README.md

---
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