File size: 3,979 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 99 100 | import argparse
import numpy as np
from scipy.fft import dct, idct
def dct_compress_vector(v, K):
"""Applies DCT-II, keeps top-K low-frequency coefficients, and returns them."""
v_dct = dct(v.astype(np.float64), norm='ortho')
# Keep only the first K low-frequency coefficients (spectral truncation)
truncated = np.zeros_like(v_dct)
truncated[:K] = v_dct[:K]
return truncated
def idct_reconstruct_vector(v_dct_trunc):
"""Applies IDCT-III to reconstruct the vector from truncated DCT coefficients."""
return idct(v_dct_trunc, norm='ortho')
def run_proof():
print("======================================================================")
print("ZYMATICA | SVD/DCT Compression & Reconstructor Pipeline Proof")
print("======================================================================\n")
M, N = 64, 64
RANK = 4
K_COEF = 8 # Keep 8 lowest frequency DCT coefficients out of 64
# 1. Generate structured weights (low-rank + smooth variations)
print(f"[1] Simulating Target Weight Delta Matrix W ({M}x{N} floats)...")
t = np.linspace(0, 2 * np.pi, M)
# Build smooth spatial features
u1 = np.sin(t)
v1 = np.cos(t)
u2 = np.sin(2 * t)
v2 = np.cos(2 * t)
W_true = np.outer(u1, v1) + np.outer(u2, v2)
# Add minor noise
rng = np.random.RandomState(42)
W_true += 0.05 * rng.standard_normal((M, N))
raw_size_bytes = W_true.nbytes
print(f" - Original weight matrix shape: {W_true.shape}")
print(f" - Original weight raw size: {raw_size_bytes} bytes ({raw_size_bytes / 1024:.2f} KB)")
# 2. Run Singular Value Decomposition (SVD)
print(f"\n[2] Executing Low-Rank SVD (Rank={RANK})...")
U, S, Vh = np.linalg.svd(W_true, full_matrices=False)
U_r = U[:, :RANK]
S_r = S[:RANK]
V_r = Vh[:RANK, :].T # Columns are right singular vectors
# Absorb square root of S
sqrt_S = np.sqrt(S_r)
U_scaled = U_r * sqrt_S
V_scaled = V_r * sqrt_S
print(f" - Absorb singular values: U_scaled shape={U_scaled.shape}, V_scaled shape={V_scaled.shape}")
# 3. Apply DCT-II to compress singular vectors
print(f"\n[3] Projecting Singular Vectors into DCT Domain (Keeping Top-{K_COEF} Coefficients)...")
U_rec = np.zeros_like(U_scaled)
V_rec = np.zeros_like(V_scaled)
for col in range(RANK):
# Compress U column
u_dct = dct_compress_vector(U_scaled[:, col], K_COEF)
U_rec[:, col] = idct_reconstruct_vector(u_dct)
# Compress V column
v_dct = dct_compress_vector(V_scaled[:, col], K_COEF)
V_rec[:, col] = idct_reconstruct_vector(v_dct)
print(" -> DCT & Inverse DCT spectral transformations completed.")
# 4. Reconstruct original weights matrix
print("\n[4] Rebuilding Layer Weights Matrix from Compressed Manifold...")
W_rec = np.dot(U_rec, V_rec.T)
# Calculate compression metrics
# Stored data: 2 matrices of (RANK x K_COEF) float32 coefficients.
stored_floats = 2 * (RANK * K_COEF)
compressed_bytes = stored_floats * 4
compression_ratio = raw_size_bytes / compressed_bytes
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" - Original Float Parameters: {W_true.size:,}")
print(f" - Compressed Float Parameters: {stored_floats:,}")
print(f" - Compression Ratio: {compression_ratio:.2f}x")
print(f" - Reconstruction MSE: {mse:.6f}")
print(f" - Cosine Similarity (Fidelity): {cosine_sim * 100:.2f}%")
print("\n[VERIFICATION] SVD/DCT spectral projection pipeline verified.")
if __name__ == "__main__":
parser = argparse.ArgumentParser(description="Zymatica SVD/DCT Compression Proof")
parser.add_argument("--test", action="store_true", help="Run test mode")
args = parser.parse_args()
run_proof()
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