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4093113 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 | #!/usr/bin/env python3
"""Independent NumPy oracle for the saved source-scale Deep-UFM state."""
from __future__ import annotations
import argparse
import csv
import hashlib
import json
from pathlib import Path
import numpy as np
K = 3
D = 65
N_PER_CLASS = 40
N = K * N_PER_CLASS
LAYER = 4
def digest(path: Path) -> str:
return hashlib.sha256(path.read_bytes()).hexdigest()
def relu(value: np.ndarray) -> np.ndarray:
return np.maximum(value, 0.0)
def analyse(state_path: Path) -> dict:
state = np.load(state_path)
h = state["H1"].astype(np.float64)
target = state["Y"].astype(np.float64)
weights = [
state[f"W{index}"].astype(np.float64) for index in range(1, 6)
]
# Accelerate-backed NumPy on macOS can leave floating-point status flags
# set after a finite BLAS matmul and consequently emit spurious divide or
# overflow RuntimeWarnings on the next operation. Suppress only those
# status-flag reports and fail explicitly on every non-finite array.
with np.errstate(divide="ignore", over="ignore", invalid="ignore"):
activations = [h]
preactivations = []
x = h
for weight in weights[:-1]:
z = weight @ x
preactivations.append(z)
x = relu(z)
activations.append(x)
output = weights[-1] @ x
residual = output - target
if not all(
np.isfinite(value).all()
for value in [*activations, *preactivations, output, residual]
):
raise RuntimeError("non-finite value in independent forward oracle")
# For output k and sample j:
# d output[k,j] / d W4[a,b]
# = W5[k,a] 1[z4[a,j]>0] activation3[b,j].
left = weights[-1][:, :, None] * (
preactivations[3] > 0
)[None, :, :]
jacobian = np.einsum(
"kaj,bj->jkab", left, activations[3], optimize=True
).reshape(N * K, D * D)
# The non-zero eigenvalues of J.T J / N equal those of J J.T / N.
with np.errstate(divide="ignore", over="ignore", invalid="ignore"):
gram = (jacobian @ jacobian.T) / N
if not np.isfinite(gram).all():
raise RuntimeError("non-finite value in independent Hessian oracle")
eigenvalues, left_eigenvectors = np.linalg.eigh(
0.5 * (gram + gram.T)
)
order = np.argsort(eigenvalues)[::-1]
eigenvalues = eigenvalues[order]
left_eigenvectors = left_eigenvectors[:, order]
with np.errstate(divide="ignore", over="ignore", invalid="ignore"):
gradient = (jacobian.T @ residual.T.reshape(-1)) / N
if not np.isfinite(gradient).all():
raise RuntimeError("non-finite value in independent gradient oracle")
gradient_norm = np.linalg.norm(gradient)
coefficients = []
for index, eigenvalue in enumerate(eigenvalues[: K * K]):
with np.errstate(divide="ignore", over="ignore", invalid="ignore"):
right = (
jacobian.T @ left_eigenvectors[:, index]
) / np.sqrt(max(N * eigenvalue, 1e-300))
right /= max(np.linalg.norm(right), 1e-300)
with np.errstate(divide="ignore", over="ignore", invalid="ignore"):
coefficient = float(
(right @ gradient) ** 2 / max(gradient_norm**2, 1e-300)
)
if not np.isfinite(right).all() or not np.isfinite(coefficient):
raise RuntimeError("non-finite value in eigenspace oracle")
coefficients.append(coefficient)
positive = eigenvalues[eigenvalues > max(eigenvalues[0] * 1e-10, 1e-14)]
top9 = eigenvalues[: K * K]
ninth_tenth_ratio = float(top9[-1] / max(eigenvalues[K * K], 1e-300))
top9_unequal_ratio = float(top9[0] / max(top9[-1], 1e-300))
coeff_sorted = sorted(coefficients, reverse=True)
coefficient_threshold = max(coeff_sorted[0] * 1e-4, 1e-12)
nonzero_coefficients = sum(
coefficient > coefficient_threshold for coefficient in coefficients
)
return {
"state_sha256": digest(state_path),
"configuration": {
"K": K,
"d": D,
"n_per_class": N_PER_CLASS,
"L": 5,
"audited_layer_l": LAYER,
"parameter_count_W4": D * D,
"jacobian_shape": list(jacobian.shape),
"gram_shape": list(gram.shape),
},
"fit": {
"mse": float(np.mean(residual**2)),
"accuracy": float(
np.mean(np.argmax(output, axis=0) == np.argmax(target, axis=0))
),
},
"hessian": {
"construction": "independent NumPy J J^T / N exact non-zero spectrum",
"strictly_positive_eigenvalues": int(len(positive)),
"top_12_eigenvalues": eigenvalues[:12].tolist(),
"top_9_eigenvalues": top9.tolist(),
"ninth_to_tenth_separation_ratio": ninth_tenth_ratio,
"top9_max_to_min_ratio": top9_unequal_ratio,
"nine_outlier_gate": ninth_tenth_ratio >= 3.0,
"unequal_top9_gate": top9_unequal_ratio >= 1.05,
},
"gradient": {
"construction": (
"non-regularization layer-W4 gradient projected onto the "
"true top-nine Hessian eigenvectors"
),
"squared_alignment_coefficients": coefficients,
"sorted_squared_alignment_coefficients": coeff_sorted,
"nonzero_threshold": coefficient_threshold,
"nonzero_coefficient_count": nonzero_coefficients,
"top3_max_to_min_ratio": float(
coeff_sorted[0] / max(coeff_sorted[2], 1e-300)
),
"fourth_to_third_ratio": float(
coeff_sorted[3] / max(coeff_sorted[2], 1e-300)
),
"K_nonzero_gate": nonzero_coefficients == K,
"unequal_top3_gate": (
coeff_sorted[0] / max(coeff_sorted[2], 1e-300)
) >= 1.05,
},
}
def main() -> None:
parser = argparse.ArgumentParser()
parser.add_argument("--state", type=Path, required=True)
parser.add_argument("--output", type=Path, required=True)
args = parser.parse_args()
args.output.mkdir(parents=True, exist_ok=True)
result = analyse(args.state)
predicates = {
"nine_hessian_outliers_separate": result["hessian"][
"nine_outlier_gate"
],
"nine_hessian_outliers_remain_unequal": result["hessian"][
"unequal_top9_gate"
],
"gradient_has_exactly_K_nonzero_coefficients": result["gradient"][
"K_nonzero_gate"
],
"top_K_gradient_coefficients_are_unequal": result["gradient"][
"unequal_top3_gate"
],
}
result["literal_claim_predicates"] = predicates
result["all_literal_claim_gates_pass"] = bool(all(predicates.values()))
result["falsified_literal_predicates"] = [
name for name, passed in predicates.items() if not passed
]
native_fit_gate = bool(
result["fit"]["accuracy"] >= 0.99 and result["fit"]["mse"] <= 1e-4
)
result["native_fit_gate"] = native_fit_gate
if not native_fit_gate:
result["decisive_literal_verdict"] = "inconclusive"
result["release_quality_gate_pass"] = False
elif result["all_literal_claim_gates_pass"]:
result["decisive_literal_verdict"] = "verified"
result["release_quality_gate_pass"] = True
else:
result["decisive_literal_verdict"] = (
"falsified_as_literally_registered"
)
result["release_quality_gate_pass"] = True
(args.output / "native_oracle.json").write_text(
json.dumps(result, indent=2, sort_keys=True) + "\n",
encoding="utf-8",
)
with (args.output / "native_spectrum.csv").open(
"w", newline="", encoding="utf-8"
) as handle:
writer = csv.writer(handle)
writer.writerow(("rank", "hessian_eigenvalue", "gradient_alignment"))
eigenvalues = result["hessian"]["top_12_eigenvalues"]
coefficients = result["gradient"]["squared_alignment_coefficients"]
for index, value in enumerate(eigenvalues, 1):
writer.writerow(
(index, value, coefficients[index - 1] if index <= 9 else "")
)
print(json.dumps(result, indent=2, sort_keys=True))
if not result["release_quality_gate_pass"]:
raise SystemExit(2)
if __name__ == "__main__":
main()
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