## Example

## What is the bias

A perceptron can be seen as a function that maps an input (real-valued) vector *x* to an output value *f(x)* (binary value):

where *w* is a vector of real-valued weights and *b* is a our *bias* value.
The bias is a value that shifts the decision boundary away from the origin *(0,0)* and that does not depend on any input value.

Thinking at the bias in a spatial way, the bias alters the position (though not the orientation) of the decision boundary.
We can see below an example of the same curve shifted by the bias: