README.md

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

# threshold-mod7

Computes Hamming weight mod 7 for 8-bit inputs. Multi-layer network with thermometer encoding.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
       ┌─────────────┐
       │ Thermometer │  Layer 1: 9 neurons
       └─────────────┘
               │
               ▼
       ┌─────────────┐
       │  MOD-7      │  Layer 2: 6 neurons
       │  Detection  │  Pattern (1,1,1,1,1,1,-6)
       └─────────────┘
               │
               ▼
       ┌─────────────┐
       │  Classify   │  Output: 7 classes
       └─────────────┘
               │
               ▼
      {0, 1, 2, 3, 4, 5, 6}
```

## Algebraic Insight

Pattern `(1, 1, 1, 1, 1, 1, -6)` cycles mod 7:

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

For 8-bit inputs, only one reset occurs (at HW=7).

## Architecture

| Layer | Neurons | Function |
|-------|---------|----------|
| Input | 8 | Binary bits |
| Hidden 1 | 9 | Thermometer encoding |
| Hidden 2 | 6 | MOD-7 detection |
| Output | 7 | One-hot classification |

**Total: 22 neurons, 190 parameters**

## Usage

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

w = load_file('model.safetensors')

def forward(x):
    x = x.float()
    x = (x @ w['layer1.weight'].T + w['layer1.bias'] >= 0).float()
    x = (x @ w['layer2.weight'].T + w['layer2.bias'] >= 0).float()
    out = x @ w['output.weight'].T + w['output.bias']
    return out.argmax(dim=-1)
```

## Files

```
threshold-mod7/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT