1{
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 94      "pred_tau_slope": -3
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100      "tau": 7005.89392999207
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106      "tau": 5901.040015157617
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112      "tau": 2766.8676651981323
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114    {
115      "m": 5,
116      "alpha": 0.016,
117      "radius": 0.2682629883901787,
118      "tau": 1055.1561486846535
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120    {
121      "m": 5,
122      "radius_slope": 0.20577766347847742,
123      "tau_slope": -0.9286053493113741,
124      "pred_radius_slope": 0.2,
125      "pred_tau_slope": -4
126    }
127  ],
128  "adaptation": [
129    {
130      "true_m": 2,
131      "mhat": 2.0,
132      "alpha": 0.0144,
133      "target_radius": 0.12,
134      "observed_radius": 0.08411992760405484,
135      "relative_radius_error": 0.2990006032995429
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137    {
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139      "mhat": 2.9999999999759552,
140      "alpha": 0.0017280000000880955,
141      "target_radius": 0.12,
142      "observed_radius": 0.08006999433122121,
143      "relative_radius_error": 0.3327500472398232
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145    {
146      "true_m": 4,
147      "mhat": 3.9999999987977546,
148      "alpha": 0.0002073600005285766,
149      "target_radius": 0.12,
150      "observed_radius": 0.04172193338952996,
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153    {
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155      "mhat": 4.999999953245995,
156      "alpha": 2.4883202466691943e-05,
157      "target_radius": 0.12,
158      "observed_radius": 0.003310643159618607,
159      "relative_radius_error": 0.9724113070031782
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161  ],
162  "empirical_C_calibration": [
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165      "C_hat": 0.7292761138269884,
166      "alpha": 0.02707562644514591,
167      "target_radius": 0.12,
168      "observed_radius": 0.11784159539835042,
169      "relative_error": 0.017986705013746503
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171    {
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174      "alpha": 0.004200087568799656,
175      "target_radius": 0.12,
176      "observed_radius": 0.10189921009017681,
177      "relative_error": 0.1508399159151932
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179    {
180      "m": 4,
181      "C_hat": 0.6857994359354151,
182      "alpha": 0.0009374249102880899,
183      "target_radius": 0.12,
184      "observed_radius": 0.11146914536423262,
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187    {
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191      "target_radius": 0.12,
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193      "relative_error": 0.8300276711101622
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195  ],
196  "noise_sweep": [
197    {
198      "m": 2,
199      "observed_slope": 0.947169387788625,
200      "predicted_slope": 1.0,
201      "sigmas": [
202        0.5,
203        1.0,
204        2.0
205      ],
206      "radii": [
207        0.022776578669000996,
208        0.0465829524843931,
209        0.08467228529776856
210      ]
211    },
212    {
213      "m": 3,
214      "observed_slope": 0.7397084436459019,
215      "predicted_slope": 0.6666666666666666,
216      "sigmas": [
217        0.5,
218        1.0,
219        2.0
220      ],
221      "radii": [
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223        0.09865419341858778,
224        0.18011532398186209
225      ]
226    },
227    {
228      "m": 4,
229      "observed_slope": 0.5343614410435243,
230      "predicted_slope": 0.5,
231      "sigmas": [
232        0.5,
233        1.0,
234        2.0
235      ],
236      "radii": [
237        0.11232096840094631,
238        0.16947806739764723,
239        0.2356017346784698
240      ]
241    },
242    {
243      "m": 5,
244      "observed_slope": 0.36216255094803856,
245      "predicted_slope": 0.4,
246      "sigmas": [
247        0.5,
248        1.0,
249        2.0
250      ],
251      "radii": [
252        0.16885692672294783,
253        0.2433415520572027,
254        0.27897318640160135
255      ]
256    }
257  ],
258  "target_radius_comparison": [
259    {
260      "m": 3,
261      "idea_alpha": 0.0017279999999999997,
262      "idea_radius": 0.08148459724314587,
263      "quadratic_alpha": 0.0144,
264      "quadratic_radius": 0.16492582582103307,
265      "idea_error": 0.038515402756854125,
266      "quadratic_error": 0.04492582582103308
267    },
268    {
269      "m": 4,
270      "idea_alpha": 0.00020735999999999997,
271      "idea_radius": 0.028659743799528303,
272      "quadratic_alpha": 0.0144,
273      "quadratic_radius": 0.2386266738201455,
274      "idea_error": 0.09134025620047169,
275      "quadratic_error": 0.1186266738201455
276    },
277    {
278      "m": 5,
279      "idea_alpha": 2.4883199999999996e-05,
280      "idea_radius": 0.0027375312841225407,
281      "quadratic_alpha": 0.0144,
282      "quadratic_radius": 0.2876697815630658,
283      "idea_error": 0.11726246871587745,
284      "quadratic_error": 0.16766978156306578
285    }
286  ],
287  "notes": "RMS stationary radius and integrated autocorrelation time from 1D constant-step SGD."
288}