Trajectory-Certified Contractive RNN / results.json
Beats tuned baseline
1{
2 "seed": 1436,
3 "b": 0.45,
4 "rows": [
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9 "impulse_l2": 3.2899080248844666e+39,
10 "cert": false,
11 "gamma": Infinity,
12 "data_cert": false,
13 "data_gamma": Infinity,
14 "lmi_maxeig": Infinity
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20 "impulse_l2": 1.4573659887214219,
21 "cert": false,
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23 "data_cert": false,
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25 "lmi_maxeig": Infinity
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27 {
28 "a": -0.8,
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31 "impulse_l2": 1.1150947983935109,
32 "cert": false,
33 "gamma": Infinity,
34 "data_cert": false,
35 "data_gamma": Infinity,
36 "lmi_maxeig": Infinity
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38 {
39 "a": -0.5,
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43 "cert": true,
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48 "linear_gain_pred": 1.0526315789473684
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50 {
51 "a": -0.2,
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60 "linear_gain_pred": 1.3333333333333333
61 },
62 {
63 "a": 0.0,
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65 "measured_rho": 0.4499999999999245,
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67 "cert": true,
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84 "linear_gain_pred": 2.857142857142857
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86 {
87 "a": 0.4,
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89 "measured_rho": 0.8499999999997829,
90 "impulse_l2": 1.6129898587029121,
91 "cert": true,
92 "gamma": 13.894954943731374,
93 "data_cert": true,
94 "data_gamma": 13.894954943731374,
95 "lmi_maxeig": -0.1038011552756935,
96 "linear_gain_pred": 6.6666666666666705
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98 {
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109 {
110 "a": 0.6,
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112 "measured_rho": 1.0450635704920672,
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114 "cert": false,
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118 "lmi_maxeig": Infinity
119 },
120 {
121 "a": 0.75,
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123 "measured_rho": 1.0495038274669848,
124 "impulse_l2": 26.311524525214264,
125 "cert": false,
126 "gamma": Infinity,
127 "data_cert": false,
128 "data_gamma": Infinity,
129 "lmi_maxeig": Infinity
130 }
131 ],
132 "prediction_boundary_a": 0.55,
133 "observed_certificate_boundary_a": 0.48888888888888893,
134 "boundary_error": -0.061111111111111116,
135 "positive_boundary_definition": "largest nonnegative certified a on the tested grid",
136 "stable_gain_rows": [
137 {
138 "a": -0.5,
139 "local_rho_pred": 0.04999999999999999,
140 "measured_rho": 0.0,
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142 "cert": true,
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144 "data_cert": true,
145 "data_gamma": 61.054022965853264,
146 "lmi_maxeig": -1.1969867225902793,
147 "linear_gain_pred": 1.0526315789473684
148 },
149 {
150 "a": -0.2,
151 "local_rho_pred": 0.25,
152 "measured_rho": 0.24999999999993577,
153 "impulse_l2": 1.010788447487706,
154 "cert": true,
155 "gamma": 5.17947467923121,
156 "data_cert": true,
157 "data_gamma": 5.17947467923121,
158 "lmi_maxeig": -0.2908815862051584,
159 "linear_gain_pred": 1.3333333333333333
160 },
161 {
162 "a": 0.0,
163 "local_rho_pred": 0.45,
164 "measured_rho": 0.4499999999999245,
165 "impulse_l2": 1.0700494149505797,
166 "cert": true,
167 "gamma": 5.17947467923121,
168 "data_cert": true,
169 "data_gamma": 5.17947467923121,
170 "lmi_maxeig": -0.48291134621173454,
171 "linear_gain_pred": 1.8181818181818181
172 },
173 {
174 "a": 0.2,
175 "local_rho_pred": 0.65,
176 "measured_rho": 0.6499999999998958,
177 "impulse_l2": 1.2165471151402139,
178 "cert": true,
179 "gamma": 5.17947467923121,
180 "data_cert": true,
181 "data_gamma": 5.17947467923121,
182 "lmi_maxeig": -0.2908815862051584,
183 "linear_gain_pred": 2.857142857142857
184 },
185 {
186 "a": 0.4,
187 "local_rho_pred": 0.8500000000000001,
188 "measured_rho": 0.8499999999997829,
189 "impulse_l2": 1.6129898587029121,
190 "cert": true,
191 "gamma": 13.894954943731374,
192 "data_cert": true,
193 "data_gamma": 13.894954943731374,
194 "lmi_maxeig": -0.1038011552756935,
195 "linear_gain_pred": 6.6666666666666705
196 }
197 ],
198 "notes": [
199 "Prediction 1: local perturbations contract for |a+b|<1 and grow for |a+b|>1.",
200 "Prediction 2: tanh sector certificate boundary is a+b=1 on the positive-a side.",
201 "Prediction 3: disturbance gain grows as 1/(1-(a+b)) near the boundary."
202 ]
203}