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phanerozoic/
threshold-not

Name: threshold-not
Rating: 2.5 (8 reviews)

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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

phanerozoic/threshold-not