1{
  2  "device": "cuda",
  3  "math_check": {
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  7      8,
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 20    "errors": [
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 26    "L_by_error": [
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 29      0.08766853098357358,
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 33    "error_monotone": true
 34  },
 35  "baseline": {
 36    "history": [
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 38        "step": 80,
 39        "width": 8,
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 41        "val_noisy_mse": 0.17820754647254944,
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 49        "train_mse": 0.14347027242183685,
 50        "val_noisy_mse": 0.16282635927200317,
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 52        "lip": 1.0039832592010498,
 53        "L_min": 0.14776556734055996
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 55      {
 56        "step": 240,
 57        "width": 8,
 58        "train_mse": 0.13440828025341034,
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 61        "lip": 1.0772188901901245,
 62        "L_min": 0.1428102548287432
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 64      {
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 66        "width": 8,
 67        "train_mse": 0.1303209811449051,
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 73      {
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 75        "width": 8,
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 77        "val_noisy_mse": 0.16975757479667664,
 78        "val_clean_mse": 0.024437502026557922,
 79        "lip": 1.1557098627090454,
 80        "L_min": 0.13836082984373332
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 82      {
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 84        "width": 8,
 85        "train_mse": 0.1218029260635376,
 86        "val_noisy_mse": 0.16326120495796204,
 87        "val_clean_mse": 0.029996026307344437,
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 89        "L_min": 0.13564506096015938
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 91      {
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 93        "width": 8,
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 97        "lip": 1.1659594774246216,
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100      {
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102        "width": 8,
103        "train_mse": 0.116698257625103,
104        "val_noisy_mse": 0.17328844964504242,
105        "val_clean_mse": 0.03547520563006401,
106        "lip": 1.217297911643982,
107        "L_min": 0.1326436338079067
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109      {
110        "step": 720,
111        "width": 8,
112        "train_mse": 0.11563277989625931,
113        "val_noisy_mse": 0.17306701838970184,
114        "val_clean_mse": 0.03700945898890495,
115        "lip": 1.2343106269836426,
116        "L_min": 0.1320093345034342
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118      {
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120        "width": 8,
121        "train_mse": 0.11480408906936646,
122        "val_noisy_mse": 0.17401330173015594,
123        "val_clean_mse": 0.03710782900452614,
124        "lip": 1.2365026473999023,
125        "L_min": 0.13151407560550563
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127    ],
128    "final_width": 8,
129    "widen_count": 0,
130    "test_clean_mse": 0.04776359349489212,
131    "seconds": 3.2510766983032227
132  },
133  "idea": {
134    "history": [
135      {
136        "step": 80,
137        "width": 8,
138        "train_mse": 0.16605648398399353,
139        "val_noisy_mse": 0.17820754647254944,
140        "val_clean_mse": 0.058361660689115524,
141        "lip": 0.9579295516014099,
142        "L_min": 0.15950508324749557
143      },
144      {
145        "step": 160,
146        "width": 8,
147        "train_mse": 0.14347027242183685,
148        "val_noisy_mse": 0.16282635927200317,
149        "val_clean_mse": 0.03278361260890961,
150        "lip": 1.0039832592010498,
151        "L_min": 0.14776556734055996
152      },
153      {
154        "step": 240,
155        "width": 8,
156        "train_mse": 0.13440828025341034,
157        "val_noisy_mse": 0.1615668535232544,
158        "val_clean_mse": 0.026324784383177757,
159        "lip": 1.0772188901901245,
160        "L_min": 0.1428102548287432
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162      {
163        "step": 320,
164        "width": 8,
165        "train_mse": 0.1303209811449051,
166        "val_noisy_mse": 0.16439856588840485,
167        "val_clean_mse": 0.023705391213297844,
168        "lip": 1.125458002090454,
169        "L_min": 0.14052335453160208
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171      {
172        "step": 400,
173        "width": 8,
174        "train_mse": 0.12651120126247406,
175        "val_noisy_mse": 0.16975757479667664,
176        "val_clean_mse": 0.024437502026557922,
177        "lip": 1.1557098627090454,
178        "L_min": 0.13836082984373332
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180      {
181        "step": 480,
182        "width": 8,
183        "train_mse": 0.1218029260635376,
184        "val_noisy_mse": 0.16326120495796204,
185        "val_clean_mse": 0.029996026307344437,
186        "lip": 1.3178538084030151,
187        "L_min": 0.13564506096015938
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189      {
190        "step": 560,
191        "width": 8,
192        "train_mse": 0.11894500255584717,
193        "val_noisy_mse": 0.17012105882167816,
194        "val_clean_mse": 0.03174234554171562,
195        "lip": 1.1659594774246216,
196        "L_min": 0.13397220359599796
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198      {
199        "step": 640,
200        "width": 8,
201        "train_mse": 0.116698257625103,
202        "val_noisy_mse": 0.17328844964504242,
203        "val_clean_mse": 0.03547520563006401,
204        "lip": 1.217297911643982,
205        "L_min": 0.1326436338079067
206      },
207      {
208        "step": 720,
209        "width": 8,
210        "train_mse": 0.11563277989625931,
211        "val_noisy_mse": 0.17306701838970184,
212        "val_clean_mse": 0.03700945898890495,
213        "lip": 1.2343106269836426,
214        "L_min": 0.1320093345034342
215      },
216      {
217        "step": 800,
218        "width": 8,
219        "train_mse": 0.11480408906936646,
220        "val_noisy_mse": 0.17401330173015594,
221        "val_clean_mse": 0.03710782900452614,
222        "lip": 1.2365026473999023,
223        "L_min": 0.13151407560550563
224      }
225    ],
226    "final_width": 8,
227    "widen_count": 0,
228    "test_clean_mse": 0.04776359349489212,
229    "seconds": 3.1248812675476074
230  },
231  "constants": {
232    "c0": 0.25,
233    "C0": 2.0,
234    "eta": 0.9
235  },
236  "interpretation": "Controller widens only when empirical error is below known noise variance and estimated Jacobian Lipschitz constant is below the bound."
237}