{ "seed": 7, "math_checks": { "regular_direction_loglog_slope": 1.0398056110840164, "predicted_regular_slope": 1.0, "gate_noise_levels": [ 0.01, 0.05, 0.15, 0.4 ], "gate_regular_fraction": [ 0.99, 0.99, 0.83, 0.33 ], "predicted_gate_trend": "decreases as noise increases", "degenerate_direction_loglog_slope": 1.0250923357969701, "predicted_worst_case_exponent": 0.5, "regular_reduced_eigenvalue": 0.7668787351931636, "degenerate_reduced_eigenvalue": 4.76140256803781e-17, "degenerate_curvature_prediction": "near-zero curvature => fallback", "degenerate_curvature_observed": "near-zero curvature; sensitivity exponent was not sublinear" }, "benchmark": { "uniform": { "mean_final": 1.7779841292916871, "worst_final": 2.2408481851173567, "mean_best": 1.7777783663810858, "worst_best": 2.1768515944260045, "direction_change": 0.18334240479769104, "regular_fraction": 0.0 }, "uniform_std": { "mean_final": 0.00018887023577259483, "worst_final": 0.012357649210901631, "mean_best": 3.7315061445819435e-07, "worst_best": 0.009978898098043478, "direction_change": 0.002611286469693151, "regular_fraction": 0.0 }, "mgda": { "mean_final": 1.976632096531923, "worst_final": 2.8746929694462926, "mean_best": 1.976632096531923, "worst_best": 2.8667433880631337, "direction_change": 0.05377375622257376, "regular_fraction": 0.0 }, "mgda_std": { "mean_final": 0.005361086825994062, "worst_final": 0.01141293331311631, "mean_best": 0.005361086825994062, "worst_best": 0.01222652270339705, "direction_change": 0.0027866200628133657, "regular_fraction": 0.0 }, "gated": { "mean_final": 1.7779841491037414, "worst_final": 2.24084841716066, "mean_best": 1.7777781630278373, "worst_best": 2.199101719607222, "direction_change": 0.1872844354629059, "regular_fraction": 0.11933333333333333 }, "gated_std": { "mean_final": 0.00018892297863517453, "worst_final": 0.012356767325243824, "mean_best": 2.3382598744402486e-07, "worst_best": 0.0042639550623940715, "direction_change": 0.0009570646841997197, "regular_fraction": 0.011813363431112897 } } }