Matching-Controllable Recurrent State Space / results.json
Failed on benchmark
1{
2 "seed": 1502,
3 "structural": [
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28 {
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54 {
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58 "min_gramian_rank": 3,
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60 "median_lambda_min": 0.0
61 },
62 {
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69 }
70 ],
71 "matched_horizon_sweep": [
72 {
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100 {
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104 "normalized_lambda_min": 1.4330752678359146e-11,
105 "rank": 8
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107 {
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112 "rank": 9
113 }
114 ],
115 "horizon_controllability_sweep": [
116 {
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122 {
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128 {
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134 {
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140 {
141 "design": "matched",
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143 "rank": 10,
144 "min_nonzero_singular": 3.920146419311282e-05
145 },
146 {
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149 "rank": 10,
150 "min_nonzero_singular": 3.920146419311282e-05
151 },
152 {
153 "design": "matched",
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156 "min_nonzero_singular": 3.920146419311282e-05
157 },
158 {
159 "design": "matched",
160 "horizon": 10,
161 "rank": 10,
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163 },
164 {
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170 {
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176 {
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181 },
182 {
183 "design": "unmatched",
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188 {
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194 {
195 "design": "unmatched",
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199 },
200 {
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205 },
206 {
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211 },
212 {
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217 },
218 {
219 "design": "inaccessible",
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224 {
225 "design": "inaccessible",
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230 {
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236 {
237 "design": "inaccessible",
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241 },
242 {
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247 },
248 {
249 "design": "inaccessible",
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252 "min_nonzero_singular": 1.0726632771101887e-08
253 },
254 {
255 "design": "inaccessible",
256 "horizon": 10,
257 "rank": 9,
258 "min_nonzero_singular": 1.519551118083831e-09
259 }
260 ],
261 "baseline_comparison": [
262 {
263 "design": "matching",
264 "rank": 10,
265 "lambda_min": 1.8061540249835195e-07
266 },
267 {
268 "design": "random_sparse",
269 "rank": 9,
270 "lambda_min": 4.3144444864294774e-05
271 },
272 {
273 "design": "matching",
274 "rank": 7,
275 "lambda_min": 2.8519836274807497e-13
276 },
277 {
278 "design": "random_sparse",
279 "rank": 10,
280 "lambda_min": 3.197166506570611e-05
281 },
282 {
283 "design": "matching",
284 "rank": 10,
285 "lambda_min": 8.347982762863937e-06
286 },
287 {
288 "design": "random_sparse",
289 "rank": 9,
290 "lambda_min": 5.9121147045837824e-08
291 },
292 {
293 "design": "matching",
294 "rank": 10,
295 "lambda_min": 3.1810950647869205e-06
296 },
297 {
298 "design": "random_sparse",
299 "rank": 10,
300 "lambda_min": 0.0010977343123756381
301 },
302 {
303 "design": "matching",
304 "rank": 10,
305 "lambda_min": 1.1218557849965952e-08
306 },
307 {
308 "design": "random_sparse",
309 "rank": 7,
310 "lambda_min": 3.5961939339453158e-06
311 },
312 {
313 "design": "matching",
314 "rank": 9,
315 "lambda_min": 1.3076005964932231e-09
316 },
317 {
318 "design": "random_sparse",
319 "rank": 9,
320 "lambda_min": 1.1612567852377557e-05
321 },
322 {
323 "design": "matching",
324 "rank": 9,
325 "lambda_min": 6.515699054929825e-08
326 },
327 {
328 "design": "random_sparse",
329 "rank": 9,
330 "lambda_min": 0.00020769065247788058
331 },
332 {
333 "design": "matching",
334 "rank": 9,
335 "lambda_min": 7.990126016306524e-09
336 },
337 {
338 "design": "random_sparse",
339 "rank": 8,
340 "lambda_min": 3.3196816978292985e-05
341 }
342 ],
343 "predictions": [
344 "accessibility plus row-saturating matching predicts generic full controllability rank",
345 "the matched finite-horizon Gramian has positive minimum eigenvalue for generic weights",
346 "increasing horizon increases the minimum Gramian eigenvalue for the matched chain, while inaccessible remains singular"
347 ]
348}