课程地址
一、LeNet
手写数字识别（MNIST）
使用了Conv2d、AvgPooling、Linear
高宽减半时通道数翻倍，保证信息能匹配更多的模式（将信息分配到多个通道）
输入超过100x100时MLP不如CNN，输入少时mlp更快
torch实现
import torch
from torch import nn
from d2l import torch as d2l
#使用类可以放在Sequential里
class Reshape(torch.nn.Module):
def forward(self, x):
return x.view(-1, 1, 28, 28)
net = torch.nn.Sequential(
Reshape(),
nn.Conv2d(1, 6, kernel_size=5, padding=2), nn.Sigmoid(),#窗口5x5，由于数据集是28x28和论文中32x32不同，所以padding了2
nn.AvgPool2d(kernel_size=2, stride=2),#stride=2防止2x2的窗口重叠
nn.Conv2d(6, 16, kernel_size=5), nn.Sigmoid(),
nn.AvgPool2d(kernel_size=2, stride=2),#输出为16*5*5
nn.Flatten(),#把16x5x5拉长变成1维的1x400
nn.Linear(16 * 5 * 5, 120), nn.Sigmoid(),
nn.Linear(120, 84), nn.Sigmoid(),nn.Linear(84, 10))#最后输出1*10的向量
#去掉了高斯层
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size=batch_size)
def evaluate_accuracy_gpu(net, data_iter, device=None):
"""使用GPU计算模型在数据集上的精度。"""
if isinstance(net, torch.nn.Module):
net.eval() # 设置为评估模式
if not device: #未设置device就看net的第一个参数的device
device = next(iter(net.parameters())).device
# 正确预测的数量，总预测的数量
metric = d2l.Accumulator(2)
for X, y in data_iter:
if isinstance(X, list):
# BERT微调所需的（之后将介绍）
X = [x.to(device) for x in X]
else:
X = X.to(device)
y = y.to(device)
metric.add(d2l.accuracy(net(X), y), y.numel())
return metric[0] / metric[1] #分类正确的个数/所有
#lr为学习率
def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
"""用GPU训练模型(在第六章定义)"""
def init_weights(m): #初始化权重
if type(m) == nn.Linear or type(m) == nn.Conv2d:
nn.init.xavier_uniform_(m.weight) #线性回归和二维卷积自动初始化权重（卷积核）
net.apply(init_weights)
print('training on', device)
net.to(device)#搬入GPU
optimizer = torch.optim.SGD(net.parameters(), lr=lr)
loss = nn.CrossEntropyLoss()
#使用动画方便查看结果
animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
legend=['train loss', 'train acc', 'test acc'])
timer, num_batches = d2l.Timer(), len(train_iter)
for epoch in range(num_epochs):
# 训练损失之和，训练准确率之和，范例数
metric = d2l.Accumulator(3)
net.train()
for i, (X, y) in enumerate(train_iter):
timer.start()
optimizer.zero_grad()
X, y = X.to(device), y.to(device)#把输入输出放在GPU上
y_hat = net(X)
l = loss(y_hat, y)
l.backward()
optimizer.step()
with torch.no_grad():
metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
timer.stop()
train_l = metric[0] / metric[2]
train_acc = metric[1] / metric[2]
if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
animator.add(epoch + (i + 1) / num_batches,
(train_l, train_acc, None))
test_acc = evaluate_accuracy_gpu(net, test_iter)
animator.add(epoch + 1, (None, None, test_acc))
print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
f'test acc {test_acc:.3f}')
print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
f'on {str(device)}')
图片的学习结果 http://poloclub.github.io/cnn-explainer/
二、AlexNet
数据集：ImageNet 自然物体彩色图片
特点
更深更大的LeNet
使用了丢弃法（正则化）、ReLU（减缓梯度消失）、MaxPooling（扩大梯度更容易训练）、隐藏全连接层后（Dense/FC 4096后）加入丢弃层
torch实现
import torch
from torch import nn
from d2l import torch as d2l
net = nn.Sequential(
# 步幅为4，以减少输出的高度和宽度 输出通道 96
nn.Conv2d(1, 96, kernel_size=11, stride=4, padding=1), nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2),
# 减小卷积窗口，使用填充为2来使得输入与输出的高和宽一致，且增大输出通道数
nn.Conv2d(96, 256, kernel_size=5, padding=2), nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2),
# 使用三个连续的卷积层和较小的卷积窗口 除了最后的卷积层，输出通道的数量进一步增加。
# 在前两个卷积层之后，汇聚层不用于减少输入的高度和宽度
nn.Conv2d(256, 384, kernel_size=3, padding=1), nn.ReLU(),
nn.Conv2d(384, 384, kernel_size=3, padding=1), nn.ReLU(),
nn.Conv2d(384, 256, kernel_size=3, padding=1), nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2),
nn.Flatten(),
# 这里，全连接层的输出数量是LeNet中的好几倍。使用dropout层来减轻过度拟合
nn.Linear(6400, 4096), nn.ReLU(),
nn.Dropout(p=0.5),
nn.Linear(4096, 4096), nn.ReLU(),
nn.Dropout(p=0.5), # 丢弃了50%
# 最后是输出层。使用Fashion-MNIST，类别数为10，论文中是1000
nn.Linear(4096, 10))
batch_size = 128
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=224)
lr, num_epochs = 0.01, 10
#train_ch6定义在上
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
三、VGG
为了让模型更深更大，使用更多的卷积层，将卷积层组成块，重复使用这些卷积块
更深的模型 窗口更小 效果更好
结构
原始 VGG 网络有 5 个卷积块，其中前两个块各有一个卷积层，后三个块各包含两个卷积层。
第一个模块有 64 个输出通道，每个后续模块将输出通道数量翻倍，直到该数字达到 512。由于该网络使用 8 个卷积层和 3 个全连接层，因此它被称为 VGG-11
torch实现
import torch
from torch import nn
from d2l import torch as d2l
def vgg_block(num_convs, in_channels, out_channels):
layers = []
for _ in range(num_convs):
layers.append(nn.Conv2d(in_channels, out_channels,
kernel_size=3, padding=1))
layers.append(nn.ReLU())
in_channels = out_channels
layers.append(nn.MaxPool2d(kernel_size=2,stride=2))
return nn.Sequential(*layers)
conv_arch = ((1, 64), (1, 128), (2, 256), (2, 512), (2, 512))
def vgg(conv_arch):
conv_blks = []
in_channels = 1
# 卷积层部分
for (num_convs, out_channels) in conv_arch:
conv_blks.append(vgg_block(num_convs, in_channels, out_channels))
in_channels = out_channels
return nn.Sequential(
*conv_blks, nn.Flatten(),
# 全连接层部分 224
nn.Linear(out_channels * 7 * 7, 4096), nn.ReLU(), nn.Dropout(0.5),
nn.Linear(4096, 4096), nn.ReLU(), nn.Dropout(0.5),
nn.Linear(4096, 10))
net = vgg(conv_arch)
ratio = 4 #将通道数除以4 以方便训练
small_conv_arch = [(pair[0], pair[1] // ratio) for pair in conv_arch]
net = vgg(small_conv_arch)
lr, num_epochs, batch_size = 0.05, 10, 128
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=224)
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
四、NiN
网络中的网络
思路、结构
全连接层会导致过拟合，用卷积层替代全连接层
使用NiN块，一个卷积层+两个卷积层（卷积核为1x1、步幅为1、无填充、输出形状和卷积层输出一致（不改变输出和通道数）），来代替全连接层
交替使用NiN块和步幅为2的最大池化层（逐步减小高宽 增大通道数），最后用全局平均池化层替代非常大的全连接层得到输出
torch实现
import torch
from torch import nn
from d2l import torch as d2l
def nin_block(in_channels, out_channels, kernel_size, strides, padding):
return nn.Sequential(
nn.Conv2d(in_channels, out_channels, kernel_size, strides, padding),nn.ReLU(),
#输入输出通道数相同
nn.Conv2d(out_channels, out_channels, kernel_size=1), nn.ReLU(),
nn.Conv2d(out_channels, out_channels, kernel_size=1), nn.ReLU())
net = nn.Sequential(
nin_block(1, 96, kernel_size=11, strides=4, padding=0),
nn.MaxPool2d(3, stride=2),
nin_block(96, 256, kernel_size=5, strides=1, padding=2),
nn.MaxPool2d(3, stride=2),
nin_block(256, 384, kernel_size=3, strides=1, padding=1),
nn.MaxPool2d(3, stride=2),
nn.Dropout(0.5),
# MNIST的类别数是10，输出降到10即可
nin_block(384, 10, kernel_size=3, strides=1, padding=1),
nn.AdaptiveAvgPool2d((1, 1)),
# 将四维的输出转成二维的输出，其形状为(批量大小, 10)
nn.Flatten())
lr, num_epochs, batch_size = 0.1, 10, 128
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, resize=224)
#内含有Softmax
d2l.train_ch6(net, train_iter, test_iter, num_epochs, lr, d2l.try_gpu())
五、GoogLeNet
并行连接的网络
Inception块
将输入的通道分为4份
为每个通道使用不同窗口大小和padding的卷积层
最后的输出高宽相同
减少计算量
GoogLeNet
保留更多高宽
9个Inception块
每个Stage将高宽减半
使用全局平均池化
Stage1&2：更小的核 更小的输出通道
Stage3：输出通道增加
Stage4&5：增加通道数 最后输出1024维特征
Inception变种
Inception-BN（V2） 加入batch normalization
Inception-V3 替换卷积层，消耗内存较多，精度提升
把Inception块中的 5x5 替换为多个 3x3 的卷积层（或者1x7和7x1）、把 3x3 换为 1x3 和 3x1 的卷积层
Inception-V4 添加残差块连接
torch实现
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` 是每条路径的输出通道数
def __init__(self, in_channels, c1, c2, c3, c4, **kwargs):
super(Inception, self).__init__(**kwargs)
# 线路1，单1 x 1卷积层
self.p1_1 = nn.Conv2d(in_channels, c1, kernel_size=1)
# 线路2，1 x 1卷积层后接3 x 3卷积层
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)
# 线路3，1 x 1卷积层后接5 x 5卷积层
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)
# 线路4，3 x 3最大汇聚层后接1 x 1卷积层
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)))
# 在通道维度上拼接输出
return torch.cat((p1, p2, p3, p4), dim=1)
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))
b2 = nn.Sequential(nn.Conv2d(64, 64, kernel_size=1),
nn.ReLU(),
nn.Conv2d(64, 192, kernel_size=3, padding=1),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
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))
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))
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))
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())
六、批量归一化
对于很深的神经网络，损失出现在最后，但数据在底部；当底部层发生变化所有层都要跟着改变，因此最后的那些层会重新学习很多次，导致loss收敛变慢。
一般作用在全连接层和卷积层的输出上，激活函数之前；全连接层和卷积层输入上
对于全连接层，作用在特征维；对于卷积层，作用在通道维。
由于是在每个小批量里加入噪音控制模型复杂度，因此不必和Dropout混用。
思想
固定小批量里的均值和方差，然后学习出适合的偏移和缩放，以加快收敛
方差和均值是可学习的参数，控制着做小量的调整（线性变换）
七、残差网络ResNet
加更多的层不一定能距离最优点更近
残差块
加入快速通道来得到 f(x) = x + g(x)，由于g(x)在反向传播，层层求梯度之后可能变得非常小，所有将x加在这里，防止变成0而消失。
也可以用1x1的Conv调整通道和分辨率
可以有各种各样的排列形式
多个块拼接成ResNet，每个块高宽减半（strides = 2）
torch实现
import torch
from torch import nn
from torch.nn import functional as F
from d2l import torch as d2l
class Residual(nn.Module): #@save
def __init__(self, input_channels, num_channels,
use_1x1conv=False, strides=1):
#use1x1是否使用1x1的卷积层
super().__init__()
self.conv1 = nn.Conv2d(input_channels, num_channels,
kernel_size=3, padding=1, stride=strides)
self.conv2 = nn.Conv2d(num_channels, num_channels,
kernel_size=3, padding=1)
if use_1x1conv:
self.conv3 = nn.Conv2d(input_channels, num_channels,
kernel_size=1, stride=strides)
else:
self.conv3 = None
self.bn1 = nn.BatchNorm2d(num_channels)
self.bn2 = nn.BatchNorm2d(num_channels)
self.relu = nn.ReLU(inplace=True)
def forward(self, X):
Y = F.relu(self.bn1(self.conv1(X)))
Y = self.bn2(self.conv2(Y))
if self.conv3:
X = self.conv3(X)
Y += X
return F.relu(Y)
b1 = nn.Sequential(nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),
nn.BatchNorm2d(64), nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
#num residuals是表示使用几个block组成一个Stage
def resnet_block(input_channels, num_channels, num_residuals,
first_block=False):
blk = []
for i in range(num_residuals):
if i == 0 and not first_block:
blk.append(Residual(input_channels, num_channels,
use_1x1conv=True, strides=2))
else:
blk.append(Residual(num_channels, num_channels))
return blk
b2 = nn.Sequential(*resnet_block(64, 64, 2, first_block=True))
b3 = nn.Sequential(*resnet_block(64, 128, 2))
b4 = nn.Sequential(*resnet_block(128, 256, 2))
b5 = nn.Sequential(*resnet_block(256, 512, 2))
net = nn.Sequential(b1, b2, b3, b4, b5,
nn.AdaptiveAvgPool2d((1,1)),
nn.Flatten(), nn.Linear(512, 10))
各块输出的Shape
Sequential output shape: torch.Size([1, 64, 56, 56])
Sequential output shape: torch.Size([1, 64, 56, 56])
Sequential output shape: torch.Size([1, 128, 28, 28])
Sequential output shape: torch.Size([1, 256, 14, 14])
Sequential output shape: torch.Size([1, 512, 7, 7])
AdaptiveAvgPool2d output shape: torch.Size([1, 512, 1, 1])
Flatten output shape: torch.Size([1, 512])
Linear output shape: torch.Size([1, 10])
lr, num_epochs, batch_size = 0.05, 10, 256
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())
DenseNet 稠密连接网络
用更高阶的泰勒展开，每一层都加上x
结构
由 稠密块（dense block）和 过渡层 （transition layer）构成。 前者定义如何连接输入和输出，而后者则通过 1×1 的卷积层来减小通道数，并使用步幅为 2 的平均池化层减半高和宽，控制通道数量。
torch实现
import torch
from torch import nn
from d2l import torch as d2l
def conv_block(input_channels, num_channels):
return nn.Sequential(
nn.BatchNorm2d(input_channels), nn.ReLU(),
nn.Conv2d(input_channels, num_channels, kernel_size=3, padding=1))
# 稠密层
class DenseBlock(nn.Module):
def __init__(self, num_convs, input_channels, num_channels):
super(DenseBlock, self).__init__()
layer = []
for i in range(num_convs):
layer.append(conv_block(
num_channels * i + input_channels, num_channels))
self.net = nn.Sequential(*layer)
def forward(self, X):
for blk in self.net:
Y = blk(X)
# 连接通道维度上每个块的输入和输出
X = torch.cat((X, Y), dim=1)
return X
blk = DenseBlock(2, 3, 10)
X = torch.randn(4, 3, 8, 8)
Y = blk(X)
Y.shape
# 过渡层
def transition_block(input_channels, num_channels):
return nn.Sequential(
nn.BatchNorm2d(input_channels), nn.ReLU(),
nn.Conv2d(input_channels, num_channels, kernel_size=1),
nn.AvgPool2d(kernel_size=2, stride=2))
blk = transition_block(23, 10)
blk(Y).shape
# DenseNet
b1 = nn.Sequential(
nn.Conv2d(1, 64, kernel_size=7, stride=2, padding=3),
nn.BatchNorm2d(64), nn.ReLU(),
nn.MaxPool2d(kernel_size=3, stride=2, padding=1))
num_channels, growth_rate = 64, 32
num_convs_in_dense_blocks = [4, 4, 4, 4]
blks = []
for i, num_convs in enumerate(num_convs_in_dense_blocks):
blks.append(DenseBlock(num_convs, num_channels, growth_rate))
# 上一个稠密块的输出通道数
num_channels += num_convs * growth_rate
# 在稠密块之间添加一个转换层，使通道数量减半
if i != len(num_convs_in_dense_blocks) - 1:
blks.append(transition_block(num_channels, num_channels // 2))
num_channels = num_channels // 2
#最后加上池化和全连接
net = nn.Sequential(
b1, *blks,
nn.BatchNorm2d(num_channels), nn.ReLU(),
nn.AdaptiveMaxPool2d((1, 1)),
nn.Flatten(),
nn.Linear(num_channels, 10))
lr, num_epochs, batch_size = 0.1, 10, 256
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())
