1{
  2  "device": "cpu",
  3  "predictions": {
  4    "P1": "nonnegative W,w => Jensen violation <= numerical tolerance (predicted 0)",
  5    "P2": "negative W entries create positive Jensen violations; violation rate rises with negative fraction",
  6    "P3": "positive output coefficients make ReLU epigraph LP exact (predicted objective gap 0)"
  7  },
  8  "convexity_sweep": [
  9    {
 10      "negative_fraction": 0.0,
 11      "max_jensen_violation": 2.842170943040401e-14,
 12      "violation_rate": 0.0,
 13      "mean_positive_violation": 1.1421049291489757e-16
 14    },
 15    {
 16      "negative_fraction": 0.05,
 17      "max_jensen_violation": 4.263256414560601e-14,
 18      "violation_rate": 0.0,
 19      "mean_positive_violation": 4.902300787534842e-16
 20    },
 21    {
 22      "negative_fraction": 0.1,
 23      "max_jensen_violation": 7.105427357601002e-15,
 24      "violation_rate": 0.0,
 25      "mean_positive_violation": 4.1011840914058814e-17
 26    },
 27    {
 28      "negative_fraction": 0.25,
 29      "max_jensen_violation": 1.0658141036401503e-14,
 30      "violation_rate": 0.0,
 31      "mean_positive_violation": 4.912366809624776e-17
 32    },
 33    {
 34      "negative_fraction": 0.5,
 35      "max_jensen_violation": 1.4250197781545362,
 36      "violation_rate": 0.22593333333333335,
 37      "mean_positive_violation": 0.03872182267024236
 38    },
 39    {
 40      "negative_fraction": 1.0,
 41      "max_jensen_violation": 1.5431175754627462,
 42      "violation_rate": 0.2742,
 43      "mean_positive_violation": 0.07106292150874202
 44    }
 45  ],
 46  "controlled_sign_sweep": [
 47    {
 48      "gamma": -2.0,
 49      "predicted_max_violation": 0.5,
 50      "observed_max_violation": 0.5
 51    },
 52    {
 53      "gamma": -1.0,
 54      "predicted_max_violation": 0.5,
 55      "observed_max_violation": 0.5
 56    },
 57    {
 58      "gamma": -0.5,
 59      "predicted_max_violation": 0.25,
 60      "observed_max_violation": 0.25
 61    },
 62    {
 63      "gamma": -0.1,
 64      "predicted_max_violation": 0.05,
 65      "observed_max_violation": 0.050000000000000044
 66    },
 67    {
 68      "gamma": 0.0,
 69      "predicted_max_violation": 0.0,
 70      "observed_max_violation": 0.0
 71    },
 72    {
 73      "gamma": 0.1,
 74      "predicted_max_violation": 0.0,
 75      "observed_max_violation": 2.220446049250313e-16
 76    },
 77    {
 78      "gamma": 0.5,
 79      "predicted_max_violation": 0.0,
 80      "observed_max_violation": 4.440892098500626e-16
 81    },
 82    {
 83      "gamma": 1.0,
 84      "predicted_max_violation": 0.0,
 85      "observed_max_violation": 2.220446049250313e-16
 86    },
 87    {
 88      "gamma": 2.0,
 89      "predicted_max_violation": 0.0,
 90      "observed_max_violation": 4.440892098500626e-16
 91    }
 92  ],
 93  "epigraph_check": {
 94    "one_layer_max_abs_gap": 0.0,
 95    "two_layer_max_abs_gap": 1.7763568394002505e-15,
 96    "predicted_gap": 0.0
 97  },
 98  "fit_comparison": {
 99    "icnn": {
100      "train_mse": 1.0684418678283691,
101      "validation_mse": 1.2404754161834717,
102      "steps": 1200
103    },
104    "relu_mlp": {
105      "train_mse": 0.005368055310100317,
106      "validation_mse": 0.007096992339938879,
107      "steps": 1200
108    },
109    "metric": "validation MSE (lower is better)"
110  }
111}