phanerozoic / threshold-not

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

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

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