Gramian-balanced neural SSM compression / results.json

Mechanism confirmed, baseline not beaten

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  1{
  2  "stein_relative_residuals": {
  3    "P": 6.238146879533592e-17,
  4    "Q": 6.238146879533592e-17
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  6  "prediction_1_finite_horizon_geometric_tail": [
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 43    {
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 49    {
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 55  ],
 56  "prediction_2_near_instability_scaling": [
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103      "predicted_1_over_1_minus_rho2": 100.25062656641649
104    }
105  ],
106  "prediction_3_balanced_truncation_bound": [
107    {
108      "r": 2,
109      "max_frequency_error": 1.4418440319158905,
110      "bound_2_sum_discarded_HSV": 3.581948825391471,
111      "biorthogonality_error": 4.471816999799014e-15
112    },
113    {
114      "r": 4,
115      "max_frequency_error": 0.09882439144167064,
116      "bound_2_sum_discarded_HSV": 0.3275781830940712,
117      "biorthogonality_error": 3.4439783705070174e-15
118    },
119    {
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122      "bound_2_sum_discarded_HSV": 0.06811590488881253,
123      "biorthogonality_error": 4.17147293327404e-15
124    },
125    {
126      "r": 8,
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128      "bound_2_sum_discarded_HSV": 0.005018489592171743,
129      "biorthogonality_error": 4.3189572173127934e-15
130    },
131    {
132      "r": 10,
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134      "bound_2_sum_discarded_HSV": 0.0005620550327309083,
135      "biorthogonality_error": 4.6410549099301975e-15
136    }
137  ],
138  "compression_comparison": {
139    "rank": 4,
140    "gramian_max_frequency_error": 0.09882439144167064,
141    "magnitude_pruning_max_frequency_error": 13.021442145047816,
142    "full_state_update_cost_units": 192,
143    "reduced_projection_state_dimension": 4,
144    "ideal_state_state_transition_cost_ratio": 0.1111111111111111
145  },
146  "factor_iteration_relative_errors": {
147    "P": 7.121766330598871e-07,
148    "Q": 1.3991895905671146e-07
149  }
150}