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

# threshold-mod9

Trivial case: computes Hamming weight mod 9 for 8-bit inputs. Since max HW is 8 < 9, this is just HW.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   │  │  │  │  │  │  │  │
   w: 1  1  1  1  1  1  1  1
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ b:  0   │
          └─────────┘
               │
               ▼
        HW (= HW mod 9)
```

## Why Trivial?

For mod m where m > (number of inputs), no reset ever occurs:

- 8 inputs → max HW = 8
- 8 mod 9 = 8 (no wraparound)

The circuit just sums the inputs. It's a degenerate case included for completeness of the MOD-m family.

## Parameters

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

## Usage

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

w = load_file('model.safetensors')

def mod9(bits):  # Actually just HW
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'])
```

## Files

```
threshold-mod9/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT