README.md

---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- parity
- error-detection
---

# threshold-parity7

7-bit parity function. Outputs 1 if an odd number of inputs are high. Essential for error detection in 7-bit data words.

## Circuit

```
x0  x1    x2  x3    x4  x5    x6
 │   │     │   │     │   │     │
 └─┬─┘     └─┬─┘     └─┬─┘     │
   │         │         │       │
   ▼         ▼         ▼       │
┌─────┐   ┌─────┐   ┌─────┐    │
│XOR01│   │XOR23│   │XOR45│    │   Level 1
└─────┘   └─────┘   └─────┘    │
   │         │         │       │
   └────┬────┘         └───┬───┘
        │                  │
        ▼                  ▼
    ┌───────┐          ┌───────┐
    │XOR0123│          │XOR456 │    Level 2
    └───────┘          └───────┘
        │                  │
        └────────┬─────────┘
                 │
                 ▼
            ┌─────────┐
            │XOR_final│              Level 3
            └─────────┘
                 │
                 ▼
              parity
```

## Function

```
parity7(x0..x6) = x0 XOR x1 XOR x2 XOR x3 XOR x4 XOR x5 XOR x6
```

Returns 1 when the Hamming weight is odd (1, 3, 5, or 7).

## Truth Table (by Hamming Weight)

| HW | Example Input | Parity |
|:--:|---------------|:------:|
| 0 | 0000000 | 0 |
| 1 | 0000001 | 1 |
| 2 | 0000011 | 0 |
| 3 | 0000111 | 1 |
| 4 | 0001111 | 0 |
| 5 | 0011111 | 1 |
| 6 | 0111111 | 0 |
| 7 | 1111111 | 1 |

## Mechanism

**XOR Implementation (3 neurons per gate):**

Each XOR is built from OR, NAND, and AND gates:
```
XOR(a, b) = AND(OR(a,b), NAND(a,b))
```

| Gate | Weights | Bias | Fires when |
|------|---------|------|------------|
| OR | [1, 1] | -1 | a + b >= 1 |
| NAND | [-1, -1] | +1 | a + b <= 1 |
| AND | [1, 1] | -2 | both inputs = 1 |

**Tree Structure (6 XOR gates):**

| Level | Gates | Computes |
|-------|-------|----------|
| 1 | XOR01, XOR23, XOR45 | Pairs of inputs |
| 2 | XOR0123, XOR456 | XOR(XOR01,XOR23), XOR(XOR45,x6) |
| 3 | XOR_final | XOR(XOR0123, XOR456) |

## Architecture

| Component | Function | Neurons |
|-----------|----------|---------|
| xor_01 | x0 XOR x1 | 3 |
| xor_23 | x2 XOR x3 | 3 |
| xor_45 | x4 XOR x5 | 3 |
| xor_0123 | xor01 XOR xor23 | 3 |
| xor_456 | xor45 XOR x6 | 3 |
| xor_final | xor0123 XOR xor456 | 3 |

**Total: 18 neurons, 6 XOR gates**

## Parameters

| | |
|---|---|
| Inputs | 7 |
| Outputs | 1 |
| Neurons | 18 |
| Layers | 6 |
| Parameters | 54 |
| Magnitude | 60 |

## Usage

```python
from safetensors.torch import load_file
import torch

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 parity7(x0, x1, x2, x3, x4, x5, x6):
    xor01 = xor2(x0, x1, 'xor_01')
    xor23 = xor2(x2, x3, 'xor_23')
    xor45 = xor2(x4, x5, 'xor_45')
    xor0123 = xor2(xor01, xor23, 'xor_0123')
    xor456 = xor2(xor45, x6, 'xor_456')
    return xor2(xor0123, xor456, 'xor_final')

# Examples
print(parity7(1, 0, 1, 0, 1, 0, 0))  # 1 (odd: 3 ones)
print(parity7(1, 1, 1, 1, 1, 1, 1))  # 1 (odd: 7 ones)
print(parity7(1, 1, 0, 0, 0, 0, 0))  # 0 (even: 2 ones)
```

## Applications

- Hamming(7,4) code parity bit
- 7-bit ASCII parity checking
- Memory word error detection
- Bus parity generation

## Files

```
threshold-parity7/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md
```

## License

MIT