threshold-2outof6

At-least-2-of-6 threshold gate. Fires when 2 or more of the 6 inputs are high.

Function

2outof6(x0, x1, x2, x3, x4, x5) = 1 if (x0 + x1 + x2 + x3 + x4 + x5) >= 2

Truth Table (selected)

Hamming Weight	Output
0	0
1	0
2	1
3	1
4	1
5	1
6	1

Mechanism

Single threshold neuron with uniform weights. The bias of -2 sets the firing threshold:

• Sum = (number of 1s) + (-2)
• Fires when sum >= 0, i.e., when Hamming weight >= 2

k-out-of-6 Family

Circuit	Bias	Fires when
1-out-of-6	-1	HW >= 1
2-out-of-6	-2	HW >= 2
3-out-of-6	-3	HW >= 3 (majority)
4-out-of-6	-4	HW >= 4
5-out-of-6	-5	HW >= 5
6-out-of-6	-6	HW = 6 (AND)

Parameters

Weights	[1, 1, 1, 1, 1, 1]
Bias	-2
Inputs	6
Outputs	1
Neurons	1
Layers	1
Parameters	7
Magnitude	8

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def at_least_2_of_6(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())

print(at_least_2_of_6([1, 1, 0, 0, 0, 0]))  # 1

License

MIT