metadata
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- canalizing
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
β β β
β β ββββββββ
β β β
ββββββ΄ββββ β
β β
βΌ βΌ
βββββββ βββββββ
β OR β β NOT β Layer 1
βx1,x2β β x0 β
βββββββ βββββββ
β β
βββββ¬ββββ
β
βΌ
βββββββ
β AND β Layer 2
βββββββ
β
βΌ
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