4-bit incrementer, magnitude 41

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-incrementer4bit
+
+4-bit incrementer. Adds 1 to input (modulo 16).
+
+## Function
+
+incrementer4bit(a3, a2, a1, a0) = (input + 1) mod 16
+
+## Truth Table (selected rows)
+
+| Input | Decimal | Output | Decimal |
+|-------|---------|--------|---------|
+| 0000 | 0 | 0001 | 1 |
+| 0001 | 1 | 0010 | 2 |
+| 0111 | 7 | 1000 | 8 |
+| 1111 | 15 | 0000 | 0 |
+
+## Architecture
+
+```
+y0 = NOT(a0)
+y1 = a1 XOR a0
+y2 = a2 XOR (a1 AND a0)
+y3 = a3 XOR (a2 AND a1 AND a0)
+```
+
+Layer 1: Compute NOT(a0), carries (c2, c3), and XOR components for y1
+Layer 2: Compute y1, XOR components for y2 and y3
+Layer 3: Final AND gates for y2 and y3
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 4 |
+| Neurons | 12 |
+| Layers | 3 |
+| Parameters | 52 |
+| Magnitude | 41 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+# See model.py for full implementation
+
+# 7 + 1 = 8
+# incrementer4(0, 1, 1, 1) = [1, 0, 0, 0]
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-incrementer4bit",
+  "description": "4-bit incrementer (adds 1)",
+  "inputs": 4,
+  "outputs": 4,
+  "neurons": 12,
+  "layers": 3,
+  "parameters": 52
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# Input: [a3, a2, a1, a0]
+# Output: input + 1 (mod 16)
+# y0 = NOT(a0)
+# y1 = a1 XOR a0
+# y2 = a2 XOR (a1 AND a0)
+# y3 = a3 XOR (a2 AND a1 AND a0)
+
+# Layer 1: NOT, carries, and XOR components
+# y0 = NOT(a0)
+weights['y0.weight'] = torch.tensor([[0.0, 0.0, 0.0, -1.0]], dtype=torch.float32)
+weights['y0.bias'] = torch.tensor([0.0], dtype=torch.float32)
+
+# c2 = a1 AND a0
+weights['c2.weight'] = torch.tensor([[0.0, 0.0, 1.0, 1.0]], dtype=torch.float32)
+weights['c2.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+# c3 = a2 AND a1 AND a0
+weights['c3.weight'] = torch.tensor([[0.0, 1.0, 1.0, 1.0]], dtype=torch.float32)
+weights['c3.bias'] = torch.tensor([-3.0], dtype=torch.float32)
+
+# XOR(a1, a0) components
+weights['y1_or.weight'] = torch.tensor([[0.0, 0.0, 1.0, 1.0]], dtype=torch.float32)
+weights['y1_or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+weights['y1_nand.weight'] = torch.tensor([[0.0, 0.0, -1.0, -1.0]], dtype=torch.float32)
+weights['y1_nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+
+# Layer 2: y1 AND, XOR(a2,c2) and XOR(a3,c3) components
+# Input order for layer 2: [a3, a2, c2, c3, y1_or, y1_nand]
+# y1 = AND(y1_or, y1_nand)
+weights['y1.weight'] = torch.tensor([[0.0, 0.0, 0.0, 0.0, 1.0, 1.0]], dtype=torch.float32)
+weights['y1.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+# y2 = XOR(a2, c2): OR(a2, c2) and NAND(a2, c2)
+weights['y2_or.weight'] = torch.tensor([[0.0, 1.0, 1.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y2_or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+weights['y2_nand.weight'] = torch.tensor([[0.0, -1.0, -1.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y2_nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+
+# y3 = XOR(a3, c3): OR(a3, c3) and NAND(a3, c3)
+weights['y3_or.weight'] = torch.tensor([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y3_or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+weights['y3_nand.weight'] = torch.tensor([[-1.0, 0.0, 0.0, -1.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y3_nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+
+# Layer 3: y2 and y3 final AND
+weights['y2.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+weights['y2.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+weights['y3.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+weights['y3.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+# Verify
+def incrementer4(a3, a2, a1, a0):
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+
+    # Layer 1
+    y0 = int((inp @ weights['y0.weight'].T + weights['y0.bias'] >= 0).item())
+    c2 = int((inp @ weights['c2.weight'].T + weights['c2.bias'] >= 0).item())
+    c3 = int((inp @ weights['c3.weight'].T + weights['c3.bias'] >= 0).item())
+    y1_or = int((inp @ weights['y1_or.weight'].T + weights['y1_or.bias'] >= 0).item())
+    y1_nand = int((inp @ weights['y1_nand.weight'].T + weights['y1_nand.bias'] >= 0).item())
+
+    # Layer 2
+    l2_in = torch.tensor([float(a3), float(a2), float(c2), float(c3), float(y1_or), float(y1_nand)])
+    y1 = int((l2_in @ weights['y1.weight'].T + weights['y1.bias'] >= 0).item())
+    y2_or = int((l2_in @ weights['y2_or.weight'].T + weights['y2_or.bias'] >= 0).item())
+    y2_nand = int((l2_in @ weights['y2_nand.weight'].T + weights['y2_nand.bias'] >= 0).item())
+    y3_or = int((l2_in @ weights['y3_or.weight'].T + weights['y3_or.bias'] >= 0).item())
+    y3_nand = int((l2_in @ weights['y3_nand.weight'].T + weights['y3_nand.bias'] >= 0).item())
+
+    # Layer 3
+    l3_y2 = torch.tensor([float(y2_or), float(y2_nand)])
+    l3_y3 = torch.tensor([float(y3_or), float(y3_nand)])
+    y2 = int((l3_y2 @ weights['y2.weight'].T + weights['y2.bias'] >= 0).item())
+    y3 = int((l3_y3 @ weights['y3.weight'].T + weights['y3.bias'] >= 0).item())
+
+    return [y3, y2, y1, y0]
+
+print("Verifying incrementer4bit...")
+errors = 0
+for i in range(16):
+    a3, a2, a1, a0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = incrementer4(a3, a2, a1, a0)
+    expected_val = (i + 1) % 16
+    expected = [(expected_val >> 3) & 1, (expected_val >> 2) & 1, (expected_val >> 1) & 1, expected_val & 1]
+    if result != expected:
+        errors += 1
+        print(f"ERROR: {i} ({a3}{a2}{a1}{a0}) + 1 = {result}, expected {expected} ({expected_val})")
+
+if errors == 0:
+    print("All 16 test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+
+mag = sum(t.abs().sum().item() for t in weights.values())
+print(f"Magnitude: {mag:.0f}")

model.py

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+import torch
+from safetensors.torch import load_file
+
+def load_model(path='model.safetensors'):
+    return load_file(path)
+
+def incrementer4(a3, a2, a1, a0, w):
+    """Add 1 to 4-bit input (mod 16)."""
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+
+    # Layer 1
+    y0 = int((inp @ w['y0.weight'].T + w['y0.bias'] >= 0).item())
+    c2 = int((inp @ w['c2.weight'].T + w['c2.bias'] >= 0).item())
+    c3 = int((inp @ w['c3.weight'].T + w['c3.bias'] >= 0).item())
+    y1_or = int((inp @ w['y1_or.weight'].T + w['y1_or.bias'] >= 0).item())
+    y1_nand = int((inp @ w['y1_nand.weight'].T + w['y1_nand.bias'] >= 0).item())
+
+    # Layer 2
+    l2_in = torch.tensor([float(a3), float(a2), float(c2), float(c3), float(y1_or), float(y1_nand)])
+    y1 = int((l2_in @ w['y1.weight'].T + w['y1.bias'] >= 0).item())
+    y2_or = int((l2_in @ w['y2_or.weight'].T + w['y2_or.bias'] >= 0).item())
+    y2_nand = int((l2_in @ w['y2_nand.weight'].T + w['y2_nand.bias'] >= 0).item())
+    y3_or = int((l2_in @ w['y3_or.weight'].T + w['y3_or.bias'] >= 0).item())
+    y3_nand = int((l2_in @ w['y3_nand.weight'].T + w['y3_nand.bias'] >= 0).item())
+
+    # Layer 3
+    y2 = int(y2_or + y2_nand - 2 >= 0)
+    y3 = int(y3_or + y3_nand - 2 >= 0)
+
+    return [y3, y2, y1, y0]
+
+if __name__ == '__main__':
+    w = load_model()
+    print('incrementer4bit:')
+    for i in range(16):
+        a3, a2, a1, a0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+        result = incrementer4(a3, a2, a1, a0, w)
+        out_val = result[0]*8 + result[1]*4 + result[2]*2 + result[3]
+        print(f'  {i:2d} ({a3}{a2}{a1}{a0}) + 1 = {out_val:2d} ({"".join(map(str, result))})')