Deep-Learning-with-PyTorch

Convolutions in action
205
The receptive field of output pixels
When the second 3 × 3 convolution kernel produces 21 in its conv output in figure
8.8, this is based on the top-left 3 × 3 pixels of the first max pool output. They, in turn,
correspond to the 6 × 6 pixels in the top-left corner in the first conv output, which in
turn are computed by the first convolution from the top-left 7 × 7 pixels. So the pixel
in the second convolution output is influenced by a 7 × 7 input square. The first
convolution also uses an implicitly “padded” column and row to produce the output in
the corner; otherwise, we would have an 8 × 8 square of input pixels informing a given
pixel (away from the boundary) in the second convolution’s output. In fancy language,
we say that a given output neuron of the 3 × 3-conv, 2 × 2-max-pool, 3 × 3-conv
construction has a receptive field of 8 × 8.
8.2.4 Putting it all together for our network
With these building blocks in our hands, we can now proceed to build our convolutional
neural network for detecting birds and airplanes. Let’s take our previous fully
connected model as a starting point and introduce nn.Conv2d and nn.MaxPool2d as
described previously:
# In[22]:
model = nn.Sequential(
nn.Conv2d(3, 16, kernel_size=3, padding=1),
nn.Tanh(),
nn.MaxPool2d(2),
nn.Conv2d(16, 8, kernel_size=3, padding=1),
nn.Tanh(),
nn.MaxPool2d(2),
# ...
)
The first convolution takes us from 3 RGB channels to 16, thereby giving the network
a chance to generate 16 independent features that operate to (hopefully) discriminate
low-level features of birds and airplanes. Then we apply the Tanh activation function.
The resulting 16-channel 32 × 32 image is pooled to a 16-channel 16 × 16 image
by the first MaxPool3d. At this point, the downsampled image undergoes another convolution
that generates an 8-channel 16 × 16 output. With any luck, this output will
consist of higher-level features. Again, we apply a Tanh activation and then pool to an
8-channel 8 × 8 output.
Where does this end? After the input image has been reduced to a set of 8 × 8 features,
we expect to be able to output some probabilities from the network that we can
feed to our negative log likelihood. However, probabilities are a pair of numbers in a
1D vector (one for airplane, one for bird), but here we’re still dealing with multichannel
2D features.