File size: 2,487 Bytes
1be05b5 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 |
---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- modular-arithmetic
---
# threshold-mod5
Computes Hamming weight mod 5 for 8-bit inputs. Multi-layer network with thermometer encoding.
## Circuit
```
x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
│ │ │ │ │ │ │ │
└──┴──┴──┴──┼──┴──┴──┴──┘
▼
┌─────────────┐
│ Thermometer │ Layer 1: 9 neurons
│ Encoding │
└─────────────┘
│
▼
┌─────────────┐
│ MOD-5 │ Layer 2: 4 neurons
│ Detection │ Pattern (1,1,1,1,-4)
└─────────────┘
│
▼
┌─────────────┐
│ Classify │ Output: 5 classes
└─────────────┘
│
▼
{0, 1, 2, 3, 4}
```
## Algebraic Insight
Pattern `(1, 1, 1, 1, -4)` causes cumulative sums to cycle mod 5:
```
HW=0: sum=0 → 0 mod 5
HW=1: sum=1 → 1 mod 5
HW=2: sum=2 → 2 mod 5
HW=3: sum=3 → 3 mod 5
HW=4: sum=4 → 4 mod 5
HW=5: sum=0 → 0 mod 5 (reset: 1+1+1+1-4=0)
HW=6: sum=1 → 1 mod 5
HW=7: sum=2 → 2 mod 5
HW=8: sum=3 → 3 mod 5
```
## Architecture
| Layer | Neurons | Function |
|-------|---------|----------|
| Input | 8 | Binary bits |
| Hidden 1 | 9 | Thermometer encoding |
| Hidden 2 | 4 | MOD-5 detection |
| Output | 5 | One-hot classification |
**Total: 18 neurons, 146 parameters**
## Output Distribution
| Class | HW values | Count/256 |
|-------|-----------|-----------|
| 0 | 0, 5 | 57 |
| 1 | 1, 6 | 36 |
| 2 | 2, 7 | 36 |
| 3 | 3, 8 | 57 |
| 4 | 4 | 70 |
## 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-mod5/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|