README.md

---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- comparison
---

# threshold-comparator8bit

8-bit magnitude comparator. Compares two 8-bit unsigned values.

## Function

compare8(A, B) -> (GT, LT, EQ)

- GT = 1 if A > B
- LT = 1 if A < B
- EQ = 1 if A = B

Exactly one output is always active.

## Architecture

```
A[7:0]          B[7:0]
   │               │
   └───────┬───────┘
           │
    ┌──────┴──────┐
    │             │
    ▼             ▼
  ┌───┐         ┌───┐
  │GT │         │LT │   Layer 1
  │A-B│         │B-A│
  │>=1│         │>=1│
  └───┘         └───┘
    │             │
    └──────┬──────┘
           │
           ▼
        ┌─────┐
        │ EQ  │         Layer 2
        │ NOR │
        └─────┘
```

Uses positional weighting: treats inputs as binary numbers.

**GT neuron:** weights A bits positively (128,64,32,16,8,4,2,1), B bits negatively.
Fires when weighted sum A - B >= 1.

**LT neuron:** opposite weights. Fires when B - A >= 1.

**EQ neuron:** NOR of GT and LT. Fires when both are zero.

## Parameters

| | |
|---|---|
| Inputs | 16 |
| Outputs | 3 |
| Neurons | 3 |
| Layers | 2 |
| Parameters | 37 |
| Magnitude | 1024 |

## Truth Table (examples)

| A | B | GT | LT | EQ |
|-----|-----|----|----|---|
| 0 | 0 | 0 | 0 | 1 |
| 100 | 50 | 1 | 0 | 0 |
| 50 | 100 | 0 | 1 | 0 |
| 255 | 255 | 0 | 0 | 1 |

## Usage

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

w = load_file('model.safetensors')

def compare(a, b):
    a_bits = [(a >> (7-i)) & 1 for i in range(8)]
    b_bits = [(b >> (7-i)) & 1 for i in range(8)]
    inp = torch.tensor([float(x) for x in a_bits + b_bits])
    gt = int((inp @ w['gt.weight'].T + w['gt.bias'] >= 0).item())
    lt = int((inp @ w['lt.weight'].T + w['lt.bias'] >= 0).item())
    eq = int((torch.tensor([float(gt), float(lt)]) @ w['eq.weight'].T + w['eq.bias'] >= 0).item())
    return gt, lt, eq

# compare(200, 100) = (1, 0, 0)  # 200 > 100
```

## License

MIT