threshold-mux

2:1 multiplexer. Selects between two inputs based on a select signal.

Circuit

    a   b   s
    │   │   │
    │   └───┼───┐
    └───┬───┘   │
        │   ┌───┘
        ▼   ▼
  ┌─────────────┐
  │  a AND ¬s   │   N1: w=[1,0,-1] b=-1
  └─────────────┘
        │
        │   ┌─────────────┐
        │   │  b AND s    │   N2: w=[0,1,1] b=-2
        │   └─────────────┘
        │         │
        └────┬────┘
             ▼
        ┌─────────┐
        │   OR    │   w=[1,1] b=-1
        └─────────┘
             │
             ▼
           output

Function

MUX(a, b, s) = a if s=0, b if s=1

Equivalent to: OR(AND(a, NOT(s)), AND(b, s))

Truth Table

a	b	s	out
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	1
1	0	1	0
1	1	0	1
1	1	1	1

Architecture

Layer	Neurons	Weights	Bias
1	N1 (a AND ¬s)	[1, 0, -1]	-1
1	N2 (b AND s)	[0, 1, 1]	-2
2	OR	[1, 1]	-1

Total: 3 neurons, 11 parameters, 2 layers

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def mux(a, b, s):
    inp = torch.tensor([float(a), float(b), float(s)])
    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(mux(1, 0, 0))  # 1 (selects a)
print(mux(1, 0, 1))  # 0 (selects b)

Files

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

License

MIT