title: Multilayer Perceptron replaced with Single Layer Perceptron
body: <p>I got a problem in understending the difference between MLP and SLP. </p>
  
  <p>I know that in the first case the MLP has more than one layer (the hidden layers) and that the neurons got a <strong>non linear</strong> activation function, like the logistic function (needed for the gradient descent). But I have read that:</p>
  
  <blockquote>
    <p>"if all neurons in an MLP had a linear activation function, the MLP
    could be replaced by a single layer of perceptrons, which can only
    solve linearly separable problems"</p>
  </blockquote>
  
  <p>I don't understand why in the specific case of the XOR, which is not linearly separable, the equivalent MLP is a two layer network, that for every neurons got a linear activation function, like the step function. I understand that I need two line for the separation, but in this case I cannot apply the rule of the previous statment (the replacement of the MLP with the SLP).</p>
  
  <p>Mlp for xor: </p>
  
  <p><a href="http://s17.postimg.org/c7hwv0s8f/xor.png" rel="nofollow">http://s17.postimg.org/c7hwv0s8f/xor.png</a></p>
  
  <p>In the linked image the neurons A B and C have a linear activation function (like the step function)</p>
  
  <p>Xor:
  <a href="http://s17.postimg.org/n77pkd81b/xor1.png" rel="nofollow">http://s17.postimg.org/n77pkd81b/xor1.png</a></p>