title: How a Convolutional Neural Net handles channels
body: <p>I've looked through a lot of explanations of the way a CNN conventionally handles multiple channels (such as 3 in an RGB image) and am still at a loss. </p>
  
  <p>When a 5x5x3 filter (say) is applied to a patch of an RGB image what <em>exactly</em> happens? Is it in fact 3 different 2D convolutions (with independent weights) that happen separately to each channel? And then the results get simply added together to produce the final output to pass to the next layer? Or is it a truly 3D convolution?</p>