Small-Gain Constrained Neural Modules / results.json

✓✓ Beats tuned baseline

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  1{
  2  "seed": 2838,
  3  "G0": [
  4    [
  5      0.18,
  6      0.574,
  7      0.14759999999999998,
  8      0.082
  9    ],
 10    [
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 13      0.33,
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 16    [
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 19      0.16,
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 21    ],
 22    [
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 24      0.0869,
 25      0.4503,
 26      0.2
 27    ]
 28  ],
 29  "rho_G0": 1.0771359584629179,
 30  "predicted_alpha_boundary": 0.9283879088272278,
 31  "boundary": {
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 33    "interpolated_crossing": 0.9127750373470908,
 34    "relative_error": 0.016817185286115737
 35  },
 36  "predictions": {
 37    "P1_boundary_alpha_critical_1_over_rho_G0": "confirmed by positive linear realization",
 38    "P2_weighted_Lyapunov_contracts_iff_rho_below_1": [
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 44        "contracts": true
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 50        "empirical_V_ratio": 0.9440646006227652,
 51        "contracts": true
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 53      {
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 60      {
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 65        "contracts": false
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 67      {
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 78        "empirical_V_ratio": 1.2102264365742423,
 79        "contracts": false
 80      }
 81    ],
 82    "P3_long_horizon_geometric_growth_equals_rho": [
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101        "observed_geometric_ratio": 1.1216362270190119
102      }
103    ]
104  },
105  "quadratic_certificate": [
106    {
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108      "rho": 0.8997135922846852,
109      "P_min_eig": 1.0025742535275537,
110      "quadratic_ratio": 0.8134194593318393
111    },
112    {
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114      "rho": 1.0327762668191791,
115      "quadratic_ratio": null
116    },
117    {
118      "alpha": 1.02,
119      "rho": 1.094880435181917,
120      "quadratic_ratio": null
121    }
122  ],
123  "training_comparison": {
124    "unconstrained": {
125      "final_loss": 2.1620126918487739e-13,
126      "max_loss": 0.11938569726146751,
127      "final_rho": 0.8287606095117684,
128      "steps_to_loss_1e-3": 31
129    },
130    "projected_small_gain": {
131      "final_loss": 8.326463544198927e-14,
132      "max_loss": 0.11938569726146751,
133      "final_rho": 0.8287609337833792,
134      "steps_to_loss_1e-3": 24
135    }
136  }
137}