threshold-or4

A 1-of-4 threshold gate. Any single active input is enough to fire.

Circuit

  x1  x2  x3  x4
   │   │   │   │
   └───┴───┴───┘
         │
         ▼
    ┌─────────┐
    │w: 1,1,1,1│
    │ b: -1   │
    └─────────┘
         │
         ▼
   OR4(x1,x2,x3,x4)

Mechanism

Same weights as AND4, but bias -1 instead of -4. A single vote suffices:

x1	x2	x3	x4	sum	output
0	0	0	0	-1	0
0	0	0	1	0	1
...	...	...	...	...	1
1	1	1	1	3	1

Parameters

Weights	[1, 1, 1, 1]
Bias	-1
Magnitude	5
Total	5 parameters

Optimality

Exhaustive enumeration of all 1,683 weight configurations at magnitudes 0-5 confirms this circuit is at minimum magnitude (5). There is exactly 1 valid configuration at magnitude 5, and no valid configurations exist below it.

Magnitude	Valid Configs
0-4	0
5	1

Properties

• Linearly separable (single neuron suffices)
• De Morgan dual: OR4(x1,x2,x3,x4) = NOT(AND4(NOT(x1), NOT(x2), NOT(x3), NOT(x4)))

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def or4_gate(x1, x2, x3, x4):
    inputs = torch.tensor([float(x1), float(x2), float(x3), float(x4)])
    return int((inputs * w['weight']).sum() + w['bias'] >= 0)

assert or4_gate(0, 0, 0, 0) == 0
assert or4_gate(0, 0, 0, 1) == 1
assert or4_gate(1, 1, 1, 1) == 1

Files

threshold-or4/
├── model.safetensors
├── model.py
├── config.json
├── create_safetensors.py
└── README.md

License

MIT