threshold-demux

1:2 demultiplexer. Routes a data signal to one of two outputs based on a select signal.

Circuit

      d       s
      │       │
      ├───────┤
      │       │
      ▼       ▼
  ┌───────┐ ┌───────┐
  │d AND¬s│ │d AND s│
  │w=[1,-1]│ │w=[1,1]│
  │b=-1   │ │b=-2   │
  └───────┘ └───────┘
      │         │
      ▼         ▼
     y0        y1

Function

• y0 = d when s=0, else 0
• y1 = d when s=1, else 0

The select signal routes the data to exactly one output.

Truth Table

d	s	y0	y1
0	0	0	0
0	1	0	0
1	0	1	0
1	1	0	1

Architecture

Output	Function	Weights	Bias
y0	d AND NOT(s)	[1, -1]	-1
y1	d AND s	[1, 1]	-2

Total: 2 neurons, 6 parameters, 1 layer

Single-layer circuit - both outputs are linearly separable.

Optimality

Exhaustive enumeration of all 19,825 weight configurations at magnitudes 0-7 confirms this circuit is already at minimum magnitude (7). There is exactly one valid configuration at magnitude 7, and no valid configurations exist below it.

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def demux(d, s):
    inp = torch.tensor([float(d), float(s)])
    y0 = int((inp @ w['y0.weight'].T + w['y0.bias'] >= 0).item())
    y1 = int((inp @ w['y1.weight'].T + w['y1.bias'] >= 0).item())
    return y0, y1

print(demux(1, 0))  # (1, 0) - routes to y0
print(demux(1, 1))  # (0, 1) - routes to y1

Files

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

License

MIT