File size: 4,475 Bytes
c8e724e | 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 | import argparse
import numpy as np
def get_dictionary(dim, dictionary_size, seed):
"""Procedurally generate a normalized dictionary matrix using deterministic PRNG seed."""
rng = np.random.RandomState(seed)
dict_mat = rng.standard_normal((dim, dictionary_size)).astype(np.float32)
norms = np.linalg.norm(dict_mat, axis=0, keepdims=True) + 1e-9
return dict_mat / norms
def sparse_matching_pursuit(W, u_dict, v_dict, rank):
"""Compresses W by projecting onto u_dict and v_dict up to a given rank."""
W_residual = W.copy()
projections = []
for r in range(rank):
# Calculate projection search space
# Find dictionary columns (u_i, v_j) that maximize projection correlation
# correlation(i, j) = u_i^T * W_residual * v_j
corr_matrix = np.dot(u_dict.T, np.dot(W_residual, v_dict))
# Locate indices of maximum absolute correlation
idx_u, idx_v = np.unravel_index(np.argmax(np.abs(corr_matrix)), corr_matrix.shape)
coeff = corr_matrix[idx_u, idx_v]
# Capture indices and coefficient
projections.append((idx_u, idx_v, coeff))
# Update residual: subtract the rank-1 component
outer_prod = np.outer(u_dict[:, idx_u], v_dict[:, idx_v])
W_residual -= coeff * outer_prod
return projections
def reconstruct_matrix(projections, u_dict, v_dict, m, n):
"""Reconstructs the weight matrix from sparse projections and dictionaries."""
W_rec = np.zeros((m, n), dtype=np.float32)
for idx_u, idx_v, coeff in projections:
W_rec += coeff * np.outer(u_dict[:, idx_u], v_dict[:, idx_v])
return W_rec
def run_proof():
print("======================================================================")
print("ZYMATICA | Genesis Protocol: Procedural Seed Reconstruction Proof")
print("======================================================================\n")
M, N = 64, 64
DICT_SIZE = 128
RANK = 4
MASTER_SEED = 42
print(f"[1] Generating Mock Layer Weight Matrix W ({M}x{N} floats)...")
# Generate structured weights (like low-rank patterns in neural networks)
rng = np.random.RandomState(MASTER_SEED)
W_true = rng.standard_normal((M, N)).astype(np.float32)
# enforce structure by making it low-rank plus noise
U_true = rng.standard_normal((M, 4))
V_true = rng.standard_normal((N, 4))
W_true = np.dot(U_true, V_true.T) + 0.1 * rng.standard_normal((M, N))
raw_size_bytes = W_true.nbytes
print(f" -> Size of raw weights matrix W: {raw_size_bytes} bytes ({raw_size_bytes / 1024:.2f} KB)")
print(f"\n[2] Instantiating Procedural Dictionaries (Seed={MASTER_SEED}, DictSize={DICT_SIZE})...")
u_dict = get_dictionary(M, DICT_SIZE, MASTER_SEED)
v_dict = get_dictionary(N, DICT_SIZE, MASTER_SEED + 500)
print(f" -> Generated U_dict shape: {u_dict.shape}")
print(f" -> Generated V_dict shape: {v_dict.shape}")
print(f"\n[3] Compiling Weight Matrix into Sparse Trajectories (Rank={RANK})...")
projections = sparse_matching_pursuit(W_true, u_dict, v_dict, RANK)
# Calculate compressed size: each projection has 1-byte U idx, 1-byte V idx, 2-byte coefficient (float16)
# Total = 4 bytes per rank.
compressed_bytes = RANK * 4
compression_ratio = raw_size_bytes / compressed_bytes
print(f" Sparse Projections:")
for r, (iu, iv, val) in enumerate(projections):
print(f" Rank {r+1}: U_idx={iu:3d}, V_idx={iv:3d}, Coefficient={val:.4f}")
print(f" -> Compressed Payload Size: {compressed_bytes} bytes")
print(f" -> Compression Ratio: {compression_ratio:.2f}x")
print("\n[4] Executing Edge Reconstructor (Procedural Inflation)...")
W_rec = reconstruct_matrix(projections, u_dict, v_dict, M, N)
mse = np.mean((W_true - W_rec) ** 2)
cosine_sim = np.dot(W_true.flatten(), W_rec.flatten()) / (np.linalg.norm(W_true) * np.linalg.norm(W_rec) + 1e-9)
print(f" - Reconstruction Mean Squared Error (MSE): {mse:.6f}")
print(f" - Cosine Similarity (Fidelity Index): {cosine_sim * 100:.2f}%")
print("\n[VERIFICATION] Deterministic procedural morphogenesis completed successfully.")
if __name__ == "__main__":
parser = argparse.ArgumentParser(description="Zymatica Genesis Protocol Proof")
parser.add_argument("--test", action="store_true", help="Run test mode")
args = parser.parse_args()
run_proof()
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