1{
  2  "finite_difference_gradient_check": {
  3    "analytic": [
  4      0.5887907974608669,
  5      0.47610356349706445,
  6      0.09578414886923187
  7    ],
  8    "finite_difference": [
  9      0.5887907974511108,
 10      0.47610356340710425,
 11      0.09578414866817653
 12    ],
 13    "max_abs_error": 2.0105533904413164e-10
 14  },
 15  "paper_witness": {
 16    "rank": 4,
 17    "singular_values": [
 18      3.335699441584531,
 19      2.083534946053332,
 20      1.732050807568877,
 21      1.2377363871144758
 22    ],
 23    "selected_minor_determinant": 1.0
 24  },
 25  "candidate_pool": {
 26    "candidates": 180,
 27    "global_edges": 30
 28  },
 29  "all_candidates": {
 30    "rank": 30,
 31    "logdet_information": 143.97731772336564,
 32    "mean_pairwise_cosine_abs": 0.08583190536581144,
 33    "smallest_singular_value": 3.1874984540089324
 34  },
 35  "budget_sweep": {
 36    "10%": {
 37      "budget": 18,
 38      "greedy": {
 39        "rank": 18,
 40        "logdet_information": 13.527887707414422,
 41        "mean_pairwise_cosine_abs": 0.08491808197644612,
 42        "smallest_singular_value": 3.894886259616979
 43      },
 44      "greedy_rank_trace": [
 45        1,
 46        2,
 47        3,
 48        4,
 49        5,
 50        6,
 51        7,
 52        8,
 53        9,
 54        10,
 55        11,
 56        12,
 57        13,
 58        14,
 59        15,
 60        16,
 61        17,
 62        18
 63      ],
 64      "random_mean": {
 65        "rank": 18.0,
 66        "logdet_information": -65.42420465003103,
 67        "mean_pairwise_cosine_abs": 0.08785599575750976,
 68        "smallest_singular_value": 0.19661288052855125
 69      },
 70      "random_std": {
 71        "rank": 0.0,
 72        "logdet_information": 7.8883767462736065,
 73        "mean_pairwise_cosine_abs": 0.01385093711095459,
 74        "smallest_singular_value": 0.0902454521127866
 75      },
 76      "message_fraction": 0.1
 77    },
 78    "25%": {
 79      "budget": 45,
 80      "greedy": {
 81        "rank": 30,
 82        "logdet_information": 134.63245768859463,
 83        "mean_pairwise_cosine_abs": 0.09705173859973731,
 84        "smallest_singular_value": 2.2128802658610316
 85      },
 86      "greedy_rank_trace": [
 87        1,
 88        2,
 89        3,
 90        4,
 91        5,
 92        6,
 93        7,
 94        8,
 95        9,
 96        10,
 97        11,
 98        12,
 99        13,
100        14,
101        15,
102        16,
103        17,
104        18,
105        19,
106        20,
107        21,
108        22,
109        23,
110        24,
111        25,
112        26,
113        27,
114        28,
115        29,
116        30,
117        30,
118        30,
119        30,
120        30,
121        30,
122        30,
123        30,
124        30,
125        30,
126        30,
127        30,
128        30,
129        30,
130        30,
131        30
132      ],
133      "random_mean": {
134        "rank": 29.725,
135        "logdet_information": 53.10032875798106,
136        "mean_pairwise_cosine_abs": 0.08491663353953435,
137        "smallest_singular_value": 0.18510807484639685
138      },
139      "random_std": {
140        "rank": 0.4993746088859544,
141        "logdet_information": 10.831666566067572,
142        "mean_pairwise_cosine_abs": 0.00556639421153242,
143        "smallest_singular_value": 0.17803958099619155
144      },
145      "message_fraction": 0.25
146    },
147    "50%": {
148      "budget": 90,
149      "greedy": {
150        "rank": 30,
151        "logdet_information": 141.86048780360787,
152        "mean_pairwise_cosine_abs": 0.09416596334657241,
153        "smallest_singular_value": 2.9078365987580344
154      },
155      "greedy_rank_trace": [
156        1,
157        2,
158        3,
159        4,
160        5,
161        6,
162        7,
163        8,
164        9,
165        10,
166        11,
167        12,
168        13,
169        14,
170        15,
171        16,
172        17,
173        18,
174        19,
175        20,
176        21,
177        22,
178        23,
179        24,
180        25,
181        26,
182        27,
183        28,
184        29,
185        30,
186        30,
187        30,
188        30,
189        30,
190        30,
191        30,
192        30,
193        30,
194        30,
195        30,
196        30,
197        30,
198        30,
199        30,
200        30,
201        30,
202        30,
203        30,
204        30,
205        30,
206        30,
207        30,
208        30,
209        30,
210        30,
211        30,
212        30,
213        30,
214        30,
215        30,
216        30,
217        30,
218        30,
219        30,
220        30,
221        30,
222        30,
223        30,
224        30,
225        30,
226        30,
227        30,
228        30,
229        30,
230        30,
231        30,
232        30,
233        30,
234        30,
235        30,
236        30,
237        30,
238        30,
239        30,
240        30,
241        30,
242        30,
243        30,
244        30,
245        30
246      ],
247      "random_mean": {
248        "rank": 30.0,
249        "logdet_information": 101.9889799835815,
250        "mean_pairwise_cosine_abs": 0.08575823816591169,
251        "smallest_singular_value": 1.180208753849413
252      },
253      "random_std": {
254        "rank": 0.0,
255        "logdet_information": 5.881708339239661,
256        "mean_pairwise_cosine_abs": 0.0025019575771706294,
257        "smallest_singular_value": 0.36951616928349934
258      },
259      "message_fraction": 0.5
260    }
261  },
262  "interpretation": "Greedy selects rank-increasing rows and maximizes regularized global edge information; random is the equal-budget control."
263}