---
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
 │    │    │
 │    │    └──────┐
 │    │           │
 └────┴───┐       │
          │       │
          ▼       ▼
       ┌─────┐ ┌─────┐
       │ 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

```python
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