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