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license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
---
# threshold-not
The minimal threshold circuit. One neuron, one weight, one bias.
## Circuit
```
x
│
▼
┌───────┐
│ w: -1 │
│ b: 0 │
└───────┘
│
▼
NOT(x)
```
## Mechanism
A threshold neuron fires when its weighted input plus bias reaches zero. NOT uses weight -1 and bias 0:
- Input 0: sum = 0, fires (output 1)
- Input 1: sum = -1, silent (output 0)
The negative weight flips the relationship between input magnitude and firing.
## Parameters
| | |
|---|---|
| Weight | -1 |
| Bias | 0 |
| Total | 2 parameters |
## Optimality
Exhaustive enumeration of all 5 weight configurations at magnitudes 0-1 confirms this circuit is **already at minimum magnitude (1)**. There is exactly one valid configuration at magnitude 1, and no valid configurations exist below it.
## Properties
- Involutive: NOT(NOT(x)) = x
- Foundation for NAND, NOR
## Usage
```python
from safetensors.torch import load_file
w = load_file('model.safetensors')
def not_gate(x):
return int(x * w['weight'].item() + w['bias'].item() >= 0)
```
## Files
```
threshold-not/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|