# Interactive single-layer perceptron

This page visualizes a single-layer perceptron with two inputs $x$ and $y$ and one output $z$:

\[ z = f(w_x x + w_y y + b) \]

Here:

- $w_x$ and $w_y$ denote two weights for the inputs $x$ and $y$, respectively;
- $b$ is a bias term;
- $f$ presents an activation function (e.g., sigmoid, tanh, ReLU functions);

In this visualization, one can see outputs from the perceptron as a *heat map* as they *interactively change* the parameters in the perceptron, more concretely, values of $w_x, w_y, b$ and an activation function $f$. The heatmap represents two inputs $x$ and $y$ as $x$-axis and $y$-axis, respectively, and an output as color thickness of the plotting area.

Supposing $0$ as false and $1$ as true, the perceptron can realize logic units (aka. *threshold logic units*) such as AND, OR, and NAND. Let’s confirm that changing the parameters of the perceptron realizes these logic units. In addition, experience the reason why a single-layer perceptron cannot realize XOR.

$x$ | $y$ | AND | OR | NAND | XOR |
---|---|---|---|---|---|

0 | 0 | 0 | 0 | 1 | 0 |

0 | 1 | 0 | 1 | 1 | 1 |

1 | 0 | 0 | 1 | 1 | 1 |

1 | 1 | 1 | 1 | 0 | 0 |