threshold-weighted

Weighted threshold function demonstrating non-uniform input weights.

Function

y = 1 iff 4·x3 + 3·x2 + 2·x1 + 1·x0 >= 6

Each input has a different "voting power":

• x3: weight 4 (most influential)
• x2: weight 3
• x1: weight 2
• x0: weight 1 (least influential)

Maximum weighted sum = 10, threshold = 6 (weighted majority).

Truth Table (selected rows)

x3	x2	x1	x0	w_sum	y
0	0	0	0	0	0
0	1	1	1	6	1
1	0	0	0	4	0
1	0	1	0	6	1
1	1	0	0	7	1
1	1	1	1	10	1

Note: x3 alone (weight 4) isn't enough, but x3 + x1 (weight 6) passes.

Architecture

Single threshold neuron:

x3 ──(×4)──┐
x2 ──(×3)──┼──► Σ ──► (≥6?) ──► y
x1 ──(×2)──┤
x0 ──(×1)──┘

Parameters

Inputs	4
Outputs	1
Neurons	1
Layers	1
Parameters	5
Magnitude	16

Theory

This is the fundamental building block of threshold logic. Any linearly separable Boolean function can be computed by a single weighted threshold neuron. Non-linearly-separable functions (like XOR) require multiple layers.

The general form: y = 1 iff Σ(wi·xi) >= θ

Applications

• Weighted voting systems
• Credit scoring
• Risk assessment
• Neural network layers

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def weighted(x3, x2, x1, x0):
    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
    return int((inp @ w['y.weight'].T + w['y.bias'] >= 0).item())

# weighted(1, 0, 1, 0) = 1  # 4+2=6 >= 6
# weighted(1, 0, 0, 1) = 0  # 4+1=5 < 6

License

MIT