Gale-Nullspace Feature Mixer / results.json

Mechanism confirmed, baseline not beaten

Raw ⬇ ZIP
  1{
  2  "seed": 2486,
  3  "predictions": {
  4    "P1_exact_nullspace": "||YX^T|| remains at floating-point roundoff",
  5    "P2_noise_scaling": "||YX^T|| ~ gamma^1 and normalized penalty ~ gamma^2",
  6    "P3_diagonal_gauge": "D=cI preserves zero; nonconstant D produces residual"
  7  },
  8  "exact_sweep": [
  9    {
 10      "a": 2,
 11      "b": 5,
 12      "residual_norm": 4.236704743275018e-16,
 13      "relative_penalty": 6.914097353818902e-33,
 14      "rank": 2
 15    },
 16    {
 17      "a": 3,
 18      "b": 7,
 19      "residual_norm": 8.900467034796993e-16,
 20      "relative_penalty": 8.414393100828013e-33,
 21      "rank": 3
 22    },
 23    {
 24      "a": 5,
 25      "b": 9,
 26      "residual_norm": 9.645516443905538e-16,
 27      "relative_penalty": 6.283162424639603e-33,
 28      "rank": 5
 29    },
 30    {
 31      "a": 8,
 32      "b": 13,
 33      "residual_norm": 2.4587513058959576e-15,
 34      "relative_penalty": 1.040637823196967e-32,
 35      "rank": 8
 36    }
 37  ],
 38  "noise_sweep": [
 39    {
 40      "gamma": 1e-06,
 41      "residual_norm": 2.303071306628882e-06,
 42      "penalty": 2.9855350370475615e-14,
 43      "norm_over_gamma": 2.3030713066288824,
 44      "penalty_over_gamma2": 0.029855350370475615
 45    },
 46    {
 47      "gamma": 5.179474679231212e-06,
 48      "residual_norm": 1.192869951601395e-05,
 49      "penalty": 8.009283807395689e-13,
 50      "norm_over_gamma": 2.3030713064098856,
 51      "penalty_over_gamma2": 0.02985535602466829
 52    },
 53    {
 54      "gamma": 2.6826957952797274e-05,
 55      "residual_norm": 6.178439709764778e-05,
 56      "penalty": 2.1486493087437117e-11,
 57      "norm_over_gamma": 2.3030713063463635,
 58      "penalty_over_gamma2": 0.029855385334873405
 59    },
 60    {
 61      "gamma": 0.00013894954943731373,
 62      "residual_norm": 0.00032001072033704367,
 63      "penalty": 5.764201760771672e-10,
 64      "norm_over_gamma": 2.3030713063334876,
 65      "penalty_over_gamma2": 0.029855537065896855
 66    },
 67    {
 68      "gamma": 0.0007196856730011522,
 69      "residual_norm": 0.0016574874230663838,
 70      "penalty": 1.546400564410417e-08,
 71      "norm_over_gamma": 2.3030713063308825,
 72      "penalty_over_gamma2": 0.02985632057650967
 73    },
 74    {
 75      "gamma": 0.0037275937203149418,
 76      "residual_norm": 0.008584914138915538,
 77      "penalty": 4.149077306033708e-07,
 78      "norm_over_gamma": 2.303071306330617,
 79      "penalty_over_gamma2": 0.029860314933266734
 80    },
 81    {
 82      "gamma": 0.019306977288832496,
 83      "residual_norm": 0.04446534540588557,
 84      "penalty": 1.113778491139982e-05,
 85      "norm_over_gamma": 2.3030713063305424,
 86      "penalty_over_gamma2": 0.029879288750542285
 87    },
 88    {
 89      "gamma": 0.1,
 90      "residual_norm": 0.23030713063305308,
 91      "penalty": 0.00029931255081029287,
 92      "norm_over_gamma": 2.303071306330531,
 93      "penalty_over_gamma2": 0.02993125508102928
 94    }
 95  ],
 96  "noise_loglog_slopes": {
 97    "residual_norm": 0.9999999999920334,
 98    "penalty": 2.000161430017986
 99  },
100  "gauge_loglog_slope": 0.8774577224640229,
101  "diagonal_sweep": [
102    {
103      "spread": 0.0,
104      "residual_norm": 1.1662567990380876e-15,
105      "penalty": 7.655891334799334e-33
106    },
107    {
108      "spread": 0.01,
109      "residual_norm": 0.034496357202347366,
110      "penalty": 6.698134373228444e-06
111    },
112    {
113      "spread": 0.03,
114      "residual_norm": 0.06985774800658698,
115      "penalty": 2.7468601307560305e-05
116    },
117    {
118      "spread": 0.1,
119      "residual_norm": 0.4842317313380071,
120      "penalty": 0.0013198174722236487
121    },
122    {
123      "spread": 0.3,
124      "residual_norm": 0.9528435122062417,
125      "penalty": 0.005110348830010954
126    },
127    {
128      "spread": 1.0,
129      "residual_norm": 1.4560688401768715,
130      "penalty": 0.011933592383219331
131    }
132  ],
133  "toy_comparison": {
134    "primary_test_mse": 0.04743790322015813,
135    "gale_combined_test_mse": 0.0024276607671189733,
136    "feature_width_primary": 3,
137    "feature_width_combined": 8
138  }
139}