卷积神经网络convolutional neural network，CNN 是为处理图像数据而生的网络，主要由卷积层（填充和步幅）、池化层（汇聚层）、全连接层组成。

卷积

虽然卷积层得名于卷积（convolution）运算，但我们通常在卷积层中使用更加直观的互相关（cross-correlation）运算。
真实的卷积运算是f(a,b)g(i-a,j-b)，其实有一个取反的过程，但是我们实际代码里使用的是互相关运算。
输入的宽度为n，卷积核宽度为k，则输出宽度为n-k+1。
卷积层的参数包括卷积核和偏置，感受野receptive field指的是在前向传播期间影响x计算的所有元素（来自之前所有层）。
一般填充p行在上下，为了上下保持一致，卷积核一般是奇数的长度。输出变为n+p-k+1
滑动步幅为s时，输出变为(n+p-k+s)/s

多输入通道可以：构造相同通道的卷积核，最后对多通道求和输出
多输出通道可以：为每个输出通道o创建一个i*w*h的卷积核，有o个这样的卷积核。
1x1卷积层的作用：看作在每个像素位置应用的全连接层，把i个输入值转换为o个输出层。看这个博主的动图1x1卷积核，没有太明白。文章2 作用：降维/升维，增加非线性，跨通道信息交互。

LeNet

import torch
from torch import nn 
from torchvision import transforms
import torchvision
from torch.utils import data
import matplotlib.pyplot as plt
def load_data_fashion_mnist(batch_size, resize=None):"""下载Fashion-MNIST数据集，然后将其加载到内存中"""trans = [transforms.ToTensor()]if resize:trans.insert(0, transforms.Resize(resize))trans = transforms.Compose(trans)mnist_train = torchvision.datasets.FashionMNIST(root="../data", train=True, transform=trans, download=True)mnist_test = torchvision.datasets.FashionMNIST(root="../data", train=False, transform=trans, download=True)#print(len(mnist_train),len(mnist_test))return (data.DataLoader(mnist_train, batch_size, shuffle=True),data.DataLoader(mnist_test, batch_size, shuffle=False)) #windows下不能多进程,linux下可以
batch_size=256
train_iter, test_iter = load_data_fashion_mnist(batch_size)net=nn.Sequential(nn.Conv2d(1,6,kernel_size=5,padding=2),nn.Sigmoid(),nn.AvgPool2d(kernel_size=2,stride=2),nn.Conv2d(6,16,kernel_size=5),nn.Sigmoid(),nn.AvgPool2d(kernel_size=2,stride=2),nn.Flatten(),nn.Linear(16*5*5,120),nn.Sigmoid(),nn.Linear(120,84),nn.Sigmoid(),nn.Linear(84,10)
)def accuracy(y_hat, y): """计算预测正确的数量"""if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:y_hat = y_hat.argmax(axis=1)cmp = y_hat.type(y.dtype) == yreturn float(cmp.type(y.dtype).sum())
class Accumulator: """在n个变量上累加"""def __init__(self, n):self.data = [0.0] * ndef add(self, *args):self.data = [a + float(b) for a, b in zip(self.data, args)]def reset(self):self.data = [0.0] * len(self.data)def __getitem__(self, idx):return self.data[idx]
def evaluate_accuracy_gpu(net, data_iter, device=None): #@save"""使⽤GPU计算模型在数据集上的精度"""if isinstance(net, nn.Module):net.eval() # 设置为评估模式if not device:device = next(iter(net.parameters())).device# 正确预测的数量，总预测的数量metric = Accumulator(2)with torch.no_grad():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(accuracy(net(X), y), y.numel())return metric[0] / metric[1]def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):"""设置matplotlib的轴"""axes.set_xlabel(xlabel)axes.set_ylabel(ylabel)axes.set_xscale(xscale)axes.set_yscale(yscale)axes.set_xlim(xlim)axes.set_ylim(ylim)if legend:axes.legend(legend)axes.grid()
class Animator: """在动画中绘制数据"""def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,ylim=None, xscale='linear', yscale='linear',fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,figsize=(3.5, 2.5)):# 增量地绘制多条线if legend is None:legend = []self.fig, self.axes = plt.subplots(nrows, ncols, figsize=figsize)if nrows * ncols == 1:self.axes = [self.axes, ]# 使⽤lambda函数捕获参数self.config_axes = lambda: set_axes(self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)self.X, self.Y, self.fmts = None, None, fmtsdef add(self, x, y):# 向图表中添加多个数据点if not hasattr(y, "__len__"):y = [y]n = len(y)if not hasattr(x, "__len__"):x = [x] * nif not self.X:self.X = [[] for _ in range(n)]if not self.Y:self.Y = [[] for _ in range(n)]for i, (a, b) in enumerate(zip(x, y)):if a is not None and b is not None:self.X[i].append(a)self.Y[i].append(b)self.axes[0].cla()for x, y, fmt in zip(self.X, self.Y, self.fmts):self.axes[0].plot(x, y, fmt)self.config_axes()#display.display(self.fig)# 通过以下两行代码实现了在PyCharm中显示动图plt.draw()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):if type(m) == nn.Linear or type(m) == nn.Conv2d:nn.init.xavier_uniform_(m.weight)net.apply(init_weights)print('training on', device)net.to(device)optimizer = torch.optim.SGD(net.parameters(), lr=lr)loss = nn.CrossEntropyLoss()animator = Animator(xlabel='epoch', xlim=[1, num_epochs],legend=['train loss', 'train acc', 'test acc'])num_batches = len(train_iter)for epoch in range(num_epochs):# 训练损失之和，训练准确率之和，样本数metric = Accumulator(3)net.train()for i, (X, y) in enumerate(train_iter):optimizer.zero_grad()X, y = X.to(device), y.to(device)y_hat = net(X)l = loss(y_hat, y)l.backward()optimizer.step()with torch.no_grad():metric.add(l * X.shape[0], accuracy(y_hat, y), X.shape[0])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}')lr, num_epochs = 0.9, 10
def try_gpu(i=0): #@save"""如果存在，则返回gpu(i)，否则返回cpu()"""if torch.cuda.device_count() >= i + 1:return torch.device(f'cuda:{i}')return torch.device('cpu')
train_ch6(net, train_iter, test_iter, num_epochs, lr, try_gpu())

现代卷积神经网络

AlexNet 第一个击败传统模型的大型神经网络
VGG 使用重复的神经网络块
NiN 重复使用1x1卷积层构造深层网络
GoogLeNet 并行连结的网络
ResNet 残差网络 是计算机视觉最流行的体系架构 特点是跨层数据通路前向传播
DenseNet 是resnet的逻辑扩展（泰勒展开），使用的是cancat而不是相加，主要由稠密层和过渡层(1x1卷积核，降低通道数）构成