1{
  2  "device": "cuda",
  3  "math_check": {
  4    "sorted_ot_cost": 0.14749999344348907,
  5    "random_coupling_cost": 2.112499952316284,
  6    "derivative_max_error": 0.00067901611328125
  7  },
  8  "locality_sweep": [
  9    {
 10      "epsilon": 0.06,
 11      "lambda": 0.0,
 12      "paired_R": 0.7111561298370361,
 13      "marginal_err": 4.0413811802864075e-05
 14    },
 15    {
 16      "epsilon": 0.06,
 17      "lambda": 0.5,
 18      "paired_R": 0.0283959973603487,
 19      "marginal_err": 1.2326985597610474e-05
 20    },
 21    {
 22      "epsilon": 0.06,
 23      "lambda": 2.0,
 24      "paired_R": 0.005961012560874224,
 25      "marginal_err": 6.226822733879089e-06
 26    },
 27    {
 28      "epsilon": 0.06,
 29      "lambda": 8.0,
 30      "paired_R": 0.0008196450653485954,
 31      "marginal_err": 2.3618340492248535e-06
 32    },
 33    {
 34      "epsilon": 0.16,
 35      "lambda": 0.0,
 36      "paired_R": 0.8314868211746216,
 37      "marginal_err": 1.30385160446167e-08
 38    },
 39    {
 40      "epsilon": 0.16,
 41      "lambda": 0.5,
 42      "paired_R": 0.10292951762676239,
 43      "marginal_err": 3.345310688018799e-06
 44    },
 45    {
 46      "epsilon": 0.16,
 47      "lambda": 2.0,
 48      "paired_R": 0.02393825724720955,
 49      "marginal_err": 7.588416337966919e-06
 50    },
 51    {
 52      "epsilon": 0.16,
 53      "lambda": 8.0,
 54      "paired_R": 0.004799625836312771,
 55      "marginal_err": 1.0259449481964111e-05
 56    },
 57    {
 58      "epsilon": 0.4,
 59      "lambda": 0.0,
 60      "paired_R": 0.9091153144836426,
 61      "marginal_err": 1.30385160446167e-08
 62    },
 63    {
 64      "epsilon": 0.4,
 65      "lambda": 0.5,
 66      "paired_R": 0.2552563548088074,
 67      "marginal_err": 9.313225746154785e-09
 68    },
 69    {
 70      "epsilon": 0.4,
 71      "lambda": 2.0,
 72      "paired_R": 0.07225342839956284,
 73      "marginal_err": 1.1175870895385742e-08
 74    },
 75    {
 76      "epsilon": 0.4,
 77      "lambda": 8.0,
 78      "paired_R": 0.01732504926621914,
 79      "marginal_err": 2.0343810319900513e-05
 80    }
 81  ],
 82  "comparison_lambda0": {
 83    "flow_w1": 0.4429539889097214,
 84    "mse_w1": 1.006102442741394,
 85    "flow_mode_coverage": 0.85107421875,
 86    "per_s_w1": [
 87      0.45495861768722534,
 88      0.29935240745544434,
 89      0.3903495669364929,
 90      0.6271553635597229
 91    ]
 92  },
 93  "comparison_lambda8": {
 94    "flow_w1": 0.17159544862806797,
 95    "mse_w1": 1.0032900869846344,
 96    "flow_mode_coverage": 0.908203125,
 97    "per_s_w1": [
 98      0.09672722965478897,
 99      0.20712798833847046,
100      0.19947239756584167,
101      0.18305417895317078
102    ]
103  },
104  "predictions": {
105    "lambda_effect_at_eps_0.16": "paired_R should decrease monotonically with lambda",
106    "epsilon_effect_at_lambda_8": "paired_R should increase with epsilon",
107    "flow_distributional_effect": "flow W1 should be lower than deterministic MSE W1 and mode coverage near 1"
108  }
109}