README.md

---

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