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I was given a target function to design neural network and train: (y = (x1 ∧ x2) ∨ (x3 ∧ x4))

The number of input and number of output seems obvious (4 and 1). And the training data can use truth table.

However, in order to train as a multilayer artificial neural network, I need to choose number of hidden units. May I know where can I find some general guideline for this?

Thank you!

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You problem is linearly separable so you can use a single layer perceptron. Hidden units are necessary only for non linear problems (xor is a classic example).

As for general guidelines, I don't think anyone has ever needed more than one hidden layer. Also the number of neurons in the hidden layer doesn't need to exceed the number of inputs.

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  • $\begingroup$ On StackExchange, such short answers are usually (with rare exceptions) preferred in a form of a comment. Posting answer implies a more detailed/comprehensive treatment of a topic. Just FYI. $\endgroup$ – Aleksandr Blekh Mar 5 '15 at 3:06
  • $\begingroup$ @Alex S Kinman multi hidden layer is common in deep learning architecture. $\endgroup$ – Xin Mar 5 '15 at 13:40
  • $\begingroup$ @Aleksandr Blekh what if a question doesn't need a long answer at all? do you have a reference where your comment based on, meta, faq etc? thx $\endgroup$ – Xin Mar 5 '15 at 13:43
  • $\begingroup$ @Xin , I don't know enough about deep neural networks. But for traditional neural networks, the universal function approximation theorem states that a multilayer network with a single hidden layer can approximate any continuous decision function. I am curious, are there any results proving that DNN have more representational power than regular ANN? $\endgroup$ – Alex S Kinman Mar 5 '15 at 14:03
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    $\begingroup$ @AlexSKinman I deleted my previous comment because the 3-D case I gave was a bad example (that one is indeed linearly separable). I tried training a 4x1 network on the y = (x1 ∧ x2) ∨ (x3 ∧ x4) problem numerous times and could not get it to learn the function (the best it would do was accuracy of 0.9375 (i.e., one input was always misclassified). Using a 4x2x1 network, the function was easily learned. If you believe you can construct a separating hyperplane, perhaps you could provide its coefficients (i.e., the a coefficients for f(x) = a1*x1 + a2*x2 + a3*x3 + a4*x4 - a0). $\endgroup$ – bogatron Mar 6 '15 at 6:05

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