tasks/computer_science.affinity_subset_bound_audit__seed31415/data/metadata.json

{
  "schema_version": 2,
  "dataset": "anonymized_pair_affinity_audit",
  "matrix_file": "affinity_matrix.npy",
  "screening_file": "screening_table.csv",
  "item_id_format": "item_0000 through item_0319",
  "matrix_row_order": "Rows and columns of affinity_matrix.npy follow item_id numeric order.",
  "candidate_group_counts": [
    6,
    7,
    8,
    9,
    10
  ],
  "target_subset_contract": {
    "name": "multi_block_selected_cross_core",
    "definition": "For g recovered blocks, select the anomaly class whose elevated cross-block affinity has coherent peer support in at least the minimum support threshold of other blocks, forming the selected_cross regime.",
    "minimum_other_block_support_fraction": 0.6,
    "minimum_other_block_support_rule": "ceil(0.60 * (g - 1)) distinct other recovered blocks",
    "excluded_anomaly_class": "An item whose unusual cross-block lift has coherent peer support in fewer other blocks than the minimum support threshold is a limited-support bridge distractor: it must remain unselected and its pairs belong to cross_background.",
    "selection_size": "not disclosed; infer from the public matrix",
    "per_group_selection_counts": "not disclosed and not assumed equal"
  },
  "output_contract": {
    "group_labels.csv": [
      "item_id",
      "group_label"
    ],
    "subset_scores.csv": [
      "item_id",
      "disruption_score",
      "selected"
    ],
    "pair_regime_summary.csv": [
      "regime",
      "n_pairs",
      "mean_affinity",
      "median_affinity",
      "std_affinity",
      "q10_affinity",
      "q90_affinity"
    ],
    "bound_comparison.csv": [
      "condition",
      "n_effective_per_group",
      "selected_per_group_effective",
      "alpha_hat",
      "beta_hat",
      "gamma_hat",
      "lambda_formula",
      "spectral_lambda_kplus1",
      "error_bound",
      "improvement_vs_raw",
      "margin_value",
      "temperature_factor"
    ],
    "spectral_report.csv": [
      "condition",
      "n_nodes",
      "lambda_k",
      "lambda_kplus1",
      "eigengap_at_group_count",
      "eig_01",
      "eig_02",
      "eig_03",
      "eig_04",
      "eig_05",
      "eig_06",
      "eig_07",
      "eig_08"
    ],
    "adjusted_affinity.npz": [
      "raw_normalized",
      "removed_normalized",
      "margin_adjusted_normalized",
      "temperature_scaled_normalized",
      "selected_indices",
      "kept_indices"
    ]
  },
  "exact_row_identifiers": {
    "pair_regime_summary.csv": {
      "index_column": "regime",
      "values": [
        "same_group",
        "cross_background",
        "selected_cross"
      ]
    },
    "bound_comparison.csv": {
      "index_column": "condition",
      "values": [
        "raw",
        "removed_subset",
        "margin_adjusted",
        "temperature_scaled"
      ]
    },
    "spectral_report.csv": {
      "index_column": "condition",
      "values": [
        "raw",
        "removed_subset",
        "margin_adjusted",
        "temperature_scaled"
      ]
    }
  },
  "public_row_identifiers": {
    "pair_regime_summary.csv": [
      "same_group",
      "cross_background",
      "selected_cross"
    ],
    "bound_comparison.csv": [
      "raw",
      "removed_subset",
      "margin_adjusted",
      "temperature_scaled"
    ],
    "spectral_report.csv": [
      "raw",
      "removed_subset",
      "margin_adjusted",
      "temperature_scaled"
    ]
  },
  "adjusted_affinity_contract": {
    "normalization": "normalize(X) = D(X)^(-1/2) X D(X)^(-1/2), using row sums and a 1e-300 degree floor",
    "raw_normalized": "normalize(affinity_matrix)",
    "removed_normalized": "normalize(affinity_matrix[keep, keep]) for the complement of the selected subset",
    "margin_adjusted_normalized": {
      "semantic_target": "Change only selected-cross raw affinities so their aggregate mean is beta_hat, then normalize.",
      "accepted_representations": [
        "replace every selected-cross raw affinity by beta_hat",
        "apply one uniform additive shift to selected-cross raw affinities so their mean is beta_hat",
        "apply one positive uniform scale to selected-cross raw affinities so their mean is beta_hat"
      ]
    },
    "temperature_scaled_normalized": {
      "semantic_target": "Multiply only selected-cross affinities by temperature_factor.",
      "accepted_representations": [
        "scale selected-cross entries of raw_normalized directly and symmetrize without another normalization",
        "scale selected-cross entries of raw_normalized, symmetrize, and normalize the result again",
        "scale selected-cross entries of the raw affinity matrix and then normalize"
      ]
    },
    "spectral_rows": "Compute each mitigated spectral row from the representation actually saved. The scorer accepts the listed equivalent representations."
  },
  "bound_formula_contract": {
    "interpretation": "Theory-inspired mean-field audit diagnostic. Because recovered selected counts may be unequal and the observed matrix includes noise, decoys, and nuisance directions, lambda_formula and error_bound are not asserted to be rigorous finite-instance generalization guarantees. spectral_lambda_kplus1 reports the corresponding empirical matrix quantity.",
    "symbols": {
      "g": "chosen recovered group count",
      "r": "g - 1",
      "n": "estimated items per group before mitigation",
      "nd": "mean selected count across recovered groups before mitigation; per-group counts need not be equal",
      "alpha_hat": "same-group mean affinity estimate",
      "beta_hat": "background cross-group mean affinity estimate",
      "gamma_hat": "selected-cross mean affinity estimate",
      "delta": "small recoverability tolerance; deterministic, computed via delta_recipe below"
    },
    "lambda_no_selected": "(1 - alpha_hat) / ((1 - alpha_hat) + n_eff * alpha_hat + n_eff * r * beta_hat)",
    "lambda_with_selected": "((1 - alpha_hat) + r * (gamma_hat - beta_hat)) / ((1 - alpha_hat) + n * alpha_hat + n * r * beta_hat + nd * r * (gamma_hat - beta_hat))",
    "error_bound": "4 * delta / (1 - lambda_formula) + 8 * delta",
    "condition_rules": {
      "raw": "Use lambda_with_selected with n_effective_per_group=n, selected_per_group_effective=nd, gamma_hat as estimated.",
      "removed_subset": "Use lambda_no_selected with n_eff=n-nd, selected_per_group_effective=0, gamma_hat set to beta_hat.",
      "margin_adjusted": "Use lambda_no_selected with n_eff=n, selected_per_group_effective=nd, gamma_hat set to beta_hat.",
      "temperature_scaled": "Use lambda_no_selected with n_eff=n, selected_per_group_effective=nd, gamma_hat set to beta_hat."
    },
    "mitigation_constants": {
      "c0": "(1 - alpha_hat) + n * alpha_hat + (n - nd) * r * beta_hat",
      "c1": "(1 - alpha_hat) + n * alpha_hat + n * r * beta_hat + nd * r * (gamma_hat - beta_hat)",
      "c2": "(1 - alpha_hat) + n * alpha_hat + n * r * beta_hat",
      "margin_value": "c0 * (gamma_hat - beta_hat) / (c1**2 * c2)",
      "temperature_factor": "(c1 / c2) * (beta_hat / gamma_hat)"
    },
    "delta_recipe": "delta = 0.25 * (std_affinity[same_group] + std_affinity[cross_background]) taken from pair_regime_summary.csv. delta is fully determined by the public regime statistics you report -- it is not a hidden generation parameter and not a free choice. Compute it exactly this way so error_bound and improvement_vs_raw are reproducible."
  },
  "notes": [
    "The affinity matrix is symmetric, finite, and nonnegative.",
    "The public files intentionally do not provide the latent group labels, the disruptive subset, its unequal per-block counts, or the graph-generation coefficients; recovering that structure from the matrix is the task.",
    "The row names for pair summaries and the condition names for bound/spectral tables are public output-contract identifiers, not hidden labels.",
    "The target subset is the public broad-support selected-cross anomaly class; limited-support multi-block bridge anomalies below the published threshold are explicitly outside that target.",
    "The adjusted-affinity contract lists scientifically equivalent margin and temperature representations accepted by the scorer.",
    "metadata.json publishes the formula contract for bound_comparison.csv; use those formulas rather than guessing condition-specific lambda values.",
    "For pair_regime_summary.csv, bound_comparison.csv, and spectral_report.csv, the scored regime/condition strings must be written verbatim as listed in metadata.json; semantic synonyms are scored as mismatches.",
    "Group labels may be permuted in the submission as long as they are consistent across rows."
  ]
}