{
  "experiment": "EXP-G4_gamma_new_formula_validation",
  "date": "2026-04-18",
  "formula": "gamma = 1 - T_eval*sqrt(2)/theta",
  "models": [
    {
      "prefix": "EleutherAI--pythia-70m",
      "pe_type": "RoPE",
      "notes": "",
      "theta": 10000,
      "d_head": 64,
      "T_train": 2048,
      "T_eval_max": 2000.0,
      "n_points": 9,
      "gamma_obs": 0.7476017873166874,
      "gamma_new_pred": 0.717157287525381,
      "gamma_old_pred": 0.99999561666838,
      "err_new_pct": 4.245163553501351,
      "err_old_pct": -25.239493568239496,
      "R2": 0.9824939571028048
    },
    {
      "prefix": "meta-llama--Meta-Llama-3-8B",
      "pe_type": "RoPE",
      "notes": "",
      "theta": 500000,
      "d_head": 128,
      "T_train": 8192,
      "T_eval_max": 2000.0,
      "n_points": 9,
      "gamma_obs": 1.0454762537473639,
      "gamma_new_pred": 0.9943431457505076,
      "gamma_old_pred": 0.7018781400200674,
      "err_new_pct": 5.1424006104313325,
      "err_old_pct": 48.95409817400391,
      "R2": 0.9936044966891108
    },
    {
      "prefix": "Qwen--Qwen2.5-7B",
      "pe_type": "RoPE",
      "notes": "",
      "theta": 1000000,
      "d_head": 128,
      "T_train": 8192,
      "T_eval_max": 2000.0,
      "n_points": 9,
      "gamma_obs": 0.9966953735480816,
      "gamma_new_pred": 0.9971715728752538,
      "gamma_old_pred": 0.6666637444455867,
      "err_new_pct": -0.047755004266634545,
      "err_old_pct": 49.5049613620367,
      "R2": 0.9993151965766267
    },
    {
      "prefix": "meta-llama--Llama-2-7b-hf",
      "pe_type": "RoPE",
      "notes": "known_artifact",
      "theta": 10000,
      "d_head": 128,
      "T_train": 4096,
      "T_eval_max": 2000.0,
      "n_points": 9,
      "gamma_obs": 0.2870574377368437,
      "gamma_new_pred": 0.717157287525381,
      "gamma_old_pred": 0.99999561666838,
      "err_new_pct": -59.97287586278841,
      "err_old_pct": -71.29413039896974,
      "R2": 0.9665564682676285
    },
    {
      "prefix": "mistralai--Mistral-7B-v0.1",
      "pe_type": "RoPE",
      "notes": "only_2pts",
      "theta": 10000,
      "d_head": 128,
      "T_train": 8192,
      "T_eval_max": 50.0,
      "n_points": 2,
      "gamma_obs": 1.213076772373502,
      "gamma_new_pred": 0.9929289321881345,
      "gamma_old_pred": 0.99999561666838,
      "err_new_pct": 22.171560627226768,
      "err_old_pct": 21.30820897145836,
      "R2": 1.0
    },
    {
      "prefix": "mistralai--Mistral-Nemo-Instruct-2407",
      "pe_type": "RoPE",
      "notes": "partial_7pts",
      "theta": 1000000,
      "d_head": 128,
      "T_train": 131072,
      "T_eval_max": 500.0,
      "n_points": 7,
      "gamma_obs": 0.6382710387667986,
      "gamma_new_pred": 0.9992928932188134,
      "gamma_old_pred": 0.6666637444455867,
      "err_new_pct": -36.127731609211246,
      "err_old_pct": -4.2589245200967385,
      "R2": 0.9904023363048612
    },
    {
      "prefix": "google--gemma-2-9b-it",
      "pe_type": "RoPE",
      "notes": "partial",
      "theta": 10000,
      "d_head": 256,
      "T_train": 8192,
      "T_eval_max": 1000.0,
      "n_points": 8,
      "gamma_obs": 0.7791408207653451,
      "gamma_new_pred": 0.8585786437626906,
      "gamma_old_pred": 0.99999561666838,
      "err_new_pct": -9.25224772062953,
      "err_old_pct": -22.085576398708866,
      "R2": 0.9981402455707831
    },
    {
      "prefix": "tiiuae--falcon-7b",
      "pe_type": "ALiBi",
      "notes": "exclude_no_rope",
      "theta": 10000,
      "d_head": 64,
      "T_train": 2048,
      "T_eval_max": 1000.0,
      "n_points": 8,
      "gamma_obs": 0.7865425131096547,
      "gamma_new_pred": 0.8585786437626906,
      "gamma_old_pred": 0.99999561666838,
      "err_new_pct": -8.390161015109813,
      "err_old_pct": -21.34540391985647,
      "R2": 0.998318162512278
    }
  ],
  "summary": {
    "n_clean": 5,
    "mean_err_new_pct": 10.963059699608019,
    "mean_err_old_pct": 30.008610804617142
  }
}