{
  "bench_version": 1,
  "track": "multiscale_diffusion_pde",
  "model": "mlp_tiny",
  "metric_direction": "lower is better",
  "n_seeds": 8,
  "baseline": {
    "best_cfg": {
      "lr": 0.01,
      "weight_decay": 0.0
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    "sweep": [
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        "cfg": {
          "lr": 0.001,
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      {
        "cfg": {
          "lr": 0.003,
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        },
        "mean": 0.0028896931326016784
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      {
        "cfg": {
          "lr": 0.01,
          "weight_decay": 0.0
        },
        "mean": 0.0006090530368965119
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    ],
    "full": {
      "mean": 0.0006244597789191175,
      "std": 0.00013816121674020655,
      "per_seed": [
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        0.0007256286917254329,
        0.0006302266265265644,
        0.00048197503201663494,
        0.0006429867353290319,
        0.00040344681474380195,
        0.000893245916813612,
        0.0006197866168804467
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      "n": 8
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  },
  "idea": {
    "mean": 0.0588950552046299,
    "std": 0.007581433628093914,
    "per_seed": [
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      0.0601036362349987,
      0.04443567618727684,
      0.06491053104400635,
      0.06635342538356781,
      0.06359688937664032
    ],
    "n": 8,
    "best_cfg": {
      "lr": 0.01,
      "weight_decay": 0.0,
      "detail_weight": 2.0
    }
  },
  "comparison": {
    "delta_mean": 0.05827059542571078,
    "idea_wins": 0,
    "n_pairs": 8,
    "per_seed_diffs": [
      0.0474972878000699,
      0.06196942750830203,
      0.06033933098660782,
      0.05962166120298207,
      0.04379268945194781,
      0.06450708422926255,
      0.0654601794667542,
      0.06297710275975987
    ],
    "p_value": 0.0081,
    "mde": 0.006764917669931772,
    "mde_rel_pct": 1083.3232016385784,
    "verdict": "idea worse (significant)",
    "system_worked": false
  },
  "mechanism_signature": {
    "idea_hyperparameter_sweep": [
      {
        "cfg": {
          "lr": 0.001,
          "weight_decay": 0.0,
          "detail_weight": 0.5
        },
        "mean": 0.46720340102910995
      },
      {
        "cfg": {
          "lr": 0.003,
          "weight_decay": 0.0,
          "detail_weight": 1.0
        },
        "mean": 0.1648601070046425
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      {
        "cfg": {
          "lr": 0.01,
          "weight_decay": 0.0,
          "detail_weight": 2.0
        },
        "mean": 0.05796597991138697
      }
    ],
    "mechanism_signature": {
      "claim": "multiscale objective reduces fine/detail residuals at NN scale",
      "predicted": "detail residual is not worse than pixel residual",
      "observed": [
        {
          "seed": 0,
          "pixel_mse": 0.8897097706794739,
          "detail_mse": 2.22203861673673
        },
        {
          "seed": 1,
          "pixel_mse": 0.8830438256263733,
          "detail_mse": 1.9818376793215673
        },
        {
          "seed": 2,
          "pixel_mse": 0.8910840749740601,
          "detail_mse": 2.0421754527837037
        },
        {
          "seed": 3,
          "pixel_mse": 0.8894067406654358,
          "detail_mse": 1.9052459951490164
        }
      ],
      "mean_detail_to_pixel_ratio": 2.2939384522012953,
      "confirmed": false
    },
    "custom_track": {
      "name": "multiscale_diffusion_pde",
      "file": "bench/custom_tracks/multiscale_diffusion_pde.py",
      "domain": "pde"
    },
    "protocol_note": "Baseline and idea use the same mlp_tiny architecture, dataset, epochs, batch size, and lr union; primary metric is held-out raw field MSE."
  }
}