1{
 2  "math_checks": {
 3    "translation_scaling": {
 4      "prediction": "S approximately k*delta^2",
 5      "fitted_k": 0.9857734603617165,
 6      "max_relative_error": 0.0027633349934145365,
 7      "deltas": [
 8        0.0,
 9        0.19999999999999998,
10        0.39999999999999997,
11        0.6,
12        0.7999999999999999,
13        0.9999999999999999,
14        1.2
15      ],
16      "S": [
17        0.0,
18        0.039322277785479934,
19        0.15734388263442262,
20        0.35421841197822845,
21        0.6301666228773719,
22        0.985437594691379,
23        1.420280987318515
24      ]
25    },
26    "radius_boundary": {
27      "prediction": "boundary delta=sqrt(rho/k)",
28      "rho": 0.36,
29      "predicted_delta": 0.6043140473283364,
30      "observed_delta": 0.6,
31      "absolute_error": 0.004314047328336401
32    },
33    "debiased_identity": {
34      "prediction": "S(A,A)=0",
35      "observed": 0.0
36    },
37    "multiplier_projection": {
38      "prediction": "lambda increases only for violations",
39      "sequence": [
40        [
41          0.2,
42          0.03932227778547999,
43          0.0
44        ],
45        [
46          0.5,
47          0.24591182732893413,
48          0.0
49        ],
50        [
51          0.8,
52          0.6301666228773722,
53          0.2161332983018978
54        ],
55        [
56          1.0,
57          0.9854375946913786,
58          0.7164833740550007
59        ]
60      ]
61    }
62  },
63  "training": {
64    "ordinary": {
65      "clean_mse": 0.18821489138674305,
66      "shifted_mse": 0.47675823278697876,
67      "psi": NaN,
68      "final_sinkhorn": NaN,
69      "lambda": 0.0
70    },
71    "unconstrained": {
72      "clean_mse": 0.45381627742423153,
73      "shifted_mse": 0.19558308193952534,
74      "psi": NaN,
75      "final_sinkhorn": NaN,
76      "lambda": 0.0
77    },
78    "sinkhorn": {
79      "clean_mse": 0.18928426842945464,
80      "shifted_mse": 0.4955903092770569,
81      "psi": -0.5193771052360537,
82      "final_sinkhorn": 0.25516605377197266,
83      "lambda": 0.8380940005704756
84    }
85  }
86}