文章目录
9、CNN 卷积神经网络
B站视频教程传送门：
PyTorch深度学习实践 – 卷积神经网络（基础篇） PyTorch深度学习实践 – 卷积神经网络（高级篇）
9.1 Revision
全连接神经网络（Fully Connected Neural Network）：该网络完全由线形层Linear串行连接起来，即每一个输入节点都要参与到下一层任一输出节点的计算上。
class Net(torch.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.l1 = torch.nn.Linear(784, 512)
self.l2 = torch.nn.Linear(512, 256)
self.l3 = torch.nn.Linear(256, 128)
self.l4 = torch.nn.Linear(128, 64)
self.l5 = torch.nn.Linear(64, 10)
def forward(self, x):
x = x.view(-1, 784)
x = F.relu(self.l1(x))
x = F.relu(self.l2(x))
x = F.relu(self.l3(x))
x = F.relu(self.l4(x))
return self.l5(x)
model = Net()
9.2 Introduction
Convolutional Neural Network
注意：
-
1×
28
×
28
<
=
=
>
C
×
W
×
H
1 \times 28 \times 28 <==> C \times W \times H
1
×
28
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28
<==>
C
×
W
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Convolution 卷积：保留图像的空间结构信息
-
Subsampling 下采样（主要是 Max Pooling）：通道数不变，宽高改变，为了减少图像数据量，进一步降低运算的需求
-
Fully Connected 全连接：将张量展开为一维向量，再进行分类
-
我们将 Convolution 及 Subsampling 等称为
特征提取
（Feature Extraction），最后的 Fully Connected 称为
分类
（Classification）。
9.3 Convolution
9.3.1 Channel
-
Single Input Channel：
-
3 Input Channels：
其中，
C H W
变化如下：
-
N Input Channels：
-
N Input Channels and M Output Channels
要想输出
M
通道的图像，卷积核也需设置为
M
个：
9.3.2 Layer
当输入为
n
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n \times width_{in} \times height_{in}
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，如何得到
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m \times width_{out} \times height_{out}
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的输出：
输出的通道数为
m
，所以需要
m
个卷积核，且每个卷积核的尺寸为：
n
×
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n \times kernel_{width} \times kernel_{height}
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，即四维张量：
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\Large m \times n \times kernel_{width} \times kernel_{height}
m
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import torch
in_channels, out_channels = 5, 10
width, height = 100, 100
kernel_size = 3
batch_size = 1
input = torch.randn(batch_size, in_channels, width, height)
conv_layer = torch.nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size)
output = conv_layer(input)
print(input.shape)
print(conv_layer.weight.shape) # m n w h
print(output.shape)
torch.Size([1, 5, 100, 100])
torch.Size([10, 5, 3, 3])
torch.Size([1, 10, 98, 98])
9.3.3 Padding
如果
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input = 5 \times 5
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，
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3
kernel = 3 \times 3
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×
3
，并且希望
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=
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×
5
output = 5 \times 5
o
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tp
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=
5
×
5
，可以采取什么方法？
可以使用参数
padding=1
，先将input填充至
7
×
7
7 \times 7
7
×
7
，这样卷积之后，output仍为
5
×
5
5 \times 5
5
×
5
。
import torch
input = [3, 4, 6, 5, 7,
2, 4, 6, 8, 2,
1, 6, 7, 8, 4,
9, 7, 4, 6, 2,
3, 7, 5, 4, 1]
input = torch.Tensor(input).view(1, 1, 5, 5) # B C W H
conv_layer = torch.nn.Conv2d(in_channels=1, out_channels=1, kernel_size=3, padding=1, bias=False) # O I W H
kernel = torch.Tensor([1, 2, 3, 4, 5, 6, 7, 8, 9]).view(1, 1, 3, 3)
conv_layer.weight.data = kernel.data
output = conv_layer(input)
print(output)
tensor([[[[ 91., 168., 224., 215., 127.],
[114., 211., 295., 262., 149.],
[192., 259., 282., 214., 122.],
[194., 251., 253., 169., 86.],
[ 96., 112., 110., 68., 31.]]]], grad_fn=<ConvolutionBackward0>)
9.3.4 Stride
参数
stride
意为步长，假设
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=
2
stride = 2
s
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=
2
时，kernel在向右或向下移动时，一次性移动两格，可以有效的降低图像的宽度和高度。
import torch
input = [3, 4, 6, 5, 7,
2, 4, 6, 8, 2,
1, 6, 7, 8, 4,
9, 7, 4, 6, 2,
3, 7, 5, 4, 1]
input = torch.Tensor(input).view(1, 1, 5, 5) # B C W H
conv_layer = torch.nn.Conv2d(in_channels=1, out_channels=1, kernel_size=3, stride=2, bias=False) # O I W H
kernel = torch.Tensor([1, 2, 3, 4, 5, 6, 7, 8, 9]).view(1, 1, 3, 3)
conv_layer.weight.data = kernel.data
output = conv_layer(input)
print(output)
tensor([[[[211., 262.],
[251., 169.]]]], grad_fn=<ConvolutionBackward0>)
9.4 Max Pooling
Max Pooling
：最大池化，默认
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=
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stride = 2
s
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=
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，若
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=
2
×
2
kernel = 2 \times 2
k
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=
2
×
2
，即在该表格中找出最大值：
import torch
input = [3, 4, 6, 5,
2, 4, 6, 8,
1, 6, 7, 8,
9, 7, 4, 6]
input = torch.Tensor(input).view(1, 1, 4, 4)
maxpooling_layer = torch.nn.MaxPool2d(kernel_size=2)
output = maxpooling_layer(input)
print(output)
tensor([[[[4., 8.],
[9., 8.]]]])
9.5 A Simple CNN
下图为一个简单的神经网络：
即：
代码如下：
class Net(torch.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = torch.nn.Conv2d(1, 10, kernel_size=5)
self.conv2 = torch.nn.Conv2d(10, 20, kernel_size=5)
self.pooling = torch.nn.MaxPool2d(2)
self.fc = torch.nn.Linear(320, 10)
def forward(self, x):
# Flatten data from (n, 1, 28, 28) to (n, 784)
batch_size = x.size(0)
x = F.relu(self.pooling(self.conv1(x)))
x = F.relu(self.pooling(self.conv2(x)))
x = x.view(batch_size, -1) # flatten
x = self.fc(x)
return x
model = Net()
9.5.1 GPU
使用GPU来跑数据的前提：安装CUDA版PyTorch
-
Move Model to GPU
：在调用模型后添加以下代码
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
model.to(device)
-
Move Tensors to GPU
：训练和测试函数添加以下代码
inputs, target = inputs.to(device), target.to(device)
9.5.2 Code 1
import torch
from torchvision import transforms
from torch.utils.data import DataLoader
from torchvision import datasets
import torch.nn.functional as F
import torch.optim as optim
import matplotlib.pyplot as plt
batch_size = 64
transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.1307,), (0.3081,))
])
train_dataset = datasets.MNIST(root='../data/mnist', train=True, download=True, transform=transform)
train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)
test_dataset = datasets.MNIST(root='../data/mnist', train=False, download=True, transform=transform)
test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)
class Net(torch.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = torch.nn.Conv2d(1, 10, kernel_size=5)
self.conv2 = torch.nn.Conv2d(10, 20, kernel_size=5)
self.pooling = torch.nn.MaxPool2d(2)
self.fc = torch.nn.Linear(320, 10)
def forward(self, x):
# Flatten data from (n, 1, 28, 28) to (n, 784)
batch_size = x.size(0)
x = F.relu(self.pooling(self.conv1(x)))
x = F.relu(self.pooling(self.conv2(x)))
x = x.view(batch_size, -1) # flatten
x = self.fc(x)
return x
model = Net()
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu") # GPU
model.to(device)
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)
def train(epoch):
running_loss = 0.0
for batch_idx, data in enumerate(train_loader, 0):
inputs, target = data
inputs, target = inputs.to(device), target.to(device) # GPU
optimizer.zero_grad()
# forward + backward + update
outputs = model(inputs)
loss = criterion(outputs, target)
loss.backward()
optimizer.step()
running_loss += loss.item()
if batch_idx % 300 == 299:
print('[%d, %3d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 2000))
running_loss = 0.0
accuracy = []
def test():
correct = 0
total = 0
with torch.no_grad():
for data in test_loader:
inputs, target = data
inputs, target = inputs.to(device), target.to(device) # GPU
outputs = model(inputs)
_, predicted = torch.max(outputs.data, dim=1)
total += target.size(0)
correct += (predicted == target).sum().item()
print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))
accuracy.append(100 * correct / total)
if __name__ == '__main__':
for epoch in range(10):
train(epoch)
test()
print(accuracy)
plt.plot(range(10), accuracy)
plt.xlabel("Epoch")
plt.ylabel("Accuracy")
plt.grid()
plt.show()
[1, 300] loss: 0.091
[1, 600] loss: 0.027
[1, 900] loss: 0.020
Accuracy on test set: 97 % [9700/10000]
[2, 300] loss: 0.017
[2, 600] loss: 0.014
[2, 900] loss: 0.013
Accuracy on test set: 97 % [9799/10000]
[3, 300] loss: 0.012
[3, 600] loss: 0.011
[3, 900] loss: 0.011
Accuracy on test set: 98 % [9813/10000]
[4, 300] loss: 0.010
[4, 600] loss: 0.009
[4, 900] loss: 0.009
Accuracy on test set: 98 % [9838/10000]
[5, 300] loss: 0.008
[5, 600] loss: 0.008
[5, 900] loss: 0.008
Accuracy on test set: 98 % [9846/10000]
[6, 300] loss: 0.007
[6, 600] loss: 0.008
[6, 900] loss: 0.007
Accuracy on test set: 98 % [9858/10000]
[7, 300] loss: 0.006
[7, 600] loss: 0.007
[7, 900] loss: 0.007
Accuracy on test set: 98 % [9869/10000]
[8, 300] loss: 0.006
[8, 600] loss: 0.006
[8, 900] loss: 0.006
Accuracy on test set: 98 % [9869/10000]
[9, 300] loss: 0.006
[9, 600] loss: 0.006
[9, 900] loss: 0.006
Accuracy on test set: 98 % [9849/10000]
[10, 300] loss: 0.005
[10, 600] loss: 0.005
[10, 900] loss: 0.005
Accuracy on test set: 98 % [9849/10000]
[97.0, 97.99, 98.13, 98.38, 98.46, 98.58, 98.69, 98.69, 98.49, 98.49]
9.5.3 Exercise
若对该神经网络进行改进：
- Conv2d Layer * 3
- ReLU Layer * 3
- MaxPooling Layer * 3
- Linear Layer * 3
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1
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×
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input: 1 \times 28 \times 28 \\ convolution: 28 -5 +1 = 24, to: 16 \times 24 \times 24 \\ pooling: 16 \times 12 \times 12 \\ convolution: 12 -5 +1 = 8, to: 32 \times 8 \times 8 \\ pooling: 20 \times 4 \times 4 \\ convolution: 4 -3 +1 = 2, to: 64 \times 2 \times 2 \\ pooling: 64 \times 1 \times 1 \\ fc: 64 — 32 — 16 — 10
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9.5.4 Code 2
将神经网络改成如下即可：
def __init__(self):
super(Net, self).__init__()
self.conv1 = torch.nn.Conv2d(1, 16, kernel_size=5)
self.conv2 = torch.nn.Conv2d(16, 32, kernel_size=5)
self.conv3 = torch.nn.Conv2d(32, 64, kernel_size=3)
self.pooling = torch.nn.MaxPool2d(2)
self.fc1 = torch.nn.Linear(64, 32)
self.fc2 = torch.nn.Linear(32, 16)
self.fc3 = torch.nn.Linear(16, 10)
def forward(self, x):
batch_size = x.size(0)
x = self.pooling(F.relu(self.conv1(x)))
x = self.pooling(F.relu(self.conv2(x)))
x = self.pooling(F.relu(self.conv3(x)))
x = x.view(batch_size, -1)
x = F.relu(self.fc1(x))
x = F.relu(self.fc2(x))
x = self.fc3(x)
return x
[1, 300] loss: 0.345
[1, 600] loss: 0.273
[1, 900] loss: 0.069
Accuracy on test set: 91 % [9194/10000]
[2, 300] loss: 0.034
[2, 600] loss: 0.025
[2, 900] loss: 0.020
Accuracy on test set: 96 % [9670/10000]
[3, 300] loss: 0.015
[3, 600] loss: 0.015
[3, 900] loss: 0.014
Accuracy on test set: 97 % [9754/10000]
[4, 300] loss: 0.011
[4, 600] loss: 0.010
[4, 900] loss: 0.011
Accuracy on test set: 98 % [9810/10000]
[5, 300] loss: 0.008
[5, 600] loss: 0.009
[5, 900] loss: 0.009
Accuracy on test set: 98 % [9808/10000]
[6, 300] loss: 0.008
[6, 600] loss: 0.007
[6, 900] loss: 0.008
Accuracy on test set: 98 % [9859/10000]
[7, 300] loss: 0.006
[7, 600] loss: 0.006
[7, 900] loss: 0.007
Accuracy on test set: 98 % [9862/10000]
[8, 300] loss: 0.005
[8, 600] loss: 0.006
[8, 900] loss: 0.006
Accuracy on test set: 97 % [9784/10000]
[9, 300] loss: 0.005
[9, 600] loss: 0.005
[9, 900] loss: 0.006
Accuracy on test set: 98 % [9842/10000]
[10, 300] loss: 0.005
[10, 600] loss: 0.005
[10, 900] loss: 0.004
Accuracy on test set: 98 % [9878/10000]
[91.94, 96.7, 97.54, 98.1, 98.08, 98.59, 98.62, 97.84, 98.42, 98.78]
9.6 GoogLeNet
注意：
Convolution
、
Pooling
、
Softmax
、
Other
若以上图来编写神经网络，则会有许多重复，为
减少代码冗余
，可以尽量多使用函数/类。
9.6.1 Inception Module
构造神经网络时，有一些超参数是难以选择的，比如卷积核Kernel，应该选择哪一种卷积核比较好用？
GoogLeNet
在一个块中将几种卷积核（
1
×
1
、
3
×
3
、
5
×
5
、
.
.
.
1 \times 1 、 3 \times 3 、 5 \times 5 、…
1
×
1
、
3
×
3
、
5
×
5
、
…
）都使用，然后将其结果罗列到一起，将来通过训练自动找到一种最优的组合。
-
Concatenate：将张量拼接到一块
-
Average Pooling 均值池化：保证输入输出宽高一致（可借助padding和stride）
9.6.2 1 x 1 convolution
为什么要引入 $1 \times 1 $ convolution ？
见上图：若
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192
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28
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28
,
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input = 192 \times 28 \times 28, output = 32 \times 28 \times 28
in
p
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=
192
×
28
×
28
,
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tp
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=
32
×
28
×
28
，则计算量
O
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=
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2
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2
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192
×
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=
120
,
422
,
400
Operations = 5^2 \times 28^2 \times 192 \times 32 = 120,422,400
Op
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=
5
2
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8
2
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192
×
32
=
120
,
422
,
400
见上图：若在其中间使用
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:
1
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convolution: 1 \times 1
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:
1
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1
，则计算量
O
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=
1
2
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2
8
2
×
192
×
16
+
5
2
×
2
8
2
×
16
×
32
=
12
,
433
,
648
Operations = 1^2 \times 28^2 \times 192 \times 16 + 5^2 \times 28^2 \times 16 \times 32 = 12,433,648
Op
er
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=
1
2
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2
8
2
×
192
×
16
+
5
2
×
2
8
2
×
16
×
32
=
12
,
433
,
648
9.6.3 Implementation of Inception Module
计算方向：由下至上
# 第一列
self.branch_pool = nn.Conv2d(in_channels, 24, kernel_size=1)
branch_pool = F.avg_pool2d(x, kernel_size=3, stride=1, padding=1)
branch_pool = self.branch_pool(branch_pool)
# 第二列
self.branch1x1 = nn.Conv2d(in_channels, 16, kernel_size=1)
branch1x1 = self.branch1x1(x)
# 第三列
self.branch5x5_1 = nn.Conv2d(in_channels,16, kernel_size=1)
self.branch5x5_2 = nn.Conv2d(16, 24, kernel_size=5, padding=2)
branch5x5 = self.branch5x5_1(x)
branch5x5 = self.branch5x5_2(branch5x5)
# 第四列
self.branch3x3_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch3x3_2 = nn.Conv2d(16, 24, kernel_size=3, padding=1)
self.branch3x3_3 = nn.Conv2d(24, 24, kernel_size=3, padding=1)
branch3x3 = self.branch3x3_1(x)
branch3x3 = self.branch3x3_2(branch3x3)
branch3x3 = self.branch3x3_3(branch3x3)
再进行拼接：
outputs = [branch1x1, branch5x5, branch3x3, branch_pool]
return torch.cat(outputs, dim=1)
Using Inception Module：
class InceptionA(nn.Module):
def __init__(self, in_channels):
super(InceptionA, self).__init__()
self.branch1x1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch5x5_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch5x5_2 = nn.Conv2d(16, 24, kernel_size=5, padding=2)
self.branch3x3_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch3x3_2 = nn.Conv2d(16, 24, kernel_size=3, padding=1)
self.branch3x3_3 = nn.Conv2d(24, 24, kernel_size=3, padding=1)
self.branch_pool = nn.Conv2d(in_channels, 24, kernel_size=1)
def forward(self, x):
branch1x1 = self.branch1x1(x)
branch5x5 = self.branch5x5_1(x)
branch5x5 = self.branch5x5_2(branch5x5)
branch3x3 = self.branch3x3_1(x)
branch3x3 = self.branch3x3_2(branch3x3)
branch3x3 = self.branch3x3_3(branch3x3)
branch_pool = F.avg_pool2d(x, kernel_size=3, stride=1, padding=1)
branch_pool = self.branch_pool(branch_pool)
outputs = [branch1x1, branch5x5, branch3x3, branch_pool]
return torch.cat(outputs, dim=1)
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
self.conv2 = nn.Conv2d(88, 20, kernel_size=5)
self.incep1 = InceptionA(in_channels=10)
self.incep2 = InceptionA(in_channels=20)
self.mp = nn.MaxPool2d(2)
self.fc = nn.Linear(1408, 10)
def forward(self, x):
in_size = x.size(0)
x = F.relu(self.mp(self.conv1(x)))
x = self.incep1(x)
x = F.relu(self.mp(self.conv2(x)))
x = self.incep2(x)
x = x.view(in_size, -1)
x = self.fc(x)
return x
完整代码：
import torch
from torch import nn
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optim
import matplotlib.pyplot as plt
# 1、准备数据集
batch_size = 64
transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.1307,), (0.3081,))
])
train_dataset = datasets.MNIST(root='../data/mnist', train=True, download=True, transform=transform)
train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)
test_dataset = datasets.MNIST(root='../data/mnist', train=False, download=True, transform=transform)
test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)
# 2、建立模型
# 定义一个Inception类
class InceptionA(nn.Module):
def __init__(self, in_channels):
super(InceptionA, self).__init__()
self.branch1X1 = nn.Conv2d(in_channels, 16, kernel_size=1)
# 设置padding保证 宽 高 不变
self.branch5X5_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch5X5_2 = nn.Conv2d(16, 24, kernel_size=5, padding=2)
self.branch3X3_1 = nn.Conv2d(in_channels, 16, kernel_size=1)
self.branch3X3_2 = nn.Conv2d(16, 24, kernel_size=3, padding=1)
self.branch3X3_3 = nn.Conv2d(24, 24, kernel_size=3, padding=1)
self.branch_pool = nn.Conv2d(in_channels, 24, kernel_size=1)
def forward(self, x):
branch1X1 = self.branch1X1(x)
branch5X5 = self.branch5X5_1(x)
branch5X5 = self.branch5X5_2(branch5X5)
branch3X3 = self.branch3X3_1(x)
branch3X3 = self.branch3X3_2(branch3X3)
branch3X3 = self.branch3X3_3(branch3X3)
branch_pool = F.avg_pool2d(x, kernel_size=3, stride=1, padding=1)
branch_pool = self.branch_pool(branch_pool)
outputs = [branch1X1, branch5X5, branch3X3, branch_pool]
# （b, c, w, h），dim=1 以第一个维度channel来拼接
return torch.cat(outputs, dim=1)
# 定义模型
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
# 88 = 24*3 + 16
self.conv2 = nn.Conv2d(88, 20, kernel_size=5)
self.incep1 = InceptionA(in_channels=10)
self.incep2 = InceptionA(in_channels=20)
self.mp = nn.MaxPool2d(2)
# 确定输出张量的尺寸
# 在定义时先不定义fc层，随便选取一个输入，经过模型后查看其尺寸
# 在init函数中把fc层去掉，forward函数中把最后两行去掉，确定输出的尺寸后再定义Lear层的大小
self.fc = nn.Linear(1408, 10)
def forward(self, x):
in_size = x.size(0)
# 1 --> 10
x = F.relu(self.mp(self.conv1(x)))
# 10 --> 88
x = self.incep1(x)
# 88 --> 20
x = F.relu(self.mp(self.conv2(x)))
# 20 --> 88
x = self.incep2(x)
x = x.view(in_size, -1)
x = self.fc(x)
return x
model = Net()
# 将模型迁移到GPU上运行
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
model.to(device)
# 3、建立损失函数和优化器
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)
# 4、定义训练函数
def train(epoch):
running_loss = 0
for batch_idx, data in enumerate(train_loader, 0):
inputs, target = data
# 将计算的张量迁移到GPU上
inputs, target = inputs.to(device), target.to(device)
optimizer.zero_grad()
# 前馈 反馈 更新
outputs = model(inputs)
loss = criterion(outputs, target)
loss.backward()
optimizer.step()
running_loss += loss.item()
if batch_idx % 300 == 299:
print('[%d, %3d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
running_loss = 0
# 5、定义测试函数
accuracy = []
def test():
correct = 0
total = 0
with torch.no_grad():
for data in test_loader:
images, labels = data
# 将测试中的张量迁移到GPU上
images, labels = images.to(device), labels.to(device)
outputs = model(images)
_, predicted = torch.max(outputs.data, dim=1)
total += labels.size(0)
# 得出其中相等元素的个数
correct += (predicted == labels).sum().item()
print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))
accuracy.append(100 * correct / total)
if __name__ == '__main__':
for epoch in range(10):
train(epoch)
test()
print(accuracy)
plt.plot(range(10), accuracy)
plt.xlabel("Epoch")
plt.ylabel("Accuracy")
plt.grid() # 表格
plt.show()
[1, 300] loss: 0.836
[1, 600] loss: 0.196
[1, 900] loss: 0.145
Accuracy on test set: 96 % [9690/10000]
[2, 300] loss: 0.106
[2, 600] loss: 0.099
[2, 900] loss: 0.091
Accuracy on test set: 97 % [9785/10000]
[3, 300] loss: 0.075
[3, 600] loss: 0.078
[3, 900] loss: 0.071
Accuracy on test set: 98 % [9831/10000]
[4, 300] loss: 0.064
[4, 600] loss: 0.067
[4, 900] loss: 0.061
Accuracy on test set: 98 % [9845/10000]
[5, 300] loss: 0.057
[5, 600] loss: 0.058
[5, 900] loss: 0.052
Accuracy on test set: 98 % [9846/10000]
[6, 300] loss: 0.051
[6, 600] loss: 0.049
[6, 900] loss: 0.050
Accuracy on test set: 98 % [9852/10000]
[7, 300] loss: 0.047
[7, 600] loss: 0.043
[7, 900] loss: 0.045
Accuracy on test set: 98 % [9848/10000]
[8, 300] loss: 0.039
[8, 600] loss: 0.044
[8, 900] loss: 0.042
Accuracy on test set: 98 % [9871/10000]
[9, 300] loss: 0.041
[9, 600] loss: 0.034
[9, 900] loss: 0.041
Accuracy on test set: 98 % [9866/10000]
[10, 300] loss: 0.032
[10, 600] loss: 0.038
[10, 900] loss: 0.037
Accuracy on test set: 98 % [9881/10000]
[96.9, 97.85, 98.31, 98.45, 98.46, 98.52, 98.48, 98.71, 98.66, 98.81]
9.7 Residual Net
如果将
3
×
3
3 \times 3
3
×
3
的卷积一直堆下去，该神经网络的性能会不会更好？
Paper：
He K, Zhang X, Ren S, et al. Deep Residual Learning for Image Recognition[C]// IEEE Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, 2016:770-778.
研究发现：20 层的错误率低于56 层的错误率，所以并不是层数越多，性能越好。为解决
梯度消失
的问题，见下图：
多一个
跳连接
：
9.7.1 Residual Network
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(1, 16, kernel_size=5)
self.conv2 = nn.Conv2d(16, 32, kernel_size=5)
self.mp = nn.MaxPool2d(2)
self.rblock1 = ResidualBlock(16)
self.rblock2 = ResidualBlock(32)
self.fc = nn.Linear(512, 10)
def forward(self, x):
in_size = x.size(0)
x = self.mp(F.relu(self.conv1(x)))
x = self.rblock1(x)
x = self.mp(F.relu(self.conv2(x)))
x = self.rblock2(x)
x = x.view(in_size, -1)
x = self.fc(x)
return x
9.7.2 Residual Block
class ResidualBlock(nn.Module):
def __init__(self, channels):
super(ResidualBlock, self).__init__()
self.channels = channels
self.conv1 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
def forward(self, x):
y = F.relu(self.conv1(x))
y = self.conv2(y)
return F.relu(x + y)
9.7.3 Code 3
import torch
from torch import nn
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optim
import matplotlib.pyplot as plt
batch_size = 64
transform = transforms.Compose([
transforms.ToTensor(),
transforms.Normalize((0.1307,), (0.3081,))
])
train_dataset = datasets.MNIST(root='../data/mnist', train=True, download=True, transform=transform)
train_loader = DataLoader(train_dataset, shuffle=True, batch_size=batch_size)
test_dataset = datasets.MNIST(root='../data/mnist', train=False, download=True, transform=transform)
test_loader = DataLoader(test_dataset, shuffle=False, batch_size=batch_size)
class ResidualBlock(nn.Module):
def __init__(self, channels):
super(ResidualBlock, self).__init__()
self.channels = channels
self.conv1 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
def forward(self, x):
y = F.relu(self.conv1(x))
y = self.conv2(y)
return F.relu(x + y)
class Net(nn.Module):
def __init__(self):
super(Net, self).__init__()
self.conv1 = nn.Conv2d(1, 16, kernel_size=5)
self.conv2 = nn.Conv2d(16, 32, kernel_size=5)
self.mp = nn.MaxPool2d(2)
self.rblock1 = ResidualBlock(16)
self.rblock2 = ResidualBlock(32)
self.fc = nn.Linear(512, 10)
def forward(self, x):
in_size = x.size(0)
x = self.mp(F.relu(self.conv1(x)))
x = self.rblock1(x)
x = self.mp(F.relu(self.conv2(x)))
x = self.rblock2(x)
x = x.view(in_size, -1)
x = self.fc(x)
return x
model = Net()
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
model.to(device)
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(), lr=0.01, momentum=0.5)
def train(epoch):
running_loss = 0
for batch_idx, data in enumerate(train_loader, 0):
inputs, target = data
inputs, target = inputs.to(device), target.to(device)
optimizer.zero_grad()
outputs = model(inputs)
loss = criterion(outputs, target)
loss.backward()
optimizer.step()
running_loss += loss.item()
if batch_idx % 300 == 299:
print('[%d, %3d] loss: %.3f' % (epoch + 1, batch_idx + 1, running_loss / 300))
running_loss = 0
accuracy = []
def test():
correct = 0
total = 0
with torch.no_grad():
for data in test_loader:
images, labels = data
images, labels = images.to(device), labels.to(device)
outputs = model(images)
_, predicted = torch.max(outputs.data, dim=1)
total += labels.size(0)
correct += (predicted == labels).sum().item()
print('Accuracy on test set: %d %% [%d/%d]' % (100 * correct / total, correct, total))
accuracy.append(100 * correct / total)
if __name__ == '__main__':
for epoch in range(10):
train(epoch)
test()
print(accuracy)
plt.plot(range(10), accuracy)
plt.xlabel("Epoch")
plt.ylabel("Accuracy")
plt.grid()
plt.show()
[1, 300] loss: 0.563
[1, 600] loss: 0.157
[1, 900] loss: 0.111
Accuracy on test set: 97 % [9721/10000]
[2, 300] loss: 0.085
[2, 600] loss: 0.077
[2, 900] loss: 0.081
Accuracy on test set: 98 % [9831/10000]
[3, 300] loss: 0.063
[3, 600] loss: 0.059
[3, 900] loss: 0.053
Accuracy on test set: 98 % [9841/10000]
[4, 300] loss: 0.047
[4, 600] loss: 0.052
[4, 900] loss: 0.042
Accuracy on test set: 98 % [9877/10000]
[5, 300] loss: 0.039
[5, 600] loss: 0.037
[5, 900] loss: 0.041
Accuracy on test set: 98 % [9871/10000]
[6, 300] loss: 0.035
[6, 600] loss: 0.032
[6, 900] loss: 0.035
Accuracy on test set: 98 % [9895/10000]
[7, 300] loss: 0.029
[7, 600] loss: 0.032
[7, 900] loss: 0.029
Accuracy on test set: 98 % [9899/10000]
[8, 300] loss: 0.026
[8, 600] loss: 0.028
[8, 900] loss: 0.025
Accuracy on test set: 98 % [9892/10000]
[9, 300] loss: 0.021
[9, 600] loss: 0.027
[9, 900] loss: 0.024
Accuracy on test set: 98 % [9886/10000]
[10, 300] loss: 0.019
[10, 600] loss: 0.021
[10, 900] loss: 0.023
Accuracy on test set: 99 % [9902/10000]
[97.21, 98.31, 98.41, 98.77, 98.71, 98.95, 98.99, 98.92, 98.86, 99.02]
9.7.4 Reading Paper
Paper 1：
He K, Zhang X, Ren S, et al. Identity Mappings in Deep Residual Networks[C]
constant scaling：
class ResidualBlock(nn.Module):
def __init__(self, channels):
super(ResidualBlock, self).__init__()
self.channels = channels
self.conv1 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
def forward(self, x):
y = F.relu(self.conv1(x))
y = self.conv2(x)
z = 0.5 * (x + y)
return F.relu(z)
[1, 300] loss: 1.204
[1, 600] loss: 0.243
[1, 900] loss: 0.165
Accuracy on test set: 96 % [9637/10000]
[2, 300] loss: 0.121
[2, 600] loss: 0.105
[2, 900] loss: 0.099
Accuracy on test set: 97 % [9777/10000]
[3, 300] loss: 0.085
[3, 600] loss: 0.076
[3, 900] loss: 0.069
Accuracy on test set: 98 % [9815/10000]
[4, 300] loss: 0.061
[4, 600] loss: 0.063
[4, 900] loss: 0.063
Accuracy on test set: 98 % [9849/10000]
[5, 300] loss: 0.053
[5, 600] loss: 0.052
[5, 900] loss: 0.052
Accuracy on test set: 98 % [9853/10000]
[6, 300] loss: 0.041
[6, 600] loss: 0.051
[6, 900] loss: 0.047
Accuracy on test set: 98 % [9871/10000]
[7, 300] loss: 0.040
[7, 600] loss: 0.044
[7, 900] loss: 0.043
Accuracy on test set: 98 % [9869/10000]
[8, 300] loss: 0.039
[8, 600] loss: 0.038
[8, 900] loss: 0.037
Accuracy on test set: 98 % [9859/10000]
[9, 300] loss: 0.031
[9, 600] loss: 0.039
[9, 900] loss: 0.036
Accuracy on test set: 98 % [9875/10000]
[10, 300] loss: 0.035
[10, 600] loss: 0.031
[10, 900] loss: 0.033
Accuracy on test set: 98 % [9888/10000]
[96.37, 97.77, 98.15, 98.49, 98.53, 98.71, 98.69, 98.59, 98.75, 98.88]
conv shortcut：
class ResidualBlock(nn.Module):
def __init__(self, channels):
super(ResidualBlock, self).__init__()
self.channels = channels
self.conv1 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
self.conv2 = nn.Conv2d(channels, channels, kernel_size=3, padding=1)
self.conv3 = nn.Conv2d(channels, channels, kernel_size=1)
def forward(self, x):
y = F.relu(self.conv1(x))
y = self.conv2(x)
z = self.conv3(x) + y
return F.relu(z)
[1, 300] loss: 0.760
[1, 600] loss: 0.170
[1, 900] loss: 0.119
Accuracy on test set: 97 % [9717/10000]
[2, 300] loss: 0.092
[2, 600] loss: 0.084
[2, 900] loss: 0.075
Accuracy on test set: 98 % [9826/10000]
[3, 300] loss: 0.064
[3, 600] loss: 0.063
[3, 900] loss: 0.055
Accuracy on test set: 98 % [9817/10000]
[4, 300] loss: 0.048
[4, 600] loss: 0.047
[4, 900] loss: 0.048
Accuracy on test set: 98 % [9851/10000]
[5, 300] loss: 0.039
[5, 600] loss: 0.039
[5, 900] loss: 0.044
Accuracy on test set: 98 % [9864/10000]
[6, 300] loss: 0.035
[6, 600] loss: 0.033
[6, 900] loss: 0.038
Accuracy on test set: 98 % [9890/10000]
[7, 300] loss: 0.030
[7, 600] loss: 0.030
[7, 900] loss: 0.030
Accuracy on test set: 98 % [9881/10000]
[8, 300] loss: 0.027
[8, 600] loss: 0.026
[8, 900] loss: 0.029
Accuracy on test set: 98 % [9884/10000]
[9, 300] loss: 0.021
[9, 600] loss: 0.026
[9, 900] loss: 0.025
Accuracy on test set: 98 % [9894/10000]
[10, 300] loss: 0.019
[10, 600] loss: 0.019
[10, 900] loss: 0.025
Accuracy on test set: 98 % [9897/10000]
[97.17, 98.26, 98.17, 98.51, 98.64, 98.9, 98.81, 98.84, 98.94, 98.97]
Paper 2：
Huang G, Liu Z, Laurens V D M, et al. Densely Connected Convolutional Networks[J]. 2016:2261-2269.
