README.md

---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- modular-arithmetic
---

# threshold-mod6

Computes Hamming weight mod 6 directly on inputs. Single-layer circuit.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   │  │  │  │  │  │  │  │
   w: 1  1  1  1  1 -5  1  1
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ b:  0   │
          └─────────┘
               │
               ▼
           HW mod 6
```

## Algebraic Insight

For 8 inputs and mod 6, position 6 gets weight 1-6 = -5:

- Positions 1-5: weight +1
- Position 6: weight -5 (reset: 1+1+1+1+1-5 = 0)
- Positions 7-8: weight +1

```
HW=0: sum=0 → 0 mod 6
HW=1: sum=1 → 1 mod 6
...
HW=5: sum=5 → 5 mod 6
HW=6: sum=0 → 0 mod 6  (reset)
HW=7: sum=1 → 1 mod 6
HW=8: sum=2 → 2 mod 6
```

## Parameters

| | |
|---|---|
| Weights | [1, 1, 1, 1, 1, -5, 1, 1] |
| Bias | 0 |
| Total | 9 parameters |

## Usage

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

w = load_file('model.safetensors')

def mod6(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'])
```

## Files

```
threshold-mod6/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT