1{
  2  "mechanism_checks": {
  3    "beta_zero_relative_error": 0.0,
  4    "L_convex_linearity_max_abs_error": 3.3306690738754696e-16,
  5    "beta_logit_sweep": [
  6      {
  7        "beta": 0.0,
  8        "predicted_logit_shift_max": 0.0,
  9        "observed_minus_predicted_relative": 0.0
 10      },
 11      {
 12        "beta": 0.1,
 13        "predicted_logit_shift_max": 0.5282469816229073,
 14        "observed_minus_predicted_relative": 0.0
 15      },
 16      {
 17        "beta": 0.3,
 18        "predicted_logit_shift_max": 1.584740944868722,
 19        "observed_minus_predicted_relative": 0.0
 20      },
 21      {
 22        "beta": 1.0,
 23        "predicted_logit_shift_max": 5.282469816229073,
 24        "observed_minus_predicted_relative": 0.0
 25      },
 26      {
 27        "beta": 2.0,
 28        "predicted_logit_shift_max": 10.564939632458145,
 29        "observed_minus_predicted_relative": 0.0
 30      },
 31      {
 32        "beta": 4.0,
 33        "predicted_logit_shift_max": 21.12987926491629,
 34        "observed_minus_predicted_relative": 0.0
 35      }
 36    ],
 37    "feasibility_sweep": [
 38      {
 39        "shape": [
 40          3,
 41          4
 42        ],
 43        "max_row_excess": 0.0,
 44        "max_col_excess": 0.0
 45      },
 46      {
 47        "shape": [
 48          5,
 49          7
 50        ],
 51        "max_row_excess": 0.0,
 52        "max_col_excess": 0.0
 53      },
 54      {
 55        "shape": [
 56          12,
 57          20
 58        ],
 59        "max_row_excess": 0.0,
 60        "max_col_excess": 0.0
 61      }
 62    ]
 63  },
 64  "beta_sweep": [
 65    {
 66      "beta": 0,
 67      "accuracy": 0.9999999999999999,
 68      "matched_mass_fraction": 0.7167839841434622,
 69      "distractor_mass_fraction": 0.15107894218325763,
 70      "transported_mass": 0.7042068460449659,
 71      "entropy": 3.6497481639520686
 72    },
 73    {
 74      "beta": 0.03,
 75      "accuracy": 1.0,
 76      "matched_mass_fraction": 0.7199725632129319,
 77      "distractor_mass_fraction": 0.1500142567697936,
 78      "transported_mass": 0.7034006698610575,
 79      "entropy": 3.640491929500397
 80    },
 81    {
 82      "beta": 0.1,
 83      "accuracy": 1.0,
 84      "matched_mass_fraction": 0.7272077127336042,
 85      "distractor_mass_fraction": 0.14760159540731255,
 86      "transported_mass": 0.7015904474266927,
 87      "entropy": 3.6195379437621127
 88    },
 89    {
 90      "beta": 0.3,
 91      "accuracy": 1.0,
 92      "matched_mass_fraction": 0.7464070118759808,
 93      "distractor_mass_fraction": 0.14120391349252584,
 94      "transported_mass": 0.6968991081465781,
 95      "entropy": 3.564335894352572
 96    },
 97    {
 98      "beta": 1,
 99      "accuracy": 1.0000000000000002,
100      "matched_mass_fraction": 0.7996902908245576,
101      "distractor_mass_fraction": 0.12303111941184133,
102      "transported_mass": 0.6841747903273336,
103      "entropy": 3.4155788099393543
104    },
105    {
106      "beta": 3,
107      "accuracy": 1.0,
108      "matched_mass_fraction": 0.8820189408463366,
109      "distractor_mass_fraction": 0.0897639006616261,
110      "transported_mass": 0.6591696378951832,
111      "entropy": 3.208341054558804
112    }
113  ],
114  "epsilon_sweep": [
115    {
116      "epsilon": 0.04,
117      "accuracy": 1.0,
118      "matched_mass_fraction": 0.9596130897984609,
119      "distractor_mass_fraction": 0.03775141613906143,
120      "transported_mass": 0.6235394991100452,
121      "entropy": 3.065345410069695
122    },
123    {
124      "epsilon": 0.06,
125      "accuracy": 1.0000000000000002,
126      "matched_mass_fraction": 0.9239846875233899,
127      "distractor_mass_fraction": 0.06344221254832429,
128      "transported_mass": 0.6406438642003803,
129      "entropy": 3.128820558591908
130    },
131    {
132      "epsilon": 0.1,
133      "accuracy": 1.0,
134      "matched_mass_fraction": 0.842856728464204,
135      "distractor_mass_fraction": 0.10495021575308063,
136      "transported_mass": 0.6703537731198164,
137      "entropy": 3.3083484359773268
138    },
139    {
140      "epsilon": 0.16,
141      "accuracy": 1.0,
142      "matched_mass_fraction": 0.7115833886822865,
143      "distractor_mass_fraction": 0.1585894747410327,
144      "transported_mass": 0.7099810030079368,
145      "entropy": 3.6523909467204354
146    },
147    {
148      "epsilon": 0.25,
149      "accuracy": 1.0,
150      "matched_mass_fraction": 0.5340271158908982,
151      "distractor_mass_fraction": 0.2318628888237309,
152      "transported_mass": 0.774757257309588,
153      "entropy": 4.144728995351831
154    },
155    {
156      "epsilon": 0.4,
157      "accuracy": 1.0000000000000002,
158      "matched_mass_fraction": 0.3417922383713152,
159      "distractor_mass_fraction": 0.3094730777126748,
160      "transported_mass": 0.8621593811847469,
161      "entropy": 4.698616168843879
162    }
163  ],
164  "comparison": {
165    "softmax": {
166      "accuracy": 1.0,
167      "matched_mass_fraction": 0.7480652976071648,
168      "distractor_mass_fraction": 0.10639082537868162,
169      "transported_mass": 12.0,
170      "entropy": 0.7691446324167127
171    },
172    "balanced_sinkhorn": {
173      "accuracy": 0.8333333512187313,
174      "matched_mass_fraction": 0.47700466754422394,
175      "distractor_mass_fraction": 0.4,
176      "transported_mass": 1.0,
177      "entropy": 3.8223186000359064
178    },
179    "partial_gw": {
180      "accuracy": 1.0000000000000002,
181      "matched_mass_fraction": 0.7996902908245576,
182      "distractor_mass_fraction": 0.12303111941184133,
183      "transported_mass": 0.6841747903273336,
184      "entropy": 3.4155788099393543
185    }
186  },
187  "notes": "Uniform upper bounds are used; the MVP does not optimize transported mass with a learned dustbin penalty."
188}