# The multilayer perceptron

An MLP (multilayer perceptron) is a network of connected units.

The analogy comes from the way neurons pass signals. A neuron's dendrites receive signals from several other neurons. Its axon carries the outgoing signal on to the next neurons, releasing neurotransmitters at the connections.

In an MLP, a unit takes inputs from several units in the previous layer, applies a function $f(x)$ and passes its output to the next layer.

Here is a simplified example:

$a_{1}^{2} =g(\theta_{10}^{1}x_{0}+\theta_{11}^{1}x_{1}+\theta_{12}^{1}x_{2}+\theta_{13}^{1}x_{3})$

$a_{2}^{2} =g(\theta_{20}^{1}x_{0}+\theta_{21}^{1}x_{1}+\theta_{22}^{1}x_{2}+\theta_{23}^{1}x_{3})$

$a_{3}^{2} =g(\theta_{30}^{1}x_{0}+\theta_{31}^{1}x_{1}+\theta_{32}^{1}x_{2}+\theta_{33}^{1}x_{3})$

$y=g(\theta_{10}^2a_0^2+\theta_{11}^2a_1^2+\theta_{12}^2a_2^2+\theta_{13}^2a_3^2)$

In the diagram, $x_i$ denotes an input, $a_i^2$ a hidden-layer activation, $y$ the output and $\theta^j$ the weights.

The three hidden units and one output unit together make up this MLP.

In practice, the output layer can have more than one output.