| 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 | |