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

enter image description here

The architecture I want to use is the following one :

enter image description here

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 ?

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The whole point of the Perceptron model is to find the optimal set of weights with respect to your data. You initialize them at some small random number, then with each iteration the Perceptron adjusts the weights in search of a better solution.

How to actually get the weights out of the model depends on your implementation. If you are running this model in Python / R, they should be saved in a matrix; have a look at the code.

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  • $\begingroup$ :/ The whole pedagogical point is to find them by hand $\endgroup$ – ThePassenger Dec 20 '17 at 20:49

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