src/reproduce.py

"""Independent NumPy checks for the WIRE theory claims.

The script intentionally has no paper-code dependency.  It implements the
rotation in Eq. (2), computes Laplacian eigenfeatures, and checks the
permutation/gauge, grid, and effective-resistance statements numerically.
"""

from __future__ import annotations

import json
from pathlib import Path

import numpy as np


ROOT = Path(__file__).resolve().parents[1]
RESULTS = ROOT / "results"


def laplacian(n: int, edges: list[tuple[int, int]]) -> np.ndarray:
    a = np.zeros((n, n), dtype=float)
    for i, j in edges:
        a[i, j] = a[j, i] = 1.0
    return np.diag(a.sum(axis=1)) - a


def wire_rotate(z: np.ndarray, features: np.ndarray, frequencies: np.ndarray) -> np.ndarray:
    """Apply block-diagonal RoPE to rows of z using graph features."""
    n, d = z.shape
    assert d % 2 == 0
    angles = features @ frequencies.T
    out = z.copy()
    for block in range(d // 2):
        c = np.cos(angles[:, block])
        s = np.sin(angles[:, block])
        x, y = z[:, 2 * block], z[:, 2 * block + 1]
        out[:, 2 * block] = c * x - s * y
        out[:, 2 * block + 1] = s * x + c * y
    return out


def spectral_features(l: np.ndarray, m: int, resistance_weighted: bool = False) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
    eigenvalues, eigenvectors = np.linalg.eigh(l)
    if resistance_weighted:
        features = eigenvectors[:, 1:m] / np.sqrt(eigenvalues[1:m])
    else:
        features = eigenvectors[:, :m]
    return features, eigenvalues, eigenvectors


def effective_resistance(l: np.ndarray, i: int, j: int) -> float:
    vals, vecs = np.linalg.eigh(l)
    pinv = (vecs[:, 1:] / vals[1:]) @ vecs[:, 1:].T
    return float(pinv[i, i] + pinv[j, j] - 2 * pinv[i, j])


def check_claim_1(rng: np.random.Generator) -> dict[str, float]:
    n, d, m = 12, 8, 4
    edges = [(i, j) for i in range(n) for j in range(i + 1, n) if rng.random() < 0.22]
    # Ensure a connected-ish graph for stable spectral features.
    edges += [(i, i + 1) for i in range(n - 1)]
    features, _, _ = spectral_features(laplacian(n, edges), m)
    frequencies = rng.normal(0, 0.7, size=(d // 2, m))
    z = rng.normal(size=(n, d))
    rotated = wire_rotate(z, features, frequencies)
    angles = features @ frequencies.T
    block_norm_error = 0.0
    for b in range(d // 2):
        c, s = np.cos(angles[0, b]), np.sin(angles[0, b])
        rot = np.array([[c, -s], [s, c]])
        block_norm_error = max(block_norm_error, abs(np.linalg.det(rot) - 1.0), np.linalg.norm(rot.T @ rot - np.eye(2)))
    return {
        "nodes": float(n),
        "spectral_feature_dim": float(m),
        "angle_std": float(angles.std()),
        "rotation_orthogonality_error": float(block_norm_error),
        "output_finite": float(np.isfinite(rotated).all()),
    }


def check_claim_2(rng: np.random.Generator) -> dict[str, float]:
    n, d, m = 14, 8, 4
    edges = [(i, i + 1) for i in range(n - 1)] + [(0, 5), (3, 9), (7, 12), (1, 10)]
    l = laplacian(n, edges)
    features, _, u = spectral_features(l, m)
    perm = rng.permutation(n)
    lp = l[np.ix_(perm, perm)]
    fp, _, up = spectral_features(lp, m)
    expected = u[perm, :m]
    signs = np.sign(np.sum(fp * expected, axis=0))
    signs[signs == 0] = 1
    aligned_feature_error = float(np.max(np.abs(fp * signs - expected)))
    z = rng.normal(size=(n, d))
    omega = rng.normal(0, 0.4, size=(d // 2, m))
    # A sign change is absorbed by the corresponding frequency reparameterisation.
    omega_perm = omega * signs[None, :]
    out = wire_rotate(z, features, omega)
    out_perm = wire_rotate(z[perm], fp, omega_perm)
    equivariance_error = float(np.max(np.abs(out[perm] - out_perm)))

    # A 4-cycle has a repeated Laplacian eigenvalue (the 2-eigenspace).
    cycle_edges = [(0, 1), (1, 2), (2, 3), (3, 0)]
    lc = laplacian(4, cycle_edges)
    _, vals_c, uc = spectral_features(lc, 4)
    p2 = np.array([1, 2, 3, 0])
    _, _, up2 = spectral_features(lc[np.ix_(p2, p2)], 4)
    # Compare subspaces, not individual basis vectors, in the repeated block.
    a, b = uc[p2, 1:3], up2[:, 1:3]
    principal_cosines = np.linalg.svd(a.T @ b, compute_uv=False)
    return {
        "permutation_feature_max_error_after_sign_alignment": aligned_feature_error,
        "permutation_wire_max_error_after_frequency_gauge": equivariance_error,
        "cycle_degenerate_eigenvalue_pair": float(vals_c[1]),
        "cycle_degenerate_subspace_min_cosine": float(principal_cosines.min()),
    }


def check_claim_3() -> dict[str, float]:
    n = 25
    i = np.arange(n, dtype=float)
    l = laplacian(n, [(k, k + 1) for k in range(n - 1)])
    _, vals, u = spectral_features(l, 2)
    # Theorem 2 uses u_1[i] = -cos((i+1/2) pi / N).
    raw_formula = -np.cos((i + 0.5) * np.pi / n)
    formula_scale = np.linalg.norm(raw_formula)
    formula = raw_formula / formula_scale
    eig_sign = np.sign(np.dot(u[:, 1], formula)) or 1.0
    u1 = eig_sign * u[:, 1]
    formula_error = float(np.max(np.abs(u1 - formula)))
    recovered_position = np.arccos(-(u1 * formula_scale)) * n / np.pi - 0.5
    position_error = float(np.max(np.abs(recovered_position - i)))
    monotone = float(np.all(np.diff(u1) > 0))
    return {
        "path_second_eigenvalue": float(vals[1]),
        "theorem_2_eigenvector_formula_max_error": formula_error,
        "bijective_coordinate_recovery_max_error": position_error,
        "coordinate_monotonicity": monotone,
    }


def check_claim_4(rng: np.random.Generator) -> dict[str, float]:
    n, d = 10, 12
    edges = [(i, i + 1) for i in range(n - 1)] + [(0, 3), (2, 7), (4, 8), (1, 6)]
    l = laplacian(n, edges)
    features, vals, vecs = spectral_features(l, n, resistance_weighted=True)
    i, j = 1, 8
    resistance = effective_resistance(l, i, j)
    std = 0.08
    q = np.ones(d)
    k = np.ones(d)
    qk = float(q @ k)
    draws = 4096
    scores = np.empty(draws)
    delta = features[i] - features[j]
    for t in range(draws):
        omega = rng.normal(0, std, size=(d // 2, n - 1))
        angles = omega @ delta
        scores[t] = 2 * np.sum(np.cos(angles))
    exact_gaussian = qk * np.exp(-std**2 * resistance / 2)
    first_order = qk * (1 - std**2 * resistance / 2)
    return {
        "effective_resistance": resistance,
        "spectral_resistance_identity_error": abs(resistance - float(delta @ delta)),
        "mc_mean_score": float(scores.mean()),
        "gaussian_expectation": float(exact_gaussian),
        "first_order_prediction": float(first_order),
        "mc_abs_error_to_first_order": float(abs(scores.mean() - first_order)),
        "mc_standard_error": float(scores.std(ddof=1) / np.sqrt(draws)),
        "omega_std": std,
        "nonzero_eigenvalues": float(np.count_nonzero(vals[1:] > 1e-10)),
    }


def main() -> None:
    rng = np.random.default_rng(18382)
    results = {
        "paper": {
            "title": "Rotary Position Encodings for Graphs",
            "arxiv": "https://huggingface.co/papers/2509.22259",
            "openreview": "https://openreview.net/forum?id=trn64znfNx",
            "reference_code": "https://anonymous.4open.science/r/WIRE_Graphs-4584/",
        },
        "claim_1": check_claim_1(rng),
        "claim_2": check_claim_2(rng),
        "claim_3": check_claim_3(),
        "claim_4": check_claim_4(rng),
    }
    RESULTS.mkdir(parents=True, exist_ok=True)
    (RESULTS / "core_results.json").write_text(json.dumps(results, indent=2) + "\n")
    print(json.dumps(results, indent=2))


if __name__ == "__main__":
    main()