{ "seed": 2486, "predictions": { "P1_exact_nullspace": "||YX^T|| remains at floating-point roundoff", "P2_noise_scaling": "||YX^T|| ~ gamma^1 and normalized penalty ~ gamma^2", "P3_diagonal_gauge": "D=cI preserves zero; nonconstant D produces residual" }, "exact_sweep": [ { "a": 2, "b": 5, "residual_norm": 4.236704743275018e-16, "relative_penalty": 6.914097353818902e-33, "rank": 2 }, { "a": 3, "b": 7, "residual_norm": 8.900467034796993e-16, "relative_penalty": 8.414393100828013e-33, "rank": 3 }, { "a": 5, "b": 9, "residual_norm": 9.645516443905538e-16, "relative_penalty": 6.283162424639603e-33, "rank": 5 }, { "a": 8, "b": 13, "residual_norm": 2.4587513058959576e-15, "relative_penalty": 1.040637823196967e-32, "rank": 8 } ], "noise_sweep": [ { "gamma": 1e-06, "residual_norm": 2.303071306628882e-06, "penalty": 2.9855350370475615e-14, "norm_over_gamma": 2.3030713066288824, "penalty_over_gamma2": 0.029855350370475615 }, { "gamma": 5.179474679231212e-06, "residual_norm": 1.192869951601395e-05, "penalty": 8.009283807395689e-13, "norm_over_gamma": 2.3030713064098856, "penalty_over_gamma2": 0.02985535602466829 }, { "gamma": 2.6826957952797274e-05, "residual_norm": 6.178439709764778e-05, "penalty": 2.1486493087437117e-11, "norm_over_gamma": 2.3030713063463635, "penalty_over_gamma2": 0.029855385334873405 }, { "gamma": 0.00013894954943731373, "residual_norm": 0.00032001072033704367, "penalty": 5.764201760771672e-10, "norm_over_gamma": 2.3030713063334876, "penalty_over_gamma2": 0.029855537065896855 }, { "gamma": 0.0007196856730011522, "residual_norm": 0.0016574874230663838, "penalty": 1.546400564410417e-08, "norm_over_gamma": 2.3030713063308825, "penalty_over_gamma2": 0.02985632057650967 }, { "gamma": 0.0037275937203149418, "residual_norm": 0.008584914138915538, "penalty": 4.149077306033708e-07, "norm_over_gamma": 2.303071306330617, "penalty_over_gamma2": 0.029860314933266734 }, { "gamma": 0.019306977288832496, "residual_norm": 0.04446534540588557, "penalty": 1.113778491139982e-05, "norm_over_gamma": 2.3030713063305424, "penalty_over_gamma2": 0.029879288750542285 }, { "gamma": 0.1, "residual_norm": 0.23030713063305308, "penalty": 0.00029931255081029287, "norm_over_gamma": 2.303071306330531, "penalty_over_gamma2": 0.02993125508102928 } ], "noise_loglog_slopes": { "residual_norm": 0.9999999999920334, "penalty": 2.000161430017986 }, "gauge_loglog_slope": 0.8774577224640229, "diagonal_sweep": [ { "spread": 0.0, "residual_norm": 1.1662567990380876e-15, "penalty": 7.655891334799334e-33 }, { "spread": 0.01, "residual_norm": 0.034496357202347366, "penalty": 6.698134373228444e-06 }, { "spread": 0.03, "residual_norm": 0.06985774800658698, "penalty": 2.7468601307560305e-05 }, { "spread": 0.1, "residual_norm": 0.4842317313380071, "penalty": 0.0013198174722236487 }, { "spread": 0.3, "residual_norm": 0.9528435122062417, "penalty": 0.005110348830010954 }, { "spread": 1.0, "residual_norm": 1.4560688401768715, "penalty": 0.011933592383219331 } ], "toy_comparison": { "primary_test_mse": 0.04743790322015813, "gale_combined_test_mse": 0.0024276607671189733, "feature_width_primary": 3, "feature_width_combined": 8 } }