batch_results.json

{
  "scope": "Independent lightweight numerical audits; not full benchmark replications or proof replacements.",
  "optimal_design_mnl": {
    "candidate_assortments": 92,
    "vectorized_lmo_matches_bruteforce": true,
    "logdet_initial": -3.090597986040936,
    "logdet_final": -1.7823579291243272,
    "logdet_gain": 1.3082400569166086,
    "active_support": 5
  },
  "wasserstein_noise": {
    "W1_loglog_slope": 1.0080943932202417,
    "W2_loglog_slope": 0.5041625838491619,
    "expected_mechanism_slopes": {
      "W1": 1.0,
      "W2": 0.5
    },
    "sigma_grid": [
      2e-05,
      3.698622388594646e-05,
      6.839903786706794e-05,
      0.0001264911064067352,
      0.0002339214190570292,
      0.0004325934988480796,
      0.0008
    ],
    "mean_W1": [
      0.0011269742688427284,
      0.002042236813882843,
      0.003985322902105246,
      0.007360052884819259,
      0.013328342199604852,
      0.024848910099849228,
      0.046338389323970934
    ],
    "mean_W2": [
      0.03277867506463554,
      0.04424370160767486,
      0.06180436655620729,
      0.08393480186436757,
      0.11321713854550827,
      0.15456198892436532,
      0.20999700567202614
    ]
  },
  "riemannian_dueling": {
    "dimension": 20,
    "cosine_to_normalized_gradient": {
      "200": 0.9396993363983441,
      "2000": 0.9932077226110302,
      "20000": 0.9989399432766883
    },
    "tangent_violation": 1.661214055315058e-16
  },
  "sinkhorn_diffusion": {
    "iterations_to_row_error_below_0.1pct": 7,
    "final_row_error": 4.0967229608668276e-14,
    "symmetry_error": 2.7755575615628914e-17,
    "minimum_entry": 3.712683991149634e-10,
    "eigenvalue_min": -1.682513188523743e-16,
    "eigenvalue_max": 0.9999999999999993
  },
  "semi_knockoffs": {
    "target_fdr": 0.1,
    "empirical_fdr": 0.09587345564793033,
    "mean_power": 0.9777875,
    "replicates": 1000,
    "scope": "sign-flip/knockoff+ calibration proxy; not the released Semi-knockoffs implementation"
  },
  "sgmcmc_covariance": {
    "step_size_error_loglog_slope": 1.0298834996115878,
    "rows": [
      {
        "lambda": 0.005,
        "proxy_relative_error": 0.00175967823026677,
        "mc_to_exact_error": 0.07629438279863397
      },
      {
        "lambda": 0.01,
        "proxy_relative_error": 0.0035389282103134357,
        "mc_to_exact_error": 0.047974964037807
      },
      {
        "lambda": 0.02,
        "proxy_relative_error": 0.007157464212678843,
        "mc_to_exact_error": 0.031040999131076347
      },
      {
        "lambda": 0.04,
        "proxy_relative_error": 0.014644351464435263,
        "mc_to_exact_error": 0.062354210035422034
      },
      {
        "lambda": 0.08,
        "proxy_relative_error": 0.03070175438596485,
        "mc_to_exact_error": 0.01728348705581277
      }
    ]
  }
}