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---
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
|