{
  "seed": 1029,
  "math_predictions": [
    "C^{-1}(C(x))=x, so insertion loss change is zero up to floating point error.",
    "Composition roundoff should increase with coupling scale (products of f and g operators).",
    "After untie, a parameter step of size eta changes the pair output proportionally to eta (log-log slope 1)."
  ],
  "cancellation_sweep": [
    {
      "scale": 0.01,
      "max_abs_error": 2.384185791015625e-07,
      "relative_error": 6.0507255780899e-09,
      "predicted": "identity; fp error increases with operator products"
    },
    {
      "scale": 0.03,
      "max_abs_error": 2.384185791015625e-07,
      "relative_error": 1.0371835612498303e-08,
      "predicted": "identity; fp error increases with operator products"
    },
    {
      "scale": 0.1,
      "max_abs_error": 2.384185791015625e-07,
      "relative_error": 1.6163652328020487e-08,
      "predicted": "identity; fp error increases with operator products"
    },
    {
      "scale": 0.3,
      "max_abs_error": 2.384185791015625e-07,
      "relative_error": 2.6485729196494805e-08,
      "predicted": "identity; fp error increases with operator products"
    },
    {
      "scale": 1.0,
      "max_abs_error": 6.556510925292969e-07,
      "relative_error": 6.519850746510443e-08,
      "predicted": "identity; fp error increases with operator products"
    }
  ],
  "untied_step_sweep": {
    "gradient_norm": 0.07650767563339522,
    "sweep": [
      [
        1e-05,
        3.784688128217252e-07
      ],
      [
        3e-05,
        1.1330147494136314e-06
      ],
      [
        0.0001,
        3.7735932737830813e-06
      ],
      [
        0.0003,
        1.1323506324797927e-05
      ],
      [
        0.001,
        3.7741692688578436e-05
      ]
    ],
    "loglog_slope": 0.999468080063024
  },
  "mini_experiment": {
    "device": "cuda",
    "before_insertion_loss": 0.001658762339502573,
    "after_insertion_loss": 0.0016587624559178948,
    "insertion_relative_change": 7.018203817060692e-08,
    "paired_loss_after_300": 5.051885423662181e-14,
    "shallow_loss_after_300": 1.8959316335311928e-14,
    "random_deep_loss_after_300": 7.667316822335124e-05,
    "paired_best_300": 2.020312492604856e-14,
    "wall_seconds": 11.218648672103882
  }
}