title: Neural network categorization: Do they always have to have one label per training data
body: <p>In all the examples of categorization with neural networks that I have seen, they all have training data that has one category as the predominant category or the label for each input data. </p>
  
  <p>Can you feed training data that has more than one label. Eg: a picture with a "cat" and a "mouse". </p>
  
  <p>I understand (maybe wrong) that if you use softmax for probability/prediction at the output layer, it tends to try and select one (maximize discerning power). I'm guessing this would hurt/prevent learning and predicting multiple labels with input data.</p>
  
  <p>Is there any approach/architecture of NN where there are multiple labels in training data and multiple outputs predictions are made ? or is that already the case and I missed some vital understanding. Please clarify.</p>