1{
  2  "seed": 945,
  3  "predictions": {
  4    "homogeneity_in_covariance_scale": [
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 15        "predicted_ratio": 0.5
 16      },
 17      {
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 26        "ratio_to_unit_scale": 2.0,
 27        "predicted_ratio": 2.0
 28      },
 29      {
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 31        "residual": 3.120820012552788,
 32        "ratio_to_unit_scale": 4.0,
 33        "predicted_ratio": 4.0
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 35    ],
 36    "isotropic_rotation_invariance": [
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 55        "se": 0.002379815275582611
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 60        "se": 0.0023722451770241456
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 64        "residual": 1.5419914007540694,
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 68    "anisotropic_rotation_gap": [
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100      },
101      {
102        "d": 5,
103        "pca_residual": 0.26737612786796927,
104        "random_rotation_mean": 1.4907712878418338,
105        "random_rotation_min": 1.2198316118044321,
106        "gap_mean": 1.2233951599738644,
107        "gap_fraction_of_pca": 4.575558669837491
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109      {
110        "d": 6,
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112        "random_rotation_mean": 0.5741189364706918,
113        "random_rotation_min": 0.4536128834032801,
114        "gap_mean": 0.49183097551229743,
115        "gap_fraction_of_pca": 5.976949359104575
116      },
117      {
118        "d": 7,
119        "pca_residual": 0.016242903285723094,
120        "random_rotation_mean": 0.13916057733169526,
121        "random_rotation_min": 0.10436279177665345,
122        "gap_mean": 0.12291767404597218,
123        "gap_fraction_of_pca": 7.567469428572675
124      }
125    ]
126  },
127  "sweeps": {},
128  "mini_experiment": {
129    "covariance_eigenbasis_vs_random_rotation": [
130      {
131        "d": 3,
132        "d_over_p": 0.09375,
133        "pca_mse": 29.376749832013772,
134        "random_rotation_mse": 48.100694237052465,
135        "pca_retained_fraction": 0.6325500460377924,
136        "random_retained_fraction": 0.3983474011242054,
137        "stored_value_fraction": 0.09375
138      },
139      {
140        "d": 8,
141        "d_over_p": 0.25,
142        "pca_mse": 9.41651619398593,
143        "random_rotation_mse": 23.5267705970362,
144        "pca_retained_fraction": 0.8822164309615418,
145        "random_retained_fraction": 0.705722694913668,
146        "stored_value_fraction": 0.25
147      },
148      {
149        "d": 16,
150        "d_over_p": 0.5,
151        "pca_mse": 1.7779910370435974,
152        "random_rotation_mse": 6.4175010602759315,
153        "pca_retained_fraction": 0.9777605511691113,
154        "random_retained_fraction": 0.9197286805846363,
155        "stored_value_fraction": 0.5
156      }
157    ],
158    "note": "MSE is exact top-d reconstruction residual; stored value fraction is d/p (indices/metadata excluded)."
159  },
160  "math_sanity": {
161    "max_abs_residual_formula_error": 3.552713678800501e-15,
162    "orthogonality_error": 2.4424906541753444e-15
163  }
164}