# How to find multi-layer perceptron weights?

I want to use a multi-layer perceptron to design the following function :

The architecture I want to use is the following one :

What would be $w_i$ weights ? Is there any guide to find them ?

I tried the following, guessing with $\forall i,w_i=1$.

\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline &w_1&w_2&w_3&w_4&w_5&w_6&w_7&y\\ &1&1&1&1&1&1&1&=\\ \hline -1&-1&-1&1&1&0&0&1&1\\ -2&-2&-2&1&1&1&1&1&0\\ -3&-3&-3&1&1&-2&-2&1&-1?\\ \hline \end{array}

As it is it seems everything goes well from there but that was only a guess ...

Why in the plotted function do I have $\sum_iw_ix_i$ ? I don't understant the $x_i$. Don't I have only one $x$ as input ?