Horizon-Dependent Error Tubes for Recurrent Rollouts / results.json

Mechanism confirmed, baseline not beaten

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  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}