Deep-Learning-with-PyTorch

Convolutions in action
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solve our birds versus airplanes problem effectively, since although CIFAR-10 images
are small, the objects still have a (wing-)span several pixels across.
One possibility could be to use large convolution kernels. Well, sure, at the limit we
could get a 32 × 32 kernel for a 32 × 32 image, but we would converge to the old fully
connected, affine transformation and lose all the nice properties of convolution.
Another option, which is used in convolutional neural networks, is stacking one convolution
after the other and at the same time downsampling the image between successive
convolutions.
FROM LARGE TO SMALL: DOWNSAMPLING
Downsampling could in principle occur in different ways. Scaling an image by half is
the equivalent of taking four neighboring pixels as input and producing one pixel as
output. How we compute the value of the output based on the values of the input is
up to us. We could
• Average the four pixels. This average pooling was a common approach early on but
has fallen out of favor somewhat.
• Take the maximum of the four pixels. This approach, called max pooling, is currently
the most commonly used approach, but it has a downside of discarding the
other three-quarters of the data.
• Perform a strided convolution, where only every Nth pixel is calculated. A 3 × 4 convolution
with stride 2 still incorporates input from all pixels from the previous layer.
The literature shows promise for this approach, but it has not yet supplanted
max pooling.
We will be focusing on max pooling, illustrated in figure 8.7, going forward. The figure
shows the most common setup of taking non-overlapping 2 x 2 tiles and taking the
maximum over each of them as the new pixel at the reduced scale.
Intuitively, the output images from a convolution layer, especially since they are followed
by an activation just like any other linear layer, tend to have a high magnitude
INput
(output of conv + activation)
2 2 2 0
2 5 2 1
2 2 2 0
0 1 0 0
maxpOol
2 2
2 5
max=5
max=2
output
5 2
2 2
2 2 2
0 1
0
2 0
2 1
max=2
max=2
0
0
Figure 8.7
Max pooling in detail