---
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