title: why do we have multiple layers and multiple nodes per layer in a neural network?
body: <p>I just started to learn about neural networks and so far my knowledge of machine learning is simply linear and logistic regression. from my understanding of the latter algorithms, is that given multiples of inputs the job of the learning algorithm is to come up with appropriate weights for each input so that eventually I have a polynomial that either describes the data which is the case of linear regression or separates it as in the case of logistic regression. 
  if I was to represent the same mechanism in neural network, according to my understanding, it would look something like this,
  <a href="https://i.stack.imgur.com/x8EaK.png" rel="noreferrer"><img src="https://i.stack.imgur.com/x8EaK.png" alt="enter image description here"></a>
  multiple nodes at the input layer and a single node in the output layer. where I can back propagate the error proportionally to each input. so that also eventually I arrive to a polynomial X1W1 + X2W2+....XnWn that describes the data.  to me having multiple nodes per layer, aside from the input layer, seems to make the learning process parallel, so that I can arrive to the result faster. it's almost like running multiple learning algorithms each with different starting points to see which one converges faster. and as for the multiple layers I'm at a lose of what mechanism and advantage does it have on the learning outcome. </p>