Exact Multi-Output Linear-Probe Coreset / results.json
Mechanism confirmed, baseline not beaten
1{
2 "prediction_checks": {
3 "P1_normal_equation_invariance": {
4 "prediction": "relative error ~ machine precision",
5 "observed_max": 1.3352320315261615e-15,
6 "pass": true
7 },
8 "P2_support_bound": {
9 "prediction": "support <= (m+1)r",
10 "observed_all_pass": true,
11 "observed_supports": [
12 2,
13 3,
14 5,
15 4,
16 6,
17 10,
18 6,
19 9,
20 15,
21 8,
22 12,
23 20
24 ]
25 },
26 "P3_rank_fixed_scaling": {
27 "prediction": "support remains 9 and compression scales as n/9",
28 "observed": [
29 {
30 "n": 40,
31 "support": 9,
32 "predicted_support": 9,
33 "compression": 4.444444444444445
34 },
35 {
36 "n": 80,
37 "support": 9,
38 "predicted_support": 9,
39 "compression": 8.88888888888889
40 },
41 {
42 "n": 160,
43 "support": 9,
44 "predicted_support": 9,
45 "compression": 17.77777777777778
46 },
47 {
48 "n": 320,
49 "support": 9,
50 "predicted_support": 9,
51 "compression": 35.55555555555556
52 }
53 ],
54 "compression_over_n": [
55 0.11111111111111112,
56 0.11111111111111112,
57 0.11111111111111112,
58 0.11111111111111112
59 ]
60 },
61 "P4_solution_exactness": {
62 "prediction": "full-data loss at coreset fit equals full optimum",
63 "observed_max_relative_parameter_error": 6.320902856305114e-15,
64 "observed_max_full_loss_relative_error": 5.093829997554436e-16,
65 "pass": true
66 }
67 },
68 "random_control_mean_parameter_error": 0.9791946844210963,
69 "sweep": [
70 {
71 "n": 160,
72 "d": 12,
73 "r": 1,
74 "m": 1,
75 "support": 2,
76 "bound": 2,
77 "compression": 80.0,
78 "iterations": 158,
79 "rank": 1,
80 "invariant_rel": 1.3352320315261615e-15,
81 "solution_rel": 9.439937571081595e-16,
82 "full_loss": 11.139955892609606,
83 "coreset_solution_full_loss": 11.139955892609605,
84 "full_loss_rel_error": 1.594581573324459e-16,
85 "random_solution_rel": 10.955716237163353,
86 "random_full_loss": 17.582165328314282,
87 "build_sec": 0.03659091501322109,
88 "core_fit_sec": 0.0002462639968143776
89 },
90 {
91 "n": 160,
92 "d": 12,
93 "r": 1,
94 "m": 2,
95 "support": 3,
96 "bound": 3,
97 "compression": 53.333333333333336,
98 "iterations": 157,
99 "rank": 1,
100 "invariant_rel": 3.1775107330550294e-17,
101 "solution_rel": 2.1166309298018646e-15,
102 "full_loss": 19.900687321686334,
103 "coreset_solution_full_loss": 19.900687321686338,
104 "full_loss_rel_error": 1.7852215963058772e-16,
105 "random_solution_rel": 0.04157051999666451,
106 "random_full_loss": 21.832637930815487,
107 "build_sec": 0.051932521993876435,
108 "core_fit_sec": 0.00020421900262590498
109 },
110 {
111 "n": 160,
112 "d": 12,
113 "r": 1,
114 "m": 4,
115 "support": 5,
116 "bound": 5,
117 "compression": 32.0,
118 "iterations": 155,
119 "rank": 1,
120 "invariant_rel": 1.8327214924579903e-16,
121 "solution_rel": 7.6871663049830885e-16,
122 "full_loss": 38.131313362510994,
123 "coreset_solution_full_loss": 38.131313362510994,
124 "full_loss_rel_error": 0.0,
125 "random_solution_rel": 0.045196392890678366,
126 "random_full_loss": 38.882031644209874,
127 "build_sec": 1.0901590899884468,
128 "core_fit_sec": 0.0003046530036954209
129 },
130 {
131 "n": 160,
132 "d": 12,
133 "r": 2,
134 "m": 1,
135 "support": 4,
136 "bound": 4,
137 "compression": 40.0,
138 "iterations": 156,
139 "rank": 2,
140 "invariant_rel": 7.175497832759502e-17,
141 "solution_rel": 7.434919458591599e-16,
142 "full_loss": 10.048259197248004,
143 "coreset_solution_full_loss": 10.048259197248008,
144 "full_loss_rel_error": 3.535650911327517e-16,
145 "random_solution_rel": 0.06866867216065083,
146 "random_full_loss": 13.046328532285134,
147 "build_sec": 0.04564334300812334,
148 "core_fit_sec": 0.00031492000562138855
149 },
150 {
151 "n": 160,
152 "d": 12,
153 "r": 2,
154 "m": 2,
155 "support": 6,
156 "bound": 6,
157 "compression": 26.666666666666668,
158 "iterations": 154,
159 "rank": 2,
160 "invariant_rel": 4.49713192587779e-17,
161 "solution_rel": 5.554878977168633e-16,
162 "full_loss": 21.76166910281451,
163 "coreset_solution_full_loss": 21.76166910281451,
164 "full_loss_rel_error": 0.0,
165 "random_solution_rel": 0.07309638339007501,
166 "random_full_loss": 29.404711543273333,
167 "build_sec": 0.07040698599303141,
168 "core_fit_sec": 0.00023753399727866054
169 },
170 {
171 "n": 160,
172 "d": 12,
173 "r": 2,
174 "m": 4,
175 "support": 10,
176 "bound": 10,
177 "compression": 16.0,
178 "iterations": 150,
179 "rank": 2,
180 "invariant_rel": 1.5988689951339358e-16,
181 "solution_rel": 7.28721230514538e-16,
182 "full_loss": 38.53181646131783,
183 "coreset_solution_full_loss": 38.531816461317845,
184 "full_loss_rel_error": 3.6880832569801916e-16,
185 "random_solution_rel": 0.03391917240895873,
186 "random_full_loss": 41.913906497642685,
187 "build_sec": 1.7594172720127972,
188 "core_fit_sec": 0.0004201729898341
189 },
190 {
191 "n": 160,
192 "d": 12,
193 "r": 3,
194 "m": 1,
195 "support": 6,
196 "bound": 6,
197 "compression": 26.666666666666668,
198 "iterations": 154,
199 "rank": 3,
200 "invariant_rel": 1.7875409700453618e-17,
201 "solution_rel": 4.3065435369315876e-15,
202 "full_loss": 10.461814628205603,
203 "coreset_solution_full_loss": 10.461814628205609,
204 "full_loss_rel_error": 5.093829997554436e-16,
205 "random_solution_rel": 0.026369930753203857,
206 "random_full_loss": 11.348506177055647,
207 "build_sec": 0.04481885299901478,
208 "core_fit_sec": 0.00029438598721753806
209 },
210 {
211 "n": 160,
212 "d": 12,
213 "r": 3,
214 "m": 2,
215 "support": 9,
216 "bound": 9,
217 "compression": 17.77777777777778,
218 "iterations": 151,
219 "rank": 3,
220 "invariant_rel": 3.351938421312999e-17,
221 "solution_rel": 6.320902856305114e-15,
222 "full_loss": 19.102779553574596,
223 "coreset_solution_full_loss": 19.1027795535746,
224 "full_loss_rel_error": 1.8597888693824672e-16,
225 "random_solution_rel": 0.07225986108633557,
226 "random_full_loss": 27.769208146458787,
227 "build_sec": 0.06074559999979101,
228 "core_fit_sec": 0.00020666400087065995
229 },
230 {
231 "n": 160,
232 "d": 12,
233 "r": 3,
234 "m": 4,
235 "support": 15,
236 "bound": 15,
237 "compression": 10.666666666666666,
238 "iterations": 145,
239 "rank": 3,
240 "invariant_rel": 1.0975485121000815e-16,
241 "solution_rel": 6.324711619539025e-16,
242 "full_loss": 39.35171301729877,
243 "coreset_solution_full_loss": 39.35171301729876,
244 "full_loss_rel_error": 1.8056208517472923e-16,
245 "random_solution_rel": 0.05636648327381763,
246 "random_full_loss": 44.772603776830294,
247 "build_sec": 1.6692419900064124,
248 "core_fit_sec": 0.0004494360036915168
249 },
250 {
251 "n": 160,
252 "d": 12,
253 "r": 4,
254 "m": 1,
255 "support": 8,
256 "bound": 8,
257 "compression": 20.0,
258 "iterations": 152,
259 "rank": 4,
260 "invariant_rel": 3.339765478528189e-17,
261 "solution_rel": 1.9640388099074253e-15,
262 "full_loss": 9.877887996169036,
263 "coreset_solution_full_loss": 9.877887996169035,
264 "full_loss_rel_error": 1.798316441823575e-16,
265 "random_solution_rel": 0.1611265639598163,
266 "random_full_loss": 38.46998116287166,
267 "build_sec": 0.04695309999806341,
268 "core_fit_sec": 0.0003123360074823722
269 },
270 {
271 "n": 160,
272 "d": 12,
273 "r": 4,
274 "m": 2,
275 "support": 12,
276 "bound": 12,
277 "compression": 13.333333333333334,
278 "iterations": 148,
279 "rank": 4,
280 "invariant_rel": 5.544242180282288e-17,
281 "solution_rel": 1.3491228180994566e-15,
282 "full_loss": 20.636562266809474,
283 "coreset_solution_full_loss": 20.63656226680947,
284 "full_loss_rel_error": 1.7215627452225696e-16,
285 "random_solution_rel": 0.14069013473096104,
286 "random_full_loss": 35.70434167282073,
287 "build_sec": 0.06117296600132249,
288 "core_fit_sec": 0.0002137179981218651
289 },
290 {
291 "n": 160,
292 "d": 12,
293 "r": 4,
294 "m": 4,
295 "support": 20,
296 "bound": 20,
297 "compression": 8.0,
298 "iterations": 140,
299 "rank": 4,
300 "invariant_rel": 4.969662158589767e-17,
301 "solution_rel": 1.6760526414921762e-15,
302 "full_loss": 40.28436185980167,
303 "coreset_solution_full_loss": 40.28436185980166,
304 "full_loss_rel_error": 1.7638177768160837e-16,
305 "random_solution_rel": 0.07535586123864042,
306 "random_full_loss": 49.05144510697594,
307 "build_sec": 0.5810113909974461,
308 "core_fit_sec": 0.0003007420018548146
309 }
310 ],
311 "scaling": [
312 {
313 "n": 40,
314 "d": 12,
315 "r": 3,
316 "m": 2,
317 "support": 9,
318 "bound": 9,
319 "compression": 4.444444444444445,
320 "iterations": 31,
321 "rank": 3,
322 "invariant_rel": 3.2897296469700414e-17,
323 "solution_rel": 1.1276474232811251e-15,
324 "full_loss": 4.896568196897997,
325 "coreset_solution_full_loss": 4.896568196897996,
326 "full_loss_rel_error": 1.8138794028495125e-16,
327 "random_solution_rel": 0.10563251560823181,
328 "random_full_loss": 6.9832008291374965,
329 "build_sec": 0.02196917300170753,
330 "core_fit_sec": 0.000323021988151595
331 },
332 {
333 "n": 80,
334 "d": 12,
335 "r": 3,
336 "m": 2,
337 "support": 9,
338 "bound": 9,
339 "compression": 8.88888888888889,
340 "iterations": 71,
341 "rank": 3,
342 "invariant_rel": 1.5699091140453346e-16,
343 "solution_rel": 1.6434327724138602e-15,
344 "full_loss": 11.4546319805748,
345 "coreset_solution_full_loss": 11.4546319805748,
346 "full_loss_rel_error": 0.0,
347 "random_solution_rel": 0.15657690326479473,
348 "random_full_loss": 13.874007068483662,
349 "build_sec": 0.03158425299625378,
350 "core_fit_sec": 0.00031079900509212166
351 },
352 {
353 "n": 160,
354 "d": 12,
355 "r": 3,
356 "m": 2,
357 "support": 9,
358 "bound": 9,
359 "compression": 17.77777777777778,
360 "iterations": 151,
361 "rank": 3,
362 "invariant_rel": 1.0478626125296877e-16,
363 "solution_rel": 1.4783775129159758e-15,
364 "full_loss": 18.771761993128592,
365 "coreset_solution_full_loss": 18.771761993128592,
366 "full_loss_rel_error": 0.0,
367 "random_solution_rel": 0.13513646776391247,
368 "random_full_loss": 35.65250412740738,
369 "build_sec": 0.06250821599678602,
370 "core_fit_sec": 0.00021155299327801913
371 },
372 {
373 "n": 320,
374 "d": 12,
375 "r": 3,
376 "m": 2,
377 "support": 9,
378 "bound": 9,
379 "compression": 35.55555555555556,
380 "iterations": 311,
381 "rank": 3,
382 "invariant_rel": 1.7291593327424068e-16,
383 "solution_rel": 1.1639898240379287e-15,
384 "full_loss": 36.83203606917343,
385 "coreset_solution_full_loss": 36.83203606917343,
386 "full_loss_rel_error": 0.0,
387 "random_solution_rel": 0.07572426956796888,
388 "random_full_loss": 63.17550104926527,
389 "build_sec": 0.11252481798874214,
390 "core_fit_sec": 0.00020924900309182703
391 }
392 ]
393}