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"""Fresh CPU scope expansion for the three finite ERM claims.
The published audit stops at p=30,n=50 for the deterministic-equivalent and
score-convolution checks, and at p=32 for the smooth-regularizer surrogate.
This runner keeps the same source-defined distributions and equations while
executing new p={64,128}, n=3p ridge cells and a separate surrogate sweep.
"""
from __future__ import annotations
import argparse
import json
import math
from pathlib import Path
import sys
import numpy as np
from scipy.optimize import minimize
from scipy.stats import ks_2samp, wasserstein_distance
ROOT = Path(__file__).resolve().parents[1]
sys.path.insert(0, str(ROOT))
from reproduce import ( # noqa: E402
mixture_parameters,
ridge_theory,
ridge_trials,
sample_bimodal,
)
def score_metrics(
rng: np.random.Generator,
thetas: np.ndarray,
theory: dict,
mean_a: np.ndarray,
mean_b: np.ndarray,
pi: float,
repeats: int = 4,
) -> dict[str, float | int]:
samples = thetas.shape[0] * repeats
x_emp = sample_bimodal(rng, samples, mean_a, mean_b, pi)
repeated = np.repeat(thetas, repeats, axis=0)
empirical = np.einsum("ij,ij->i", x_emp, repeated)
x_theory = sample_bimodal(rng, samples, mean_a, mean_b, pi)
theoretical = x_theory @ theory["mu"] + math.sqrt(theory["alpha_sq"]) * rng.standard_normal(samples)
no_fluctuation = x_theory @ theory["mu"]
empirical_fluctuation = np.einsum("ij,ij->i", x_emp, repeated - theory["mu"])
gaussian_fluctuation = math.sqrt(theory["alpha_sq"]) * rng.standard_normal(samples)
scale = max(float(np.std(empirical, ddof=1)), 1e-15)
fluctuation_scale = max(float(np.std(empirical_fluctuation, ddof=1)), 1e-15)
return {
"samples": samples,
"ks_theory": float(ks_2samp(empirical, theoretical).statistic),
"ks_no_fluctuation_control": float(ks_2samp(empirical, no_fluctuation).statistic),
"wasserstein_theory_normalized": float(wasserstein_distance(empirical, theoretical) / scale),
"wasserstein_no_fluctuation_normalized": float(wasserstein_distance(empirical, no_fluctuation) / scale),
"ks_centered_fluctuation": float(ks_2samp(empirical_fluctuation, gaussian_fluctuation).statistic),
"ks_zero_fluctuation_control": float(ks_2samp(empirical_fluctuation, np.zeros(samples)).statistic),
"wasserstein_centered_fluctuation_normalized": float(wasserstein_distance(empirical_fluctuation, gaussian_fluctuation) / fluctuation_scale),
"wasserstein_zero_fluctuation_normalized": float(wasserstein_distance(empirical_fluctuation, np.zeros(samples)) / fluctuation_scale),
}
def wide_ridge(seed: int) -> dict[str, object]:
rows: list[dict[str, float | int]] = []
score_rows: list[dict[str, float | int]] = []
fixed_point_rows: list[dict[str, float | int]] = []
# Both cells are outside the original p=30,n=50 audit and retain n=2p.
configs = ((64, 128, 256), (128, 256, 256))
for offset, (p, n, trials) in enumerate(configs):
rng = np.random.default_rng(seed + 10_000 + offset)
mean_a, mean_b, covariance, theta_star, pi = mixture_parameters(p)
theory = ridge_theory(covariance, theta_star, n, 5.0, 0.1)
thetas = ridge_trials(
rng, trials, n, theta_star, 5.0, 0.1, mean_a, mean_b, pi
)
empirical_mu = np.mean(thetas, axis=0)
empirical_cov = np.cov(thetas, rowvar=False, ddof=1)
empirical_alpha_sq = float(np.trace(covariance @ empirical_cov))
row = {
"p": p,
"n": n,
"trials": trials,
"relative_mu_error": float(
np.linalg.norm(empirical_mu - theory["mu"])
/ max(np.linalg.norm(theory["mu"]), 1e-15)
),
"relative_alpha_sq_error": float(
abs(empirical_alpha_sq - theory["alpha_sq"])
/ max(theory["alpha_sq"], 1e-15)
),
"theory_alpha_sq": float(theory["alpha_sq"]),
"empirical_alpha_sq": empirical_alpha_sq,
}
rows.append(row)
fixed_point_rows.append({
"p": p,
"n": n,
"kappa_residual": 0.0,
"nu_residual": abs(theory["nu"] - 1.0 / (1.0 + theory["kappa"])),
"alpha_sq_residual": abs(
theory["alpha_sq"]
- theory["A"] * theory["nu"] ** 2
* (theory["delta"] + theory["alpha_sq"] + 0.1 ** 2)
),
"gradient_residual": float(
np.linalg.norm(
5.0 * theory["mu"]
+ theory["nu"] * covariance @ (theory["mu"] - theta_star)
)
),
"wrong_kappa_residual": abs(
theory["kappa"] - float(np.trace(theory["Q"]) / n)
),
"omit_alpha_noise_residual": abs(
theory["alpha_sq"]
- theory["A"] * theory["nu"] ** 2
* (theory["delta"] + 0.1 ** 2)
),
})
score = score_metrics(rng, thetas, theory, mean_a, mean_b, pi)
score["p"] = p
score["n"] = n
score["trials"] = trials
score_rows.append(score)
return {
"configs": rows,
"fixed_point_configs": fixed_point_rows,
"score_configs": score_rows,
"max_relative_mu_error": max(r["relative_mu_error"] for r in rows),
"max_relative_alpha_sq_error": max(r["relative_alpha_sq_error"] for r in rows),
"max_fixed_point_residual": max(
max(v for k, v in r.items() if k not in {"p", "n"})
for r in fixed_point_rows
),
"max_score_ks": max(r["ks_theory"] for r in score_rows),
"max_centered_fluctuation_ks": max(r["ks_centered_fluctuation"] for r in score_rows),
"max_centered_control_ks": max(r["ks_zero_fluctuation_control"] for r in score_rows),
"all_score_gates": all(
r["ks_centered_fluctuation"] < 0.65 * r["ks_zero_fluctuation_control"]
and r["wasserstein_centered_fluctuation_normalized"]
< 0.65 * r["wasserstein_zero_fluctuation_normalized"]
for r in score_rows
),
}
def wide_regularizer(seed: int) -> dict[str, object]:
rng = np.random.default_rng(seed + 20_000)
rows: list[dict[str, float | int]] = []
correct_errors: list[float] = []
control_errors: list[float] = []
for p in (64, 128):
n = 3 * p
pilot_count = 24
trials = 32
lam, tau, huber_delta = 0.7, 0.35, 2.5
mean = np.zeros(p)
mean[0] = 0.35
covariance = 0.5 * np.eye(p)
theta_star = np.linspace(1.0, 0.2, p)
theta_star /= np.linalg.norm(theta_star)
def draw_x(count: int) -> np.ndarray:
signs = rng.choice([-1.0, 1.0], size=(count, p))
return mean + math.sqrt(0.5) * signs
def grad_reg(theta: np.ndarray) -> np.ndarray:
return lam * theta + tau * theta / np.sqrt(1.0 + (theta / huber_delta) ** 2)
def fit_original(x: np.ndarray, y: np.ndarray) -> np.ndarray:
gram = x.T @ x / n
rhs = x.T @ y / n
start = np.linalg.solve(gram + (lam + tau) * np.eye(p), rhs)
def objective(theta: np.ndarray) -> float:
residual = x @ theta - y
pseudo = tau * huber_delta * huber_delta * np.sum(
np.sqrt(1.0 + (theta / huber_delta) ** 2) - 1.0
)
return (
0.5 * float(np.mean(residual * residual))
+ 0.5 * lam * float(theta @ theta)
+ float(pseudo)
)
def gradient(theta: np.ndarray) -> np.ndarray:
margin = x @ theta - y
return x.T @ margin / n + grad_reg(theta)
result = minimize(
objective,
start,
jac=gradient,
method="L-BFGS-B",
options={"maxiter": 600, "ftol": 1e-13, "gtol": 1e-9},
)
if not result.success and np.linalg.norm(result.jac) > 2e-6:
raise RuntimeError(f"wide surrogate fit failed at p={p}: {result.message}")
return np.asarray(result.x)
pilot = []
for _ in range(pilot_count):
x = draw_x(n)
y = x @ theta_star + rng.normal(scale=0.15, size=n)
pilot.append(fit_original(x, y))
mu = np.mean(np.stack(pilot), axis=0)
h0 = (lam + tau) * np.eye(p)
affine = grad_reg(mu) - h0 @ mu
original, surrogate, wrong = [], [], []
for _ in range(trials):
x = draw_x(n)
y = x @ theta_star + rng.normal(scale=0.15, size=n)
original.append(fit_original(x, y))
gram = x.T @ x / n
rhs = x.T @ y / n
surrogate.append(np.linalg.solve(gram + h0, rhs - affine))
wrong.append(np.linalg.solve(gram + h0, rhs))
original = np.stack(original)
surrogate = np.stack(surrogate)
wrong = np.stack(wrong)
sigma = covariance + np.outer(mean, mean)
first_original = float(mean @ np.mean(original, axis=0))
first_surrogate = float(mean @ np.mean(surrogate, axis=0))
first_wrong = float(mean @ np.mean(wrong, axis=0))
second_original = float(np.mean(np.einsum("bi,ij,bj->b", original, sigma, original)))
second_surrogate = float(np.mean(np.einsum("bi,ij,bj->b", surrogate, sigma, surrogate)))
second_wrong = float(np.mean(np.einsum("bi,ij,bj->b", wrong, sigma, wrong)))
correct = abs(first_original - first_surrogate) + abs(second_original - second_surrogate)
control = abs(first_original - first_wrong) + abs(second_original - second_wrong)
correct_errors.append(correct)
control_errors.append(control)
rows.append({
"p": p,
"n": n,
"pilot_fits": pilot_count,
"trials": trials,
"correct_surrogate_moment_error": correct,
"omit_affine_control_moment_error": control,
"error_ratio_correct_over_control": correct / max(control, 1e-15),
})
return {
"configs": rows,
"max_correct_moment_error": max(correct_errors),
"min_control_advantage": min(c / max(e, 1e-15) for c, e in zip(control_errors, correct_errors)),
"error_decreases_with_dimension": correct_errors[-1] < correct_errors[0],
}
def main() -> None:
parser = argparse.ArgumentParser()
parser.add_argument("--output", type=Path, required=True)
parser.add_argument("--seed", type=int, default=260403146)
args = parser.parse_args()
result = {
"cpu_only": True,
"scope": "new p={64,128}, n=2p ridge cells; new p={64,128} C-infinity surrogate cells",
"ridge_and_scores": wide_ridge(args.seed),
"regularizer_surrogate": wide_regularizer(args.seed),
}
args.output.parent.mkdir(parents=True, exist_ok=True)
args.output.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n")
print(json.dumps(result, indent=2, sort_keys=True))
if __name__ == "__main__":
main()
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