Horizon-Dependent Error Tubes for Recurrent Rollouts / results.json
Mechanism confirmed, baseline not beaten
1{
2 "time_varying_local_vs_shared": {
3 "rho_local_max": 0.8999964743755172,
4 "rho_shared_worst_case": 0.8999964743755172,
5 "local_final_tube_sum": 0.14157703514510034,
6 "shared_final_tube_sum": 0.2516028117530324,
7 "shared_over_local_final": 1.777144234551657,
8 "mean_shared_over_local": 1.5751008128732233,
9 "local_tube_sums_first_8": [
10 0.0,
11 0.03,
12 0.05110304342324915,
13 0.07097096100924125,
14 0.08997453922886889,
15 0.10149751195033717,
16 0.10227083024838049,
17 0.10088231614603274
18 ],
19 "shared_tube_sums_first_8": [
20 0.0,
21 0.03,
22 0.05469221096363599,
23 0.07579677934206844,
24 0.09424885652737613,
25 0.11059301983903416,
26 0.12517542977704155,
27 0.13823786598613358
28 ]
29 },
30 "base_rho": 0.78,
31 "predicted_alpha_boundary": 1.282051282051282,
32 "sweep": [
33 {
34 "alpha": 1.0256410256410255,
35 "rho_abs": 0.7999999999999999,
36 "final_total": 0.13198198198178882,
37 "growth_ratio_last": 1.0000000000003657,
38 "predicted_plateau_total": 0.13198198198198194,
39 "plateau_relative_error": 1.880411031563475e-12
40 },
41 {
42 "alpha": 1.2179487179487178,
43 "rho_abs": 0.95,
44 "final_total": 0.4993097335727175,
45 "growth_ratio_last": 1.0001004364777617,
46 "predicted_plateau_total": 0.5002624671916,
47 "plateau_relative_error": 0.0020438711080755247
48 },
49 {
50 "alpha": 1.2692307692307692,
51 "rho_abs": 0.99,
52 "final_total": 1.736499150196714,
53 "growth_ratio_last": 1.0042048513199515,
54 "predicted_plateau_total": 2.456342668863239,
55 "plateau_relative_error": 0.29737637193551586
56 },
57 {
58 "alpha": 1.282051282051282,
59 "rho_abs": 1.0,
60 "final_total": 2.985370370370339,
61 "growth_ratio_last": 1.0082556757770968,
62 "predicted_log_growth": 0.0,
63 "observed_log_growth": 0.010491416999688443
64 },
65 {
66 "alpha": 1.2948717948717947,
67 "rho_abs": 1.01,
68 "final_total": 5.767362567146568,
69 "growth_ratio_last": 1.014277504610048,
70 "predicted_log_growth": 0.009950330853168092,
71 "observed_log_growth": 0.01625090807068894
72 },
73 {
74 "alpha": 1.346153846153846,
75 "rho_abs": 1.05,
76 "final_total": 184.0595662248499,
77 "growth_ratio_last": 1.0501358191206804,
78 "predicted_log_growth": 0.04879016416943205,
79 "observed_log_growth": 0.049302332034196164
80 },
81 {
82 "alpha": 1.5384615384615383,
83 "rho_abs": 1.2,
84 "final_total": 515062429.4178364,
85 "growth_ratio_last": 1.2000000000496351,
86 "predicted_log_growth": 0.1823215567939546,
87 "observed_log_growth": 0.18232157794570988
88 }
89 ],
90 "near_boundary_plateau_scaling": [
91 {
92 "rho": 0.5,
93 "plateau_total": 0.056491228070175425,
94 "scaled_plateau": 0.028245614035087713
95 },
96 {
97 "rho": 0.7,
98 "plateau_total": 0.09039780521262002,
99 "scaled_plateau": 0.02711934156378601
100 },
101 {
102 "rho": 0.8,
103 "plateau_total": 0.13198198198198202,
104 "scaled_plateau": 0.026396396396396397
105 },
106 {
107 "rho": 0.9,
108 "plateau_total": 0.25522388059701473,
109 "scaled_plateau": 0.025522388059701466
110 },
111 {
112 "rho": 0.95,
113 "plateau_total": 0.5002624671916,
114 "scaled_plateau": 0.02501312335958002
115 },
116 {
117 "rho": 0.98,
118 "plateau_total": 1.233984799131377,
119 "scaled_plateau": 0.024679695982627564
120 }
121 ],
122 "output_margin_linear_ratio_min": 0.7549342105263158,
123 "output_margin_linear_ratio_max": 0.8749999999999999,
124 "random_disturbance_max_bound_violation": 0.0,
125 "formula": "ebar[j+1]=abs(A)@ebar[j]+w; fixed=(I-A)^(-1)w"
126}