{
  "bench_version": 1,
  "track": "torus_cayley_graph",
  "model": "graph_gcn_vs_relative",
  "metric_direction": "lower is better",
  "n_seeds": 8,
  "baseline": {
    "best_cfg": {
      "lr": 0.003
    },
    "sweep": [
      {
        "cfg": {
          "lr": 0.003
        },
        "mean": 2.9559298753738403
      },
      {
        "cfg": {
          "lr": 0.01
        },
        "mean": 2.957487165927887
      },
      {
        "cfg": {
          "lr": 0.03
        },
        "mean": 2.9612218737602234
      }
    ],
    "full": {
      "mean": 2.97136652469635,
      "std": 0.12454350264904765,
      "per_seed": [
        2.927370071411133,
        2.830188035964966,
        3.2255756855010986,
        2.840585947036743,
        3.015153169631958,
        2.9980242252349854,
        3.061436891555786,
        2.872598171234131
      ],
      "n": 8
    }
  },
  "idea": {
    "mean": 0.002413061651168391,
    "std": 0.0009268086641061233,
    "per_seed": [
      0.0015994536224752665,
      0.0017226150957867503,
      0.002087869681417942,
      0.0018045055912807584,
      0.0025380728766322136,
      0.002770226914435625,
      0.004656101576983929,
      0.0021256478503346443
    ],
    "n": 8
  },
  "comparison": {
    "delta_mean": -2.9689534630451817,
    "idea_wins": 8,
    "n_pairs": 8,
    "per_seed_diffs": [
      -2.9257706177886575,
      -2.828465420869179,
      -3.2234878158196807,
      -2.8387814414454624,
      -3.012615096755326,
      -2.9952539983205497,
      -3.056780789978802,
      -2.870472523383796
    ],
    "p_value": 0.0081,
    "mde": 0.11099329110372932,
    "mde_rel_pct": 3.73542914282754,
    "verdict": "idea better (significant)",
    "system_worked": true
  },
  "custom_track": {
    "name": "torus_cayley_graph",
    "file": "graph_track.py",
    "domain": "graph-nn"
  },
  "idea_lr_candidates": [
    {
      "lr": 0.003,
      "mean": 0.037418782245367765,
      "per_seed": [
        0.03436176851391792,
        0.018733929842710495,
        0.055476997047662735,
        0.040908731520175934,
        0.05387932434678078,
        0.03398267179727554,
        0.038339413702487946,
        0.02366742119193077
      ]
    },
    {
      "lr": 0.01,
      "mean": 0.004221850220346823,
      "per_seed": [
        0.005596912000328302,
        0.003076694905757904,
        0.0050314078107476234,
        0.0033882788848131895,
        0.0050455559976398945,
        0.004197766538709402,
        0.003719017840921879,
        0.003719167783856392
      ]
    },
    {
      "lr": 0.03,
      "mean": 0.002413061651168391,
      "per_seed": [
        0.0015994536224752665,
        0.0017226150957867503,
        0.002087869681417942,
        0.0018045055912807584,
        0.0025380728766322136,
        0.002770226914435625,
        0.004656101576983929,
        0.0021256478503346443
      ]
    }
  ],
  "protocol": {
    "epochs": 18,
    "batch": 64,
    "paired_seeds": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7
    ],
    "structural_match": "Cayley torus graph"
  },
  "mechanism_signature": {
    "baseline": {
      "observed_directional_input_std": [
        5.888908030792329,
        5.888908030792329,
        5.888908030792329,
        5.888908030792329
      ],
      "predicted_sensitivity_common": -0.010245620358298103,
      "test_mse": 2.929424524307251
    },
    "idea": {
      "observed_directional_input_std": [
        5.888908030792329,
        5.888908030792329,
        5.888908030792329,
        5.888908030792329
      ],
      "predicted_sensitivity_common": -0.010788307526496725,
      "test_mse": 0.005596912000328302
    },
    "prediction": "relation-tied message passing should exploit directional structure",
    "confirmed": true
  }
}