1{
 2  "toy": {
 3    "contraction": [
 4      {
 5        "alpha": 0.2,
 6        "predicted": 0.84,
 7        "observed": 0.8399999999999999
 8      },
 9      {
10        "alpha": 0.5,
11        "predicted": 0.6,
12        "observed": 0.6000000000000001
13      },
14      {
15        "alpha": 1.0,
16        "predicted": 0.19999999999999996,
17        "observed": 0.2
18      },
19      {
20        "alpha": 1.4,
21        "predicted": 0.11999999999999988,
22        "observed": 0.11999999999999993
23      }
24    ],
25    "boundary": [
26      {
27        "B": 1,
28        "predicted_alpha_boundary": 0.7692307692307692,
29        "observed_alpha_boundary": 0.7703739335650314,
30        "relative_error": 0.0014861136345408644
31      },
32      {
33        "B": 2,
34        "predicted_alpha_boundary": 1.176470588235294,
35        "observed_alpha_boundary": 1.1757770492239783,
36        "relative_error": 0.0005895081596182906
37      },
38      {
39        "B": 4,
40        "predicted_alpha_boundary": 1.6,
41        "observed_alpha_boundary": 1.5999654117820772,
42        "relative_error": 2.1617636201815005e-05
43      },
44      {
45        "B": 8,
46        "predicted_alpha_boundary": 1.9512195121951217,
47        "observed_alpha_boundary": 1.9512481857774988,
48        "relative_error": 1.4695210968276864e-05
49      },
50      {
51        "B": 16,
52        "predicted_alpha_boundary": 2.191780821917808,
53        "observed_alpha_boundary": 2.1913190702532237,
54        "relative_error": 0.00021067419696663148
55      },
56      {
57        "B": 32,
58        "predicted_alpha_boundary": 2.335766423357664,
59        "observed_alpha_boundary": 2.334316225856176,
60        "relative_error": 0.0006208658053246469
61      }
62    ],
63    "variance_scaling": [
64      {
65        "B": 1,
66        "predicted_second_moment": 0.25000000000000006,
67        "observed_second_moment": 0.25006536910026594,
68        "B_times_moment": 0.25006536910026594
69      },
70      {
71        "B": 4,
72        "predicted_second_moment": 0.06250000000000001,
73        "observed_second_moment": 0.0624919571631688,
74        "B_times_moment": 0.2499678286526752
75      },
76      {
77        "B": 16,
78        "predicted_second_moment": 0.015625000000000003,
79        "observed_second_moment": 0.01563363442412024,
80        "B_times_moment": 0.25013815078592383
81      }
82    ]
83  },
84  "optimizer_demo": {
85    "adam": {
86      "final_loss": 0.07669686133472393,
87      "best_loss": 0.0659149937860606
88    },
89    "prox": {
90      "final_loss": 0.07718435039454627,
91      "best_loss": 0.06636830733006006
92    },
93    "relaxed_prox": {
94      "final_loss": 0.06763020266651175,
95      "best_loss": 0.06509818190498257
96    }
97  }
98}