threshold-canalizing

Canalizing Boolean function where one input can override all others.

Function

y = NOT(x0) AND (x1 OR x2)

Canalizing property: If x0 = 1, then y = 0 regardless of x1 and x2.

• Canalizing input: x0
• Canalizing value: 1
• Canalized output: 0

When x0 = 0, the function reduces to y = x1 OR x2.

Truth Table

x2	x1	x0	y	Note
0	0	0	0
0	0	1	0	x0 canalizes
0	1	0	1
0	1	1	0	x0 canalizes
1	0	0	1
1	0	1	0	x0 canalizes
1	1	0	1
1	1	1	0	x0 canalizes

Architecture

Not linearly separable; requires 2 layers:

x2   x1   x0
 │    │    │
 │    │    └──────┐
 │    │           │
 └────┴───┐       │
          │       │
          ▼       ▼
       ┌─────┐ ┌─────┐
       │ OR  │ │ NOT │   Layer 1
       │x1,x2│ │ x0  │
       └─────┘ └─────┘
          │       │
          └───┬───┘
              │
              ▼
           ┌─────┐
           │ AND │       Layer 2
           └─────┘
              │
              ▼
              y

Parameters

Inputs	3
Outputs	1
Neurons	3
Layers	2
Parameters	11
Magnitude	8

Biological Significance

Canalizing functions are important in gene regulatory networks. A canalizing gene can suppress or activate a developmental pathway regardless of other genes' states, providing robustness to genetic variation.

Usage

from safetensors.torch import load_file

w = load_file('model.safetensors')

# When x0=1 (canalizing value), output is always 0
# When x0=0, output is x1 OR x2

License

MIT