threshold-or3

3-input OR gate. Fires when at least one input is active. The 1-of-3 threshold gate.

Circuit

    a   b   c
    │   │   │
    └───┼───┘
        │
        ▼
   ┌─────────┐
   │ w: 1,1,1│
   │ b:  -1  │
   └─────────┘
        │
        ▼
   OR(a,b,c)

The Existence Test

3-input OR detects "at least one active":

Inputs	Sum	Output
000	-1	0
001	0	1
010	0	1
011	+1	1
100	0	1
101	+1	1
110	+1	1
111	+2	1

Only complete silence fails.

Same Weights, Different Threshold

AND and OR use identical weights but different biases:

Gate	Weights	Bias	Meaning
OR(a,b,c)	[1, 1, 1]	-1	Need 1+ vote
MAJ(a,b,c)	[1, 1, 1]	-2	Need 2+ votes
AND(a,b,c)	[1, 1, 1]	-3	Need 3 votes

The bias is the threshold. OR is the most permissive.

De Morgan Dual

OR(a,b,c) = NOT(AND(NOT(a), NOT(b), NOT(c)))

But threshold logic computes OR directly - no inversion needed.

Parameters

Component	Value
Weights	[1, 1, 1]
Bias	-1
Total	4 parameters

Optimality

Exhaustive enumeration of all 321 weight configurations at magnitudes 0-4 confirms this circuit is already at minimum magnitude (4). There is exactly one valid configuration at magnitude 4, and no valid configurations exist below it.

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def or3(a, b, c):
    inp = torch.tensor([float(a), float(b), float(c)])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

print(or3(0, 0, 1))  # 1
print(or3(0, 0, 0))  # 0

Files

threshold-or3/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT