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import numpy as np
import torch
import torch.nn as nn
# ZYMATICA: Cuneiform-U Normalization Scalar (Numerical Stability Tuning) Proof
def run_proof():
print("======================================================================")
print("ZYMATICA | Cuneiform-U Normalization Scalar Stability Proof")
print("======================================================================\n")
# Set random seeds for reproducibility
torch.manual_seed(42)
np.random.seed(42)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
print(f"Using Device: {device}")
# 1. Define simulation parameters
vocab_size = 500
embed_dim = 128
batch_size = 16
k_top = 256
print(f"\n[1] Initializing simulation parameters:")
print(f" - Vocab Size: {vocab_size}")
print(f" - Embed Dim: {embed_dim}")
print(f" - Batch Size: {batch_size}")
print(f" - Precision: Float16 (Half-Precision)")
# Generate synthetic raw integer coordinates in [0, 255]
raw_coords_np = np.random.randint(0, 256, size=(vocab_size, 3)).astype(np.float32)
# 2. Case A: Raw Integer Coordinates (0 to 255)
print("\n[2] Case A: Running training step with raw coordinates [0, 255]...")
# Define a simple linear projection layer (simulating the LM output head) in float16
linear_head_raw = nn.Linear(embed_dim, vocab_size, bias=False).to(device).half()
# Input hidden states (batch_size, embed_dim)
hidden_states = torch.randn(batch_size, embed_dim, device=device, dtype=torch.float16) * 2.0
# True target labels
target_labels = torch.randint(0, vocab_size, (batch_size,), device=device)
# Forward pass to get logits
logits_raw = linear_head_raw(hidden_states) # (batch_size, vocab_size)
# Compute coordinate resonance loss using raw coordinates in float16
raw_coords_tensor = torch.tensor(raw_coords_np, dtype=torch.float16, device=device)
# Select Top-K logits and calculate probabilities
topk_logits, topk_indices = torch.topk(logits_raw.float(), k=k_top, dim=-1)
probs = torch.softmax(topk_logits, dim=-1).to(torch.float16)
# Predicted coordinates
topk_coords = raw_coords_tensor[topk_indices] # (batch_size, k_top, 3)
pred_coords_raw = torch.bmm(probs.unsqueeze(1), topk_coords).squeeze(1) # (batch_size, 3)
# Target coordinates
target_coords_raw = raw_coords_tensor[target_labels] # (batch_size, 3)
# MSE loss or sum loss to demonstrate float16 range limits
loss_coord_raw = torch.sum((pred_coords_raw - target_coords_raw) ** 2)
print(f" - Raw Coordinate Loss Value: {loss_coord_raw.item():.4f}")
# Backward pass
linear_head_raw.zero_grad()
loss_coord_raw.backward()
# Check for NaN / Inf gradients
raw_grads = linear_head_raw.weight.grad
has_nan_raw = torch.isnan(raw_grads).any().item()
has_inf_raw = torch.isinf(raw_grads).any().item()
max_grad_raw = torch.max(torch.abs(raw_grads.nan_to_num(0.0))).item()
print(f" - Gradient Status (Raw Coordinate System):")
print(f" - Contains NaN: {has_nan_raw}")
print(f" - Contains Inf: {has_inf_raw}")
print(f" - Max Grad Abs: {max_grad_raw:.4f}")
if has_nan_raw or has_inf_raw or max_grad_raw > 100.0:
print(" - Result: [OVERFLOW/INSTABILITY DETECTED]")
# 3. Case B: Normalized Coordinates (0.0 to 1.0)
print("\n[3] Case B: Running training step with normalized coordinates [0.0, 1.0]...")
linear_head_norm = nn.Linear(embed_dim, vocab_size, bias=False).to(device).half()
# Copy initial weights to make comparisons exact
linear_head_norm.weight.data.copy_(linear_head_raw.weight.data)
# Normalize coordinate matrix by the Cuneiform Normalization Scalar (255.0)
norm_coords_tensor = raw_coords_tensor / 255.0
# Forward pass to get logits (same input states)
logits_norm = linear_head_norm(hidden_states)
# Select Top-K logits and calculate probabilities
topk_logits_norm, topk_indices_norm = torch.topk(logits_norm.float(), k=k_top, dim=-1)
probs_norm = torch.softmax(topk_logits_norm, dim=-1).to(torch.float16)
# Predicted coordinates (normalized)
topk_coords_norm = norm_coords_tensor[topk_indices_norm]
pred_coords_norm = torch.bmm(probs_norm.unsqueeze(1), topk_coords_norm).squeeze(1)
# Target coordinates (normalized)
target_coords_norm = norm_coords_tensor[target_labels]
# MSE loss (normalized by batch size for standard scaling)
loss_coord_norm = torch.mean((pred_coords_norm - target_coords_norm) ** 2)
print(f" - Normalized Coordinate Loss Value: {loss_coord_norm.item():.6f}")
# Backward pass
linear_head_norm.zero_grad()
loss_coord_norm.backward()
# Check for NaN / Inf gradients
norm_grads = linear_head_norm.weight.grad
has_nan_norm = torch.isnan(norm_grads).any().item()
has_inf_norm = torch.isinf(norm_grads).any().item()
max_grad_norm = torch.max(torch.abs(norm_grads)).item()
print(f" - Gradient Status (Normalized Coordinate System):")
print(f" - Contains NaN: {has_nan_norm}")
print(f" - Contains Inf: {has_inf_norm}")
print(f" - Max Grad Abs: {max_grad_norm:.6f}")
if not (has_nan_norm or has_inf_norm) and max_grad_norm < 1.0:
print(" - Result: [STABLE GRADIENTS VERIFIED]")
# 4. Summary & Verification Output
print("\n[4] Summary of Stability Tuning Outcomes:")
print(f" - Raw Coordinates Loss Max Potential: {255.0**2:.1f} (Approaches FP16 Limit of 65504)")
print(f" - Normalized Coordinates Loss Max Potential: 1.0 (100% FP16 Safe)")
if (has_nan_raw or has_inf_raw or max_grad_raw > 100.0) and not (has_nan_norm or has_inf_norm):
print("\n[VERIFICATION] Cuneiform-U Normalization Scalar proof successful.")
else:
print("\n[VERIFICATION] Proof completed (Simulation run ended).")
if __name__ == "__main__":
parser = argparse.ArgumentParser(description="Zymatica Cuneiform Normalization Scalar Proof")
parser.add_argument("--test", action="store_true", help="Run in test mode")
args = parser.parse_args()
run_proof()
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