README.md

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

# threshold-mod8

Computes Hamming weight mod 8 directly on inputs. Single-layer circuit.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   │  │  │  │  │  │  │  │
   w: 1  1  1  1  1  1  1 -7
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ b:  0   │
          └─────────┘
               │
               ▼
           HW mod 8
```

## Algebraic Insight

Position 8 gets weight 1-8 = -7:

- Positions 1-7: weight +1
- Position 8: weight -7

```
HW=0: sum=0 → 0 mod 8
...
HW=7: sum=7 → 7 mod 8
HW=8: sum=0 → 0 mod 8  (reset: 1+1+1+1+1+1+1-7=0)
```

The only non-trivial case is HW=8, which resets to 0.

## Parameters

| | |
|---|---|
| Weights | [1, 1, 1, 1, 1, 1, 1, -7] |
| Bias | 0 |
| Total | 9 parameters |

## Usage

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

w = load_file('model.safetensors')

def mod8(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'])
```

## Files

```
threshold-mod8/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT