threshold-exactly2outof4

Exactly 2 of 4 inputs high.

Function

exactly2outof4(a, b, c, d) = 1 if (a + b + c + d) == 2, else 0

Truth Table

a	b	c	d	sum	out
0	0	0	0	0	0
0	0	0	1	1	0
0	0	1	1	2	1
0	1	0	1	2	1
1	0	0	1	2	1
0	1	1	0	2	1
1	0	1	0	2	1
1	1	0	0	2	1
0	1	1	1	3	0
1	1	1	1	4	0

Architecture

Layer 1:
  N1: [1,1,1,1] b=-2  (fires when sum >= 2)
  N2: [-1,-1,-1,-1] b=2  (fires when sum <= 2)

Layer 2:
  AND: [1,1] b=-2  (fires when both N1 and N2 fire)

Parameters

Inputs	4
Outputs	1
Neurons	3
Layers	2
Parameters	13
Magnitude	16

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def exactly2of4(a, b, c, d):
    inp = torch.tensor([float(a), float(b), float(c), float(d)])
    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(exactly2of4(0, 0, 1, 1))  # 1
print(exactly2of4(0, 1, 1, 1))  # 0

License

MIT