title: About max-pooling?
body: <p>Max-pooling is useful in vision for two reasons:</p>
  
  <blockquote>
    <p>By eliminating non-maximal values, it reduces computation for upper
    layers.</p>
    
    <p>It provides a form of translation invariance. Imagine cascading a
    max-pooling layer with a convolutional layer. There are 8 directions
    in which one can translate the input image by a single pixel. If
    max-pooling is done over a 2x2 region, 3 out of these 8 possible
    configurations will produce exactly the same output at the
    convolutional layer. For max-pooling over a 3x3 window, this jumps to
    5/8.</p>
    
    <p>Since it provides additional robustness to position, max-pooling is a
    “smart” way of reducing the dimensionality of intermediate
    representations.</p>
  </blockquote>
  
  <p>I can't understand, what does <code>8 directions</code> mean? And what does </p>
  
  <blockquote>
    <p>"If max-pooling is done over a 2x2 region, 3 out of these 8 possible
    configurations will produce exactly the same output at the
    convolutional layer. For max-pooling over a 3x3 window, this jumps to
    5/8."</p>
  </blockquote>
  
  <p>mean?</p>