{ "toy": { "rows": [ { "r": 0.0, "q": 0.0, "block_q": [ 0.0, 0.0 ], "determinant": 1.0, "cond2": 1.0, "converged": true, "iterations": 2 }, { "r": 0.024999999999999998, "q": 0.024999999999999998, "block_q": [ 0.024999999999999998, 0.024999999999999998 ], "determinant": 0.999375, "cond2": 1.051282051282051, "converged": true, "iterations": 6 }, { "r": 0.049999999999999996, "q": 0.049999999999999996, "block_q": [ 0.049999999999999996, 0.049999999999999996 ], "determinant": 0.9975, "cond2": 1.1052631578947367, "converged": true, "iterations": 8 }, { "r": 0.075, "q": 0.075, "block_q": [ 0.075, 0.075 ], "determinant": 0.994375, "cond2": 1.1621621621621625, "converged": true, "iterations": 9 }, { "r": 0.09999999999999999, "q": 0.09999999999999999, "block_q": [ 0.09999999999999999, 0.09999999999999999 ], "determinant": 0.99, "cond2": 1.2222222222222225, "converged": true, "iterations": 9 }, { "r": 0.12499999999999999, "q": 0.12499999999999999, "block_q": [ 0.12499999999999999, 0.12499999999999999 ], "determinant": 0.984375, "cond2": 1.2857142857142858, "converged": true, "iterations": 10 }, { "r": 0.15, "q": 0.15, "block_q": [ 0.15, 0.15 ], "determinant": 0.9775, "cond2": 1.352941176470588, "converged": true, "iterations": 11 }, { "r": 0.175, "q": 0.175, "block_q": [ 0.175, 0.175 ], "determinant": 0.969375, "cond2": 1.4242424242424239, "converged": true, "iterations": 12 }, { "r": 0.19999999999999998, "q": 0.19999999999999998, "block_q": [ 0.19999999999999998, 0.19999999999999998 ], "determinant": 0.96, "cond2": 1.5000000000000004, "converged": true, "iterations": 13 }, { "r": 0.22499999999999998, "q": 0.22499999999999998, "block_q": [ 0.22499999999999998, 0.22499999999999998 ], "determinant": 0.949375, "cond2": 1.5806451612903227, "converged": true, "iterations": 14 }, { "r": 0.24999999999999997, "q": 0.24999999999999997, "block_q": [ 0.24999999999999997, 0.24999999999999997 ], "determinant": 0.9375, "cond2": 1.6666666666666659, "converged": true, "iterations": 15 }, { "r": 0.27499999999999997, "q": 0.27499999999999997, "block_q": [ 0.27499999999999997, 0.27499999999999997 ], "determinant": 0.9243750000000001, "cond2": 1.7586206896551715, "converged": true, "iterations": 16 }, { "r": 0.3, "q": 0.3, "block_q": [ 0.3, 0.3 ], "determinant": 0.91, "cond2": 1.857142857142857, "converged": true, "iterations": 17 }, { "r": 0.32499999999999996, "q": 0.32499999999999996, "block_q": [ 0.32499999999999996, 0.32499999999999996 ], "determinant": 0.894375, "cond2": 1.9629629629629624, "converged": true, "iterations": 18 }, { "r": 0.35, "q": 0.35, "block_q": [ 0.35, 0.35 ], "determinant": 0.8775000000000001, "cond2": 2.076923076923077, "converged": true, "iterations": 19 }, { "r": 0.37499999999999994, "q": 0.37499999999999994, "block_q": [ 0.37499999999999994, 0.37499999999999994 ], "determinant": 0.859375, "cond2": 2.2000000000000006, "converged": true, "iterations": 20 }, { "r": 0.39999999999999997, "q": 0.39999999999999997, "block_q": [ 0.39999999999999997, 0.39999999999999997 ], "determinant": 0.8400000000000001, "cond2": 2.333333333333334, "converged": true, "iterations": 22 }, { "r": 0.425, "q": 0.425, "block_q": [ 0.425, 0.425 ], "determinant": 0.819375, "cond2": 2.4782608695652173, "converged": true, "iterations": 23 }, { "r": 0.44999999999999996, "q": 0.44999999999999996, "block_q": [ 0.44999999999999996, 0.44999999999999996 ], "determinant": 0.7975000000000001, "cond2": 2.6363636363636376, "converged": true, "iterations": 25 }, { "r": 0.475, "q": 0.475, "block_q": [ 0.475, 0.475 ], "determinant": 0.774375, "cond2": 2.8095238095238093, "converged": true, "iterations": 26 }, { "r": 0.49999999999999994, "q": 0.49999999999999994, "block_q": [ 0.49999999999999994, 0.49999999999999994 ], "determinant": 0.75, "cond2": 2.999999999999999, "converged": true, "iterations": 28 }, { "r": 0.5249999999999999, "q": 0.5249999999999999, "block_q": [ 0.5249999999999999, 0.5249999999999999 ], "determinant": 0.7243750000000001, "cond2": 3.2105263157894735, "converged": true, "iterations": 30 }, { "r": 0.5499999999999999, "q": 0.5499999999999999, "block_q": [ 0.5499999999999999, 0.5499999999999999 ], "determinant": 0.6975, "cond2": 3.4444444444444415, "converged": true, "iterations": 32 }, { "r": 0.575, "q": 0.575, "block_q": [ 0.575, 0.575 ], "determinant": 0.669375, "cond2": 3.7058823529411766, "converged": true, "iterations": 35 }, { "r": 0.6, "q": 0.6, "block_q": [ 0.6, 0.6 ], "determinant": 0.64, "cond2": 4.000000000000001, "converged": true, "iterations": 38 }, { "r": 0.625, "q": 0.625, "block_q": [ 0.625, 0.625 ], "determinant": 0.609375, "cond2": 4.333333333333335, "converged": true, "iterations": 41 }, { "r": 0.6499999999999999, "q": 0.6499999999999999, "block_q": [ 0.6499999999999999, 0.6499999999999999 ], "determinant": 0.5775000000000001, "cond2": 4.714285714285713, "converged": true, "iterations": 44 }, { "r": 0.6749999999999999, "q": 0.6749999999999999, "block_q": [ 0.6749999999999999, 0.6749999999999999 ], "determinant": 0.544375, "cond2": 5.153846153846154, "converged": true, "iterations": 48 }, { "r": 0.7, "q": 0.7, "block_q": [ 0.7, 0.7 ], "determinant": 0.51, "cond2": 5.6666666666666625, "converged": true, "iterations": 53 }, { "r": 0.725, "q": 0.725, "block_q": [ 0.725, 0.725 ], "determinant": 0.474375, "cond2": 6.272727272727273, "converged": true, "iterations": 59 }, { "r": 0.7499999999999999, "q": 0.7499999999999999, "block_q": [ 0.7499999999999999, 0.7499999999999999 ], "determinant": 0.4375000000000001, "cond2": 6.999999999999994, "converged": true, "iterations": 66 }, { "r": 0.7749999999999999, "q": 0.7749999999999999, "block_q": [ 0.7749999999999999, 0.7749999999999999 ], "determinant": 0.39937500000000015, "cond2": 7.888888888888881, "converged": true, "iterations": 74 }, { "r": 0.7999999999999999, "q": 0.7999999999999999, "block_q": [ 0.7999999999999999, 0.7999999999999999 ], "determinant": 0.36000000000000015, "cond2": 8.999999999999996, "converged": true, "iterations": 84 }, { "r": 0.825, "q": 0.825, "block_q": [ 0.825, 0.825 ], "determinant": 0.3193750000000001, "cond2": 10.428571428571423, "converged": true, "iterations": 97 }, { "r": 0.85, "q": 0.85, "block_q": [ 0.85, 0.85 ], "determinant": 0.2775000000000001, "cond2": 12.333333333333329, "converged": true, "iterations": 115 }, { "r": 0.8749999999999999, "q": 0.8749999999999999, "block_q": [ 0.8749999999999999, 0.8749999999999999 ], "determinant": 0.23437500000000025, "cond2": 14.999999999999986, "converged": true, "iterations": 139 }, { "r": 0.8999999999999999, "q": 0.8999999999999999, "block_q": [ 0.8999999999999999, 0.8999999999999999 ], "determinant": 0.19000000000000017, "cond2": 18.99999999999998, "converged": true, "iterations": 176 }, { "r": 0.9249999999999999, "q": 0.9249999999999999, "block_q": [ 0.9249999999999999, 0.9249999999999999 ], "determinant": 0.14437500000000014, "cond2": 25.666666666666654, "converged": true, "iterations": 238 }, { "r": 0.95, "q": 0.95, "block_q": [ 0.95, 0.95 ], "determinant": 0.09750000000000002, "cond2": 39.0000000000001, "converged": true, "iterations": 361 }, { "r": 0.9749999999999999, "q": 0.9749999999999999, "block_q": [ 0.9749999999999999, 0.9749999999999999 ], "determinant": 0.049375000000000294, "cond2": 78.99999999999986, "converged": true, "iterations": 729 }, { "r": 0.9999999999999999, "q": 0.9999999999999999, "block_q": [ 0.9999999999999999, 0.9999999999999999 ], "determinant": 2.2204460492503185e-16, "cond2": Infinity, "converged": false, "iterations": 2000 }, { "r": 1.025, "q": 1.025, "block_q": [ 1.025, 1.025 ], "determinant": -0.0506249999999998, "cond2": 81.00000000000033, "converged": false, "iterations": 2000 }, { "r": 1.0499999999999998, "q": 1.0499999999999998, "block_q": [ 1.0499999999999998, 1.0499999999999998 ], "determinant": -0.10249999999999959, "cond2": 41.00000000000033, "converged": false, "iterations": 2000 }, { "r": 1.075, "q": 1.075, "block_q": [ 1.075, 1.075 ], "determinant": -0.15562499999999999, "cond2": 27.66666666666675, "converged": false, "iterations": 2000 }, { "r": 1.0999999999999999, "q": 1.0999999999999999, "block_q": [ 1.0999999999999999, 1.0999999999999999 ], "determinant": -0.20999999999999971, "cond2": 21.000000000000014, "converged": false, "iterations": 2000 }, { "r": 1.125, "q": 1.125, "block_q": [ 1.125, 1.125 ], "determinant": -0.26562500000000006, "cond2": 16.999999999999996, "converged": false, "iterations": 2000 }, { "r": 1.15, "q": 1.15, "block_q": [ 1.15, 1.15 ], "determinant": -0.32249999999999973, "cond2": 14.333333333333341, "converged": false, "iterations": 2000 }, { "r": 1.1749999999999998, "q": 1.1749999999999998, "block_q": [ 1.1749999999999998, 1.1749999999999998 ], "determinant": -0.3806249999999996, "cond2": 12.428571428571454, "converged": false, "iterations": 2000 }, { "r": 1.2, "q": 1.2, "block_q": [ 1.2, 1.2 ], "determinant": -0.4399999999999999, "cond2": 11.000000000000007, "converged": false, "iterations": 2000 } ], "predictions": { "q_equals_coupling_max_abs_error": 0.0, "predicted_singularity_q": 1.0, "observed_zero_determinant_r": 0.9999999999999999, "observed_fixed_point_boundary_midpoint": 0.9874999999999998, "predicted_fixed_point_boundary_q": 1.0, "condition_scaled_c_times_1_minus_q_median_q_le_0.9": 1.4500000000000008, "condition_scaled_range_q_le_0.9": [ 1.0, 1.8999999999999995 ] } }, "random_block_certificate": { "samples": 1000, "worst_q": 0.8500000000000003, "near_singular_count": 0 }, "fit_unconstrained": { "r_learned": 0.9500012527120318, "q": 0.9500012527120318, "task_loss": 2.2060410379253905e-08, "total_loss": 2.2060410379253905e-08, "target_q": 0.95, "certificate_limit": 0.8, "optimizer_success": true }, "fit_bdd_lam_10": { "r_learned": 0.9498965131434333, "q": 0.9498965131434333, "task_loss": 0.00015734900980612695, "total_loss": 0.2248469955354006, "target_q": 0.95, "certificate_limit": 0.8, "optimizer_success": true }, "fit_bdd_lam_1000": { "r_learned": 0.8576117443675801, "q": 0.8576117443675801, "task_loss": 15.157600108768255, "total_loss": 18.47671319784365, "target_q": 0.95, "certificate_limit": 0.8, "optimizer_success": true }, "fit_bdd_lam_100000": { "r_learned": 0.8003385305863355, "q": 0.8003385305863355, "task_loss": 20.22936546963947, "total_loss": 20.24082576542793, "target_q": 0.95, "certificate_limit": 0.8, "optimizer_success": true } }