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I am new in neural network and I am trying to figure out how to build a feed-forward neural network to solve a classification problem defined in the following way (X1, X2 being the features and Y the target):

if X1>0 and X2>0 then Y=1

if X1<0 and X2>0 then Y=0

if X1>1 and X2<0 then Y=1

if X1<1 and X2<0 then Y=0

If someone could at least give me a clue

Thanks

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Try simplifying your set of rules to a simpler set of rules (one with fewer rules).

What nodes are you allowed to use? I assume you can use some sort of a threshold node to produce the zeros and ones.

Can you do these problems well with only one feature (positive goes to 1 and negative goes to zero)?

edit

I misread the last rule before thinking it said X1 < 0. It's quite easy to do it in three layers (counting the output layer) as long as you can,

1) construct a node asking if the input is greater than a certain value.

2) construct a node performing "and" on two outputs from the previous layer.

Are these things you can handle? Am I correct in assuming you need to cut out one layer? It's possible but harder to lead you there.

(In the future I suggest adding more information by editing your original question)

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  • $\begingroup$ Thanks for your answer. To have less rules I could say: if x1>1 or (x2>0 and x1>0) then y=1 else y=0 It has to be a two layers feed-forward neural network with threshold (I think by two layers they don't count the input layer). How would you move from 2 to 1 feature? $\endgroup$ Sep 10, 2015 at 8:13
  • $\begingroup$ Edited my answer $\endgroup$ Sep 10, 2015 at 20:46
  • $\begingroup$ You don't have to simplify your rules or use less features (by features I assume you mean inputs into the network?) Just feed it examples where x1 and x2 are randomly generated and calculate the target Y using a straightforward function that doesn't involve a neural network. $\endgroup$
    – Frobot
    Dec 16, 2015 at 5:12
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Ah the old XOR problem. This has been written about at length. See here: https://web.stanford.edu/group/pdplab/pdphandbook/

Ultimately, this can be solved with a fully connected 1 hidden layer network. You need two input nodes to read in your input pattern, a two-node hidden layer, and a single output node. Then train with stochastic gradient descent.

Consider a network with input nodes $i_0$ and $i_1$, hidden nodes $h_0$ and $h_1$ and output node $o$ and a sigmoid activation function.

One solution would have strong positive weights from both input nodes to $h_0$ and weak positive weights from both input nodes to $h_1$. $h_0$ will have a weak negative bias weight and $h_1$ will have a strong negative bias weight. $h_0$ will have a strong positive weight to $o$ and $h_1$ will have a strong negative weight to $o$. Finally, $o$ will have a weak negative bias.

It might help to draw a diagram of this configuration and walk yourself through how the activation would flow for each of the possible 4 input patterns.

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