threshold-exactly2outof3

Exactly 2 of 3 inputs high.

Function

exactly2outof3(a, b, c) = 1 if (a + b + c) == 2, else 0

Truth Table

a	b	c	sum	out
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	2	1
1	0	0	1	0
1	0	1	2	1
1	1	0	2	1
1	1	1	3	0

Architecture

Two layers (not linearly separable):

Layer 1:

• N1: weights [1, 1, 1], bias -2 (fires when sum >= 2)
• N2: weights [-1, -1, -1], bias 2 (fires when sum <= 2)

Layer 2:

• AND: weights [1, 1], bias -2 (fires when both N1 and N2 fire)

Parameters

Inputs	3
Outputs	1
Neurons	3
Layers	2
Parameters	11
Magnitude	14

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def exactly2of3(a, b, c):
    inp = torch.tensor([float(a), float(b), float(c)])
    l1 = (inp @ w['layer1.weight'].T + w['layer1.bias'] >= 0).float()
    out = (l1 @ w['layer2.weight'].T + w['layer2.bias'] >= 0).float()
    return int(out.item())

print(exactly2of3(0, 1, 1))  # 1 (sum=2)
print(exactly2of3(1, 1, 1))  # 0 (sum=3)

License

MIT