3-bit parity threshold circuit, magnitude 20

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-parity3
+
+3-bit parity function. Outputs 1 if odd number of inputs are high.
+
+## Function
+
+parity3(a, b, c) = a XOR b XOR c
+
+## Truth Table
+
+| a | b | c | out |
+|---|---|---|-----|
+| 0 | 0 | 0 | 0 |
+| 0 | 0 | 1 | 1 |
+| 0 | 1 | 0 | 1 |
+| 0 | 1 | 1 | 0 |
+| 1 | 0 | 0 | 1 |
+| 1 | 0 | 1 | 0 |
+| 1 | 1 | 0 | 0 |
+| 1 | 1 | 1 | 1 |
+
+## Architecture
+
+Cascade of two XOR2 gates: parity(a,b,c) = XOR(XOR(a,b), c)
+
+Each XOR2 uses OR-NAND-AND structure:
+- OR: fires if either input is 1
+- NAND: fires if not both inputs are 1
+- AND: fires if both OR and NAND fire (XOR condition)
+
+**Layers:**
+1. xor1.or, xor1.nand (on inputs a, b)
+2. xor1.and (combines layer 1)
+3. xor2.or, xor2.nand (on xor1 output and c)
+4. xor2.and (final output)
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 3 |
+| Outputs | 1 |
+| Neurons | 6 |
+| Layers | 4 |
+| Parameters | 18 |
+| Magnitude | 20 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+
+w = load_file('model.safetensors')
+
+def xor2(a, b, prefix):
+    or_out = int(a * w[f'{prefix}.or.weight'][0] + b * w[f'{prefix}.or.weight'][1] + w[f'{prefix}.or.bias'] >= 0)
+    nand_out = int(a * w[f'{prefix}.nand.weight'][0] + b * w[f'{prefix}.nand.weight'][1] + w[f'{prefix}.nand.bias'] >= 0)
+    return int(or_out * w[f'{prefix}.and.weight'][0] + nand_out * w[f'{prefix}.and.weight'][1] + w[f'{prefix}.and.bias'] >= 0)
+
+def parity3(a, b, c):
+    return xor2(xor2(a, b, 'xor1'), c, 'xor2')
+
+print(parity3(1, 0, 1))  # 0 (even parity)
+print(parity3(1, 1, 1))  # 1 (odd parity)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-parity3",
+  "description": "3-bit parity (XOR of 3 inputs)",
+  "inputs": 3,
+  "outputs": 1,
+  "neurons": 6,
+  "layers": 4,
+  "parameters": 18
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+# Cascade of two XOR2 gates: parity(a,b,c) = XOR(XOR(a,b), c)
+# Each XOR uses OR-NAND-AND structure
+
+def xor_block(prefix):
+    return {
+        f'{prefix}.or.weight': torch.tensor([1.0, 1.0], dtype=torch.float32),
+        f'{prefix}.or.bias': torch.tensor([-1.0], dtype=torch.float32),
+        f'{prefix}.nand.weight': torch.tensor([-1.0, -1.0], dtype=torch.float32),
+        f'{prefix}.nand.bias': torch.tensor([1.0], dtype=torch.float32),
+        f'{prefix}.and.weight': torch.tensor([1.0, 1.0], dtype=torch.float32),
+        f'{prefix}.and.bias': torch.tensor([-2.0], dtype=torch.float32),
+    }
+
+weights = {}
+weights.update(xor_block('xor1'))
+weights.update(xor_block('xor2'))
+
+save_file(weights, 'model.safetensors')
+
+def xor2(a, b, prefix):
+    or_out = int(a * weights[f'{prefix}.or.weight'][0] + b * weights[f'{prefix}.or.weight'][1] + weights[f'{prefix}.or.bias'] >= 0)
+    nand_out = int(a * weights[f'{prefix}.nand.weight'][0] + b * weights[f'{prefix}.nand.weight'][1] + weights[f'{prefix}.nand.bias'] >= 0)
+    and_out = int(or_out * weights[f'{prefix}.and.weight'][0] + nand_out * weights[f'{prefix}.and.weight'][1] + weights[f'{prefix}.and.bias'] >= 0)
+    return and_out
+
+def parity3(a, b, c):
+    xor_ab = xor2(a, b, 'xor1')
+    return xor2(xor_ab, c, 'xor2')
+
+print("Verifying parity3...")
+errors = 0
+for i in range(8):
+    a, b, c = (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = parity3(a, b, c)
+    expected = a ^ b ^ c
+    if result != expected:
+        errors += 1
+        print(f"ERROR: parity({a},{b},{c}) = {result}, expected {expected}")
+if errors == 0:
+    print("All 8 test cases passed!")
+print(f"Magnitude: {sum(t.abs().sum().item() for t in weights.values()):.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 xor2(a, b, prefix, w):
+    or_out = int(a * w[f'{prefix}.or.weight'][0] + b * w[f'{prefix}.or.weight'][1] + w[f'{prefix}.or.bias'] >= 0)
+    nand_out = int(a * w[f'{prefix}.nand.weight'][0] + b * w[f'{prefix}.nand.weight'][1] + w[f'{prefix}.nand.bias'] >= 0)
+    and_out = int(or_out * w[f'{prefix}.and.weight'][0] + nand_out * w[f'{prefix}.and.weight'][1] + w[f'{prefix}.and.bias'] >= 0)
+    return and_out
+
+def parity3(a, b, c, weights):
+    xor_ab = xor2(a, b, 'xor1', weights)
+    return xor2(xor_ab, c, 'xor2', weights)
+
+if __name__ == '__main__':
+    w = load_model()
+    print('parity3 truth table:')
+    for i in range(8):
+        a, b, c = (i >> 2) & 1, (i >> 1) & 1, i & 1
+        print(f'  parity({a},{b},{c}) = {parity3(a, b, c, w)}')