The following additional libraries are needed to run this notebook. Note that running on Colab is experimental, please report a Github issue if you have any problem.
!pip install d2l==0.17.6
:label:sec_googlenet
In 2014, GoogLeNet
won the ImageNet Challenge, proposing a structure
that combined the strengths of NiN and paradigms of repeated blocks :cite:Szegedy.Liu.Jia.ea.2015
.
One focus of the paper was to address the question
of which sized convolution kernels are best.
After all, previous popular networks employed choices
as small as $1 \times 1$ and as large as $11 \times 11$.
One insight in this paper was that sometimes
it can be advantageous to employ a combination of variously-sized kernels.
In this section, we will introduce GoogLeNet,
presenting a slightly simplified version of the original model:
we
omit a few ad-hoc features that were added to stabilize training
but are unnecessary now with better training algorithms available.
The basic convolutional block in GoogLeNet is called an Inception block, likely named due to a quote from the movie Inception ("We need to go deeper"), which launched a viral meme.
:label:
fig_inception
As depicted in :numref:fig_inception
,
the inception block consists of four parallel paths.
The first three paths use convolutional layers
with window sizes of $1\times 1$, $3\times 3$, and $5\times 5$
to extract information from different spatial sizes.
The middle two paths perform a $1\times 1$ convolution on the input
to reduce the number of channels, reducing the model's complexity.
The fourth path uses a $3\times 3$ maximum pooling layer,
followed by a $1\times 1$ convolutional layer
to change the number of channels.
The four paths all use appropriate padding to give the input and output the same height and width.
Finally, the outputs along each path are concatenated
along the channel dimension and comprise the block's output.
The commonly-tuned hyperparameters of the Inception block
are the number of output channels per layer.
import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l
class Inception(nn.Module):
# `c1`--`c4` are the number of output channels for each path
def __init__(self, in_channels, c1, c2, c3, c4, **kwargs):
super(Inception, self).__init__(**kwargs)
# Path 1 is a single 1 x 1 convolutional layer
self.p1_1 = nn.Conv2d(in_channels, c1, kernel_size=1)
# Path 2 is a 1 x 1 convolutional layer followed by a 3 x 3
# convolutional layer
self.p2_1 = nn.Conv2d(in_channels, c2[0], kernel_size=1)
self.p2_2 = nn.Conv2d(c2[0], c2[1], kernel_size=3, padding=1)
# Path 3 is a 1 x 1 convolutional layer followed by a 5 x 5
# convolutional layer
self.p3_1 = nn.Conv2d(in_channels, c3[0], kernel_size=1)
self.p3_2 = nn.Conv2d(c3[0], c3[1], kernel_size=5, padding=2)
# Path 4 is a 3 x 3 maximum pooling layer followed by a 1 x 1
# convolutional layer
self.p4_1 = nn.MaxPool2d(kernel_size=3, stride=1, padding=1)
self.p4_2 = nn.Conv2d(in_channels, c4, kernel_size=1)
def forward(self, x):
p1 = F.relu(self.p1_1(x))
p2 = F.relu(self.p2_2(F.relu(self.p2_1(x))))
p3 = F.relu(self.p3_2(F.relu(self.p3_1(x))))
p4 = F.relu(self.p4_2(self.p4_1(x)))
# Concatenate the outputs on the channel dimension
return torch.cat((p1, p2, p3, p4), dim=1)
To gain some intuition for why this network works so well, consider the combination of the filters. They explore the image in a variety of filter sizes. This means that details at different extents can be recognized efficiently by filters of different sizes. At the same time, we can allocate different amounts of parameters for different filters.
As shown in :numref:fig_inception_full
, GoogLeNet uses a stack of a total of 9 inception blocks
and global average pooling to generate its estimates.
Maximum pooling between inception blocks reduces the dimensionality.
The first module is similar to AlexNet and LeNet.
The stack of blocks is inherited from VGG
and the global average pooling avoids
a stack of fully-connected layers at the end.
:label:
fig_inception_full
We can now implement GoogLeNet piece by piece. The first module uses a 64-channel $7\times 7$ convolutional layer.
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),
nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
The second module uses two convolutional layers: first, a 64-channel $1\times 1$ convolutional layer, then a $3\times 3$ convolutional layer that triples the number of channels. This corresponds to the second path in the Inception block.
b2 = nn.Sequential(nn.Conv2d(64, 64, kernel_size=1),
nn.ReLU(),
nn.Conv2d(64, 192, kernel_size=3, padding=1),
nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
The third module connects two complete Inception blocks in series. The number of output channels of the first Inception block is $64+128+32+32=256$, and the number-of-output-channel ratio among the four paths is $64:128:32:32=2:4:1:1$. The second and third paths first reduce the number of input channels to $96/192=1/2$ and $16/192=1/12$, respectively, and then connect the second convolutional layer. The number of output channels of the second Inception block is increased to $128+192+96+64=480$, and the number-of-output-channel ratio among the four paths is $128:192:96:64 = 4:6:3:2$. The second and third paths first reduce the number of input channels to $128/256=1/2$ and $32/256=1/8$, respectively.
b3 = nn.Sequential(Inception(192, 64, (96, 128), (16, 32), 32),
Inception(256, 128, (128, 192), (32, 96), 64),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
The fourth module is more complicated. It connects five Inception blocks in series, and they have $192+208+48+64=512$, $160+224+64+64=512$, $128+256+64+64=512$, $112+288+64+64=528$, and $256+320+128+128=832$ output channels, respectively. The number of channels assigned to these paths is similar to that in the third module: the second path with the $3\times 3$ convolutional layer outputs the largest number of channels, followed by the first path with only the $1\times 1$ convolutional layer, the third path with the $5\times 5$ convolutional layer, and the fourth path with the $3\times 3$ maximum pooling layer. The second and third paths will first reduce the number of channels according to the ratio. These ratios are slightly different in different Inception blocks.
b4 = nn.Sequential(Inception(480, 192, (96, 208), (16, 48), 64),
Inception(512, 160, (112, 224), (24, 64), 64),
Inception(512, 128, (128, 256), (24, 64), 64),
Inception(512, 112, (144, 288), (32, 64), 64),
Inception(528, 256, (160, 320), (32, 128), 128),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
The fifth module has two Inception blocks with $256+320+128+128=832$ and $384+384+128+128=1024$ output channels. The number of channels assigned to each path is the same as that in the third and fourth modules, but differs in specific values. It should be noted that the fifth block is followed by the output layer. This block uses the global average pooling layer to change the height and width of each channel to 1, just as in NiN. Finally, we turn the output into a two-dimensional array followed by a fully-connected layer whose number of outputs is the number of label classes.
b5 = nn.Sequential(Inception(832, 256, (160, 320), (32, 128), 128),
Inception(832, 384, (192, 384), (48, 128), 128),
nn.AdaptiveAvgPool2d((1,1)),
nn.Flatten())
net = nn.Sequential(b1, b2, b3, b4, b5, nn.Linear(1024, 10))
The GoogLeNet model is computationally complex, so it is not as easy to modify the number of channels as in VGG. [To have a reasonable training time on Fashion-MNIST, we reduce the input height and width from 224 to 96.] This simplifies the computation. The changes in the shape of the output between the various modules are demonstrated below.
X = torch.rand(size=(1, 1, 96, 96))
for layer in net:
X = layer(X)
print(layer.__class__.__name__,'output shape:\t', X.shape)
Sequential output shape: torch.Size([1, 64, 24, 24]) Sequential output shape: torch.Size([1, 192, 12, 12]) Sequential output shape: torch.Size([1, 480, 6, 6]) Sequential output shape: torch.Size([1, 832, 3, 3]) Sequential output shape: torch.Size([1, 1024]) Linear output shape: torch.Size([1, 10])
As before, we train our model using the Fashion-MNIST dataset. We transform it to $96 \times 96$ pixel resolution before invoking the training procedure.
lr, num_epochs, batch_size = 0.1, 10, 128
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=96)
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
loss 0.248, train acc 0.905, test acc 0.889 3512.5 examples/sec on cuda:0
Ioffe.Szegedy.2015
, as described
later in :numref:sec_batch_norm
.Szegedy.Vanhoucke.Ioffe.ea.2016
.Szegedy.Vanhoucke.Ioffe.ea.2016
.Szegedy.Ioffe.Vanhoucke.ea.2017
, as described later in
:numref:sec_resnet
.