1{
  2  "seed": 2678,
  3  "quadratic_verification": {
  4    "predictions": {
  5      "boundary": "Euler energy descent is guaranteed for eta*L < 2; with eta=gamma*2/L, transition is gamma=1.",
  6      "contraction": "Quadratic mode factor is |1-eta*lambda|; instability begins when eta*lambda_max>2.",
  7      "scaling": "The sufficient descent coefficient 1-eta*L/2 depends only on eta*L, not absolute L when eta is scaled by 1/L."
  8    },
  9    "sweep": [
 10      {
 11        "gamma": 0.2,
 12        "eta": 0.05714285714285715,
 13        "eta_L": 0.4,
 14        "monotone_energy": true,
 15        "max_energy_increase": -0.0018225211027255717,
 16        "final_norm": 0.5793798156406682,
 17        "observed_contraction_factor": 0.9857142857142858,
 18        "predicted_contraction_factor": 0.9857142857142858,
 19        "diverged_by_40_steps": false
 20      },
 21      {
 22        "gamma": 0.5,
 23        "eta": 0.14285714285714285,
 24        "eta_L": 1.0,
 25        "monotone_energy": true,
 26        "max_energy_increase": -0.000553914262213814,
 27        "final_norm": 0.24212844032697112,
 28        "observed_contraction_factor": 0.9642857142857143,
 29        "predicted_contraction_factor": 0.9642857142857143,
 30        "diverged_by_40_steps": false
 31      },
 32      {
 33        "gamma": 0.8,
 34        "eta": 0.2285714285714286,
 35        "eta_L": 1.6,
 36        "monotone_energy": true,
 37        "max_energy_increase": -0.00015856319958101233,
 38        "final_norm": 0.10078362154379822,
 39        "observed_contraction_factor": 0.9428571428571428,
 40        "predicted_contraction_factor": 0.9428571428571428,
 41        "diverged_by_40_steps": false
 42      },
 43      {
 44        "gamma": 0.99,
 45        "eta": 0.28285714285714286,
 46        "eta_L": 1.98,
 47        "monotone_energy": true,
 48        "max_energy_increase": -0.02991478224457711,
 49        "final_norm": 0.4583862502349583,
 50        "observed_contraction_factor": 0.98,
 51        "predicted_contraction_factor": 0.98,
 52        "diverged_by_40_steps": false
 53      },
 54      {
 55        "gamma": 1.0,
 56        "eta": 0.2857142857142857,
 57        "eta_L": 2.0,
 58        "monotone_energy": true,
 59        "max_energy_increase": -6.165691387405303e-05,
 60        "final_norm": 1.0015425167112906,
 61        "observed_contraction_factor": 1.0,
 62        "predicted_contraction_factor": 1.0,
 63        "diverged_by_40_steps": false
 64      },
 65      {
 66        "gamma": 1.01,
 67        "eta": 0.2885714285714286,
 68        "eta_L": 2.02,
 69        "monotone_energy": false,
 70        "max_energy_increase": 0.6368284018447827,
 71        "final_norm": 2.165416232595698,
 72        "observed_contraction_factor": 1.02,
 73        "predicted_contraction_factor": 1.02,
 74        "diverged_by_40_steps": false
 75      },
 76      {
 77        "gamma": 1.2,
 78        "eta": 0.34285714285714286,
 79        "eta_L": 2.4,
 80        "monotone_energy": false,
 81        "max_energy_increase": 428617588905.42065,
 82        "final_norm": 500026.9261364795,
 83        "observed_contraction_factor": 1.4,
 84        "predicted_contraction_factor": 1.4,
 85        "diverged_by_40_steps": true
 86      },
 87      {
 88        "gamma": 1.5,
 89        "eta": 0.42857142857142855,
 90        "eta_L": 3.0,
 91        "monotone_energy": false,
 92        "max_energy_increase": 7.933575691221004e+23,
 93        "final_norm": 549755813888.0,
 94        "observed_contraction_factor": 2.0,
 95        "predicted_contraction_factor": 2.0,
 96        "diverged_by_40_steps": true
 97      }
 98    ],
 99    "scaling_sweep": [
100      {
101        "lambda_max": 1.0,
102        "eta": 1.6,
103        "descent_coefficient": 0.19999999999999996
104      },
105      {
106        "lambda_max": 2.0,
107        "eta": 0.8,
108        "descent_coefficient": 0.19999999999999996
109      },
110      {
111        "lambda_max": 5.0,
112        "eta": 0.32,
113        "descent_coefficient": 0.19999999999999996
114      },
115      {
116        "lambda_max": 10.0,
117        "eta": 0.16,
118        "descent_coefficient": 0.19999999999999996
119      }
120    ],
121    "observed_transition_gamma": 1.0
122  },
123  "mini_experiment": {
124    "device": "cuda",
125    "train_loss_4_steps": {
126      "baseline": 0.23115138709545135,
127      "energy_gradient": 0.22093874216079712
128    },
129    "12_step_mse": {
130      "baseline": 0.408142626285553,
131      "energy_gradient": 0.4640645682811737
132    },
133    "energy_mean_first_last": [
134      -4.184106826782227,
135      -6.150582313537598
136    ],
137    "energy_nonincreasing_fraction": 1.0,
138    "gradient_norm_first_last": [
139      1.1651203632354736,
140      0.499337375164032
141    ],
142    "mean_cumulative_path_length": 2.355754792690277
143  }
144}