pytorch学习笔记系列（5）：卷积神经网络Conv2d&&Conv1d

卷积层原理

• 卷积层是用一个固定大小的矩形区去席卷原始数据，将原始数据分成一个个和卷积核大小相同的小块，然后将这些小块和卷积核相乘输出一个卷积值（注意这里是一个单独的值，不再是矩阵了）.
• 卷积的本质就是用卷积核的参数来提取原始数据的特征，通过矩阵点乘的运算，提取出和卷积核特征一致的值，如果卷积层有多个卷积核，则神经网络会自动学习卷积核的参数值，使得每个卷积核代表一个特征.

---

关于 nn.torch.Conv2d 函数

CLASS torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, 
padding=0, dilation=1, groups=1, bias=True)

假设 Conv2d 的输入 input 尺寸为 $(N,C_{in},H_{in},W_{in})$，输出 output 尺寸为 $(N,C_{out},H_{out},W_{out})$，有：
$out(N_i,C_{ou{t}_j})=bias(C_{ou{t}_j})+{\sum }_{k=0}^{C_{in}-1}weight(C_{out},k)\ast input(N_i,k)$
其中，*是2D cross-correlation操作，N为batch-size，C为channels数，H为Height，W为Width.

• [1]-kernel_size
• [2]-stride-步长
• [3]-padding-每一维补零的数量
• [4]-dilation-控制 kernel 点之间的空间距离(the spacing between the kernel points). 带孔卷积(atrous conv). 参考dilated-convolution-animations.
• [5]-groups-控制 inputs 和 outputs 间的关联性(分组). 其中，要求 in_channels 和out_channels必须都可以被groups整除.

$H_{out}=\frac{H_{in}+2\times padding[0]-dilation[0]\times (kerne{l}_{s}ize[0]-1)-1}{stride[0]}+1$
$W_{out}=\frac{W_{in}+2\times padding[1]-dilation[1]\times (kerne{l}_{s}ize[1]-1)-1}{stride[1]}+1$

• Demo

import torch
import torch.nn as nn

### 输入通道为16，输出通道为33，kernel_size为3(长和宽相同),stride为2
m = nn.Conv2d(16, 33, 3, stride=2)
# non-square kernels and unequal stride and with padding
### 输入通道为16，输出通道为33，kernel_size为(3,5)，对应的padding为(4,2)
m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2))
# non-square kernels and unequal stride and with padding and dilation
m = nn.Conv2d(16, 33, (3, 5), stride=(2, 1), padding=(4, 2), dilation=(3, 1))
### input为4维向量，第一维为batch_size，第二维为in_chanels，第三维和第四维为50和100
input = torch.randn(20, 16, 50, 100)
output = m(input)

---

卷积神经网络CNN的PyTorch实现

• 使用Mnist数据集实现的CNN。
• 导入包

import torch
import torch.nn as nn
import torchvision
import torchvision.transforms as transforms

• 下载数据

# Device configuration
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')

# Hyper parameters
num_epochs = 5
num_classes = 10
batch_size = 100
learning_rate = 0.001

# MNIST dataset
train_dataset = torchvision.datasets.MNIST(root='../../data/',
                                           train=True,
                                           transform=transforms.ToTensor(),
                                           download=True)

test_dataset = torchvision.datasets.MNIST(root='../../data/',
                                          train=False,
                                          transform=transforms.ToTensor())

• 处理数据，使用 DataLoader 进行batch训练

# Data loader
train_loader = torch.utils.data.DataLoader(dataset=train_dataset,
                                           batch_size=batch_size,
                                           shuffle=True)

test_loader = torch.utils.data.DataLoader(dataset=test_dataset,
                                          batch_size=batch_size,
                                          shuffle=False)

• 建立计算图模型

# Convolutional neural network (two convolutional layers)
class ConvNet(nn.Module):
    def __init__(self, num_classes=10):
        super(ConvNet, self).__init__()
        self.layer1 = nn.Sequential(
            nn.Conv2d(1, 16, kernel_size=5, stride=1, padding=2),
            nn.BatchNorm2d(16),
            nn.ReLU(),
            nn.MaxPool2d(kernel_size=2, stride=2))
        self.layer2 = nn.Sequential(
            nn.Conv2d(16, 32, kernel_size=5, stride=1, padding=2),
            nn.BatchNorm2d(32),
            nn.ReLU(),
            nn.MaxPool2d(kernel_size=2, stride=2))
        self.fc = nn.Linear(7 * 7 * 32, num_classes)

    def forward(self, x):
        out = self.layer1(x)
        out = self.layer2(out)
        out = out.reshape(out.size(0), -1) # out.size(0)为batch_size
        out = self.fc(out)
        return out

model = ConvNet(num_classes).to(device)

• 定义优化器optimizer和损失

# Loss and optimizer
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)

• 进行batch训练

# Train the model
total_step = len(train_loader)
for epoch in range(num_epochs):
    for i, (images, labels) in enumerate(train_loader):  
        # Move tensors to the configured device
        images = images.reshape(-1, 28*28).to(device)
        labels = labels.to(device)
        
        # Forward pass
        outputs = model(images)
        loss = criterion(outputs, labels)
        
        # Backward and optimize
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        
        if (i+1) % 100 == 0:
            print ('Epoch [{}/{}], Step [{}/{}], Loss: {:.4f}' 
                   .format(epoch+1, num_epochs, i+1, total_step, loss.item()))

• 测试模型

# Test the model
# In test phase, we don't need to compute gradients (for memory efficiency)
with torch.no_grad():
    correct = 0
    total = 0
    for images, labels in test_loader:
        images = images.reshape(-1, 28*28).to(device)
        labels = labels.to(device)
        outputs = model(images)
        _, predicted = torch.max(outputs.data, 1)
        total += labels.size(0)
        correct += (predicted == labels).sum().item()

    print('Accuracy of the network on the 10000 test images: {} %'.format(100 * correct / total))

# Save the model checkpoint
torch.save(model.state_dict(), 'model.ckpt')

---

关于conv1d

• conv1d是一维卷积,它和conv2d的区别在于只对宽度进行卷积，对高度不卷积.
  函数定义：

torch.nn.functional.conv1d(input, weight, bias=None, stride=1, padding=0, dilation=1, groups=1)

参数说明:

• input：输入的Tensor数据，格式为(batch, channels, W)，三维数组，第一维度是样本数量，第二维度是通道数或者记录数，三维度是宽度.
• weight：卷积核权重，也就是卷积核本身. 是一个三维数组，(out_channels, in_channels/groups, kW). out_channels 是卷积核输出层的神经元个数，也就是这层有多少个卷积核；in_channels是输入通道数；kW是卷积核的宽度.
• bias：位移参数，可选项，一般也不用管.
• stride：滑动窗口，默认为1，指每次卷积对原数据滑动1个单元格.
• padding：是否对输入数据填充0. Padding可以将输入数据的区域改造成是卷积核大小的整数倍，这样对不满足卷积核大小的部分数据就不会忽略了. 通过padding参数指定填充区域的高度和宽度，默认0（填充区域为0，不填充）.
• dilation：卷积核之间的空格，默认1.
• groups：将输入数据分组，通常不用管这个参数.

Demo

import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.autograd import Variable

print("conv1d sample")

a=range(16)
x = Variable(torch.Tensor(a))
x=x.view(1,1,16)
print("x variable:", x)

b=torch.ones(3)
b[0]=0.1
b[1]=0.2
b[2]=0.3
weights = Variable(b) #torch.randn(1,1,2,2)) #out_channel*in_channel*H*W
weights=weights.view(1,1,3)
print ("weights:",weights)

y=F.conv1d(x, weights, padding=0)
print ("y:",y)