, "learned_error": 0.720155988937691, "learned_oracle_gap": 0.5161254100376418, "feature_fill_proxy": 3.065619852428132, "kernel_solve_flops_proxy": 4096, "wall_seconds": 0.16841927800010126 }, { "m": 16, "kappa": 1.5, "N": 64, "oracle_error": 0.2040305789000492, "learned_error": 0.47095998892156093, "learned_oracle_gap": 0.2669294100215117, "feature_fill_proxy": 2.438866293718865, "kernel_solve_flops_proxy": 262144, "wall_seconds": 0.20934817600004862 }, { "m": 32, "kappa": 0.5, "N": 6, "oracle_error": 0.01423599500130251, "learned_error": 0.9564053342258948, "learned_oracle_gap": 0.9421693392245923, "feature_fill_proxy": 3.3869926876237337, "kernel_solve_flops_proxy": 216, "wall_seconds": 0.16910652899991874 }, { "m": 32, "kappa": 1.0, "N": 32, "oracle_error": 0.01423599500130251, "learned_error": 0.632156643121925, "learned_oracle_gap": 0.6179206481206225, "feature_fill_proxy": 2.8187333910505727, "kernel_solve_flops_proxy": 32768, "wall_seconds": 0.18333994299996448 }, { "m": 32, "kappa": 1.5, "N": 128, "oracle_error": 0.01423599500130251, "learned_error": 0.30988224237125184, "learned_oracle_gap": 0.2956462473699493, "feature_fill_proxy": 2.1391915442230114, "kernel_solve_flops_proxy": 2097152, "wall_seconds": 0.33267084400017666 }, { "m": 64, "kappa": 0.5, "N": 8, "oracle_error": 0.0003845574505827757, "learned_error": 0.9333357967169278, "learned_oracle_gap": 0.932951239266345, "feature_fill_proxy": 3.3869926876237337, "kernel_solve_flops_proxy": 512, "wall_seconds": 0.16631164000000354 }, { "m": 64, "kappa": 1.0, "N": 64, "oracle_error": 0.0003845574505827757, "learned_error": 0.47002880668486247, "learned_oracle_gap": 0.46964424923427966, "feature_fill_proxy": 2.438866293718865, "kernel_solve_flops_proxy": 262144, "wall_seconds": 0.23882444099990607 }, { "m": 64, "kappa": 1.5, "N": 128, "oracle_error": 0.0003845574505827757, "learned_error": 0.3112644305641941, "learned_oracle_gap": 0.3108798731136113, "feature_fill_proxy": 2.1391915442230114, "kernel_solve_flops_proxy": 2097152, "wall_seconds": 0.34122536399991077 } ], "fixed_N_baseline": [ { "m": 16, "N": 16, "error": 0.720155988937691, "wall_seconds": 0.191977715999883 }, { "m": 32, "N": 16, "error": 0.7272770405371206, "wall_seconds": 0.1931695779999245 }, { "m": 64, "N": 16, "error": 0.7276208762842657, "wall_seconds": 0.19215197300013642 } ] }