?十、CNN 卷積神經(jīng)網(wǎng)絡(luò) 基礎(chǔ)篇

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首先引入 ——

• 二維卷積：卷積層保留原空間信息
• 關(guān)鍵：判斷輸入輸出的維度大小
• 特征提取：卷積層、下采樣
• 分類器：全連接

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引例：RGB圖像（柵格圖像）

• 首先，老師介紹了CCD相機(jī)模型，這是一種通過(guò)光敏電阻，利用光強(qiáng)對(duì)電阻的阻值影響，對(duì)應(yīng)地影響色彩亮度實(shí)現(xiàn)不同亮度等級(jí)像素采集的原件。三色圖像是采用不同敏感度的光敏電阻實(shí)現(xiàn)的。
• 還介紹了矢量圖像（也就是PPT里通過(guò)圓心、邊、填充信息描述而來(lái)的圖像，而非采集的圖像）
• 紅綠藍(lán) Channel
• 拿出一個(gè)圖像塊做卷積，通道高度寬度都可能會(huì)改變，將整個(gè)圖像遍歷，每個(gè)塊分別做卷積

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引例：

深度學(xué)習(xí) | CNN卷積核與通道-CSDN博客

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?實(shí)現(xiàn)：A Simple Convolutional Neural Network

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• 池化層一個(gè)就行，因?yàn)樗麤](méi)有權(quán)重，但是有權(quán)重的，必須每一層做一個(gè)實(shí)例
• relu 非線性激活
• 交叉熵?fù)p失 最后一層不做激活！

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代碼實(shí)現(xiàn)：

import torch
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# 1、數(shù)據(jù)準(zhǔn)備
batch_size = 64
transform = transforms.Compose([transforms.ToTensor(),transforms.Normalize((0.1307,),(0.3081,))
])train_dataset = datasets.MNIST(root='../dataset/mnist',train=True,download=True,transform=transform)
train_loader = DataLoader(train_dataset,shuffle=True,batch_size=batch_size)test_dataset = datasets.MNIST(root='../dataset/mnist',train=False,download=True,transform=transform)
test_loader = DataLoader(test_dataset,shuffle=False,batch_size=batch_size)# 2、構(gòu)建模型
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 = self.pooling(F.relu(self.conv1(x)))x = self.pooling(F.relu(self.conv2(x)))x = x.view(batch_size,-1) #flattenx = self.fc(x)return xmodel = Net()# 3、損失函數(shù)和優(yōu)化器
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(),lr=0.01,momentum=0.5)# 4、訓(xùn)練和測(cè)試
def train(epoch):running_loss = 0.0for batch_idx,data in enumerate(train_loader,0):inputs,target = dataoptimizer.zero_grad()outputs = model(inputs)loss = criterion(outputs,target)loss.backward()optimizer.step()running_loss += loss.item()if batch_idx % 300 == 299: # 每三百次迭代輸出一次print('[%d , %5d] loss: %.3f' % (epoch + 1 ,batch_idx + 1,running_loss / 300))running_loss = 0.0def test():correct = 0total = 0with torch.no_grad():for data in test_loader:images,labels = dataoutputs = model(images) # 輸出為一個(gè)矩陣，下面要求每一行最大值(即分類)的下標(biāo)_,predicted = torch.max(outputs.data,dim=1)total += labels.size(0)correct += (predicted == labels).sum().item()print('Accuracy on test set: %d %%' % (100 * correct / total))if __name__ == '__main__':for epoch in range(10):train(epoch)test()

實(shí)驗(yàn)結(jié)果：

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十一、CNN 卷積神經(jīng)網(wǎng)絡(luò) 高級(jí)篇

基礎(chǔ)篇中設(shè)計(jì)的模型類似于LeNet5

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再來(lái)看一些更為復(fù)雜的結(jié)構(gòu)：

11.1、GoogLeNet

GoogLeNet是一種串行結(jié)構(gòu)的復(fù)雜網(wǎng)絡(luò)；想要實(shí)現(xiàn)復(fù)雜網(wǎng)絡(luò)，并且較少代碼冗余和多次重寫相同功能的程序，面向過(guò)程的語(yǔ)言使用函數(shù)，面向?qū)ο蟮恼Z(yǔ)言python使用類，

而在CNN當(dāng)中，使用Module和block這種模塊將具有復(fù)用價(jià)值的代碼塊封裝成一塊積木，供拼接使用；

GoogLeNet為自己框架里被重復(fù)使用的Module命名為Inception，這也電影盜夢(mèng)空間的英文名，意為：夢(mèng)中夢(mèng)、嵌套；

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Inception Module的構(gòu)造方式之一：

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• 為什么要做成這個(gè)樣子？
  • —— 在構(gòu)建神經(jīng)網(wǎng)絡(luò)時(shí)，一些超參數(shù)我們是難以確定的，比如卷積核的大小，所以你不知道哪個(gè)好用，那我就都用一下，將來(lái)通過(guò)訓(xùn)練，找到最優(yōu)的卷積組合。
  • GoogLeNet的設(shè)計(jì)思路是：我把各種形式的核都寫進(jìn)我的Block當(dāng)中，至于每一個(gè)支路的權(quán)重，讓網(wǎng)絡(luò)訓(xùn)練的時(shí)候自己去搭配；
• Concatenate：將四條通道算出來(lái)的張量拼接到一起
• GoogLeNet設(shè)計(jì)了四條通路支線，并要求他們保證圖像的寬和高W、H必須相同，只有通道數(shù)C可以不相同，因?yàn)?span style="background-color:#fefcd8;">各支線進(jìn)行過(guò)卷積和池化等操作后，要將W和H構(gòu)成的面為粘合面，按照C的方向，拼接concatenate起來(lái)；
• Average Pooling：均值池化
• 1x1的卷積可以將信息融合：也叫network in network（網(wǎng)絡(luò)里的網(wǎng)絡(luò)）
  • 1 * 1的卷積核：以往我只是表面上覺(jué)得，單位像素大小的卷積核，他的意義不過(guò)是調(diào)整輸入和輸出的通道數(shù)之間的關(guān)系；劉老師舉了個(gè)例子，讓我對(duì)這個(gè)卷積核有了新的認(rèn)識(shí)：
  • 就是加速運(yùn)算，他的作用的確是加速運(yùn)算，不過(guò)其中的原理是：通過(guò)1*1的核處理過(guò)的圖像，可以減少后續(xù)卷積層的輸入通道數(shù)；
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Inception塊 代碼實(shí)現(xiàn)：

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然后再沿著通道將他們拼接在一起：

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將四個(gè)分支可以放到一個(gè)列表里，然后用torch提供的函數(shù)cat沿著dim=1的維度將他們拼接起來(lái)

因?yàn)槲覀兊木S度是 batch，channel，width，height ，所以是第一個(gè)維度dim=1，索引從零開始，C的位置是1

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MNIST數(shù)據(jù)集 代碼實(shí)現(xiàn)：

初始的輸入通道并沒(méi)有寫死，而是作為構(gòu)造函數(shù)里的參數(shù)，這是因?yàn)槲覀儗?lái)實(shí)例化時(shí)可以指明輸入通道是多少。

先是1個(gè)卷積層(conv,maxpooling,relu)，然后inceptionA模塊(輸出的channels是24+16+24+24=88)，接下來(lái)又是一個(gè)卷積層(conv,mp,relu),然后inceptionA模塊，最后一個(gè)全連接層(fc)。

1408這個(gè)數(shù)據(jù)可以通過(guò)x = x.view(in_size, -1)后調(diào)用x.shape得到。

也可通過(guò)查看網(wǎng)絡(luò)結(jié)構(gòu)：

最后一層線性層的輸入尺寸（input size）1408是根據(jù)倒數(shù)第二個(gè)InceptionA模塊的輸出形狀推導(dǎo)出來(lái)的。在該模塊中，輸入形狀為[-1, 88, 4, 4]，其中-1表示批量大小（Batch Size）。因此，通過(guò)展平這個(gè)特征圖（Flatten），我們可以將其轉(zhuǎn)換為一維向量，即 [-1, 88 * 4 * 4] = [-1, 1408]。

所以，線性層的輸入尺寸為1408，它接收展平后的特征向量作為輸入，并將其映射到10個(gè)輸出類別的向量。

import torch
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optimfrom torchvision import models
from torchsummary import summary# 1、數(shù)據(jù)準(zhǔn)備
batch_size = 64
transform = transforms.Compose([transforms.ToTensor(),transforms.Normalize((0.1307,),(0.3081,))
])train_dataset = datasets.MNIST(root='../dataset/mnist',train=True,download=True,transform=transform)
train_loader = DataLoader(train_dataset,shuffle=True,batch_size=batch_size)test_dataset = datasets.MNIST(root='../dataset/mnist',train=False,download=True,transform=transform)
test_loader = DataLoader(test_dataset,shuffle=False,batch_size=batch_size)# 2、構(gòu)建模型
class InceptionA(torch.nn.Module):def __init__(self,in_channels):super(InceptionA,self).__init__()self.branch1x1 = torch.nn.Conv2d(in_channels,16,kernel_size=1)self.branch5x5_1 = torch.nn.Conv2d(in_channels,16,kernel_size=1)self.branch5x5_2 = torch.nn.Conv2d(16, 24, kernel_size=5,padding=2)self.branch3x3_1 = torch.nn.Conv2d(in_channels,16,kernel_size=1)self.branch3x3_2 = torch.nn.Conv2d(16, 24,kernel_size=3,padding=1)self.branch3x3_3 = torch.nn.Conv2d(24, 24, kernel_size=3, padding=1)self.branch_pool = torch.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(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(88,20,kernel_size=5)self.incep1 = InceptionA(in_channels=10)self.incep2 = InceptionA(in_channels=20)self.mp = torch.nn.MaxPool2d(2)self.fc = torch.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 xmodel = Net()
#summary(model,(1,28,28),device='cpu')# 3、損失函數(shù)和優(yōu)化器
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(),lr=0.01,momentum=0.5)# 4、訓(xùn)練和測(cè)試
def train(epoch):running_loss = 0.0for batch_idx,data in enumerate(train_loader,0):inputs,target = dataoptimizer.zero_grad()outputs = model(inputs)loss = criterion(outputs,target)loss.backward()optimizer.step()running_loss += loss.item()if batch_idx % 300 == 299: # 每三百次迭代輸出一次print('[%d , %5d] loss: %.3f' % (epoch + 1 ,batch_idx + 1,running_loss / 300))running_loss = 0.0def test():correct = 0total = 0with torch.no_grad():for data in test_loader:images,labels = dataoutputs = model(images) # 輸出為一個(gè)矩陣，下面要求每一行最大值(即分類)的下標(biāo)_,predicted = torch.max(outputs.data,dim=1)total += labels.size(0)correct += (predicted == labels).sum().item()print('Accuracy on test set: %d %%' % (100 * correct / total))if __name__ == '__main__':for epoch in range(10):train(epoch)test()

??????? Layer (type)?????????????? Output Shape???????? Param #
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??????????? Conv2d-1?????????? [-1, 10, 24, 24]???????????? 260
???????? MaxPool2d-2?????????? [-1, 10, 12, 12]?????????????? 0
??????????? Conv2d-3?????????? [-1, 16, 12, 12]???????????? 176
??????????? Conv2d-4?????????? [-1, 16, 12, 12]???????????? 176
??????????? Conv2d-5?????????? [-1, 24, 12, 12]?????????? 9,624
??????????? Conv2d-6?????????? [-1, 16, 12, 12]???????????? 176
??????????? Conv2d-7?????????? [-1, 24, 12, 12]?????????? 3,480
??????????? Conv2d-8?????????? [-1, 24, 12, 12]?????????? 5,208
??????????? Conv2d-9?????????? [-1, 24, 12, 12]???????????? 264
?????? InceptionA-10?????????? [-1, 88, 12, 12]?????????????? 0
?????????? Conv2d-11???????????? [-1, 20, 8, 8]????????? 44,020
??????? MaxPool2d-12???????????? [-1, 20, 4, 4]?????????????? 0
?????????? Conv2d-13???????????? [-1, 16, 4, 4]???????????? 336
?????????? Conv2d-14???????????? [-1, 16, 4, 4]???????????? 336
?????????? Conv2d-15???????????? [-1, 24, 4, 4]?????????? 9,624
?????????? Conv2d-16???????????? [-1, 16, 4, 4]???????????? 336
?????????? Conv2d-17???????????? [-1, 24, 4, 4]?????????? 3,480
?????????? Conv2d-18???????????? [-1, 24, 4, 4]?????????? 5,208
?????????? Conv2d-19???????????? [-1, 24, 4, 4]???????????? 504
?????? InceptionA-20???????????? [-1, 88, 4, 4]?????????????? 0
?????????? Linear-21?????????????????? [-1, 10]????????? 14,090?

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11.2、ResNet

GoogLeNet最后留下了一個(gè)問(wèn)題：通過(guò)測(cè)試，網(wǎng)絡(luò)的層數(shù)會(huì)影響模型的精度，但當(dāng)時(shí)沒(méi)有意識(shí)到梯度消失的問(wèn)題，

所以GoogLeNet認(rèn)為We Need To Go Deeper；

直到何凱明大神的ResNet的出現(xiàn)，提出了層數(shù)越多，模型效果不一定越好的問(wèn)題，

并針對(duì)這個(gè)問(wèn)題提出了解決方案ResNet網(wǎng)絡(luò)結(jié)構(gòu)。

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Residual Net提出了這樣一種塊：跳連接

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以往的網(wǎng)絡(luò)模型是這種Plain Net形式：

輸入數(shù)據(jù)x，經(jīng)過(guò)Weight Layer(可以是卷積層，也可以是池化或者線性層)，再通過(guò)激活函數(shù)加入非線性影響因素，最后輸出結(jié)果H(x)；

這種方式使得H(x)對(duì)x的偏導(dǎo)數(shù)的值分布在（0,1）之間，這在反向傳播、復(fù)合函數(shù)的偏導(dǎo)數(shù)逐步累乘的過(guò)程中，必然會(huì)導(dǎo)致?lián)p失函數(shù)L對(duì)x的偏導(dǎo)數(shù)的值，趨近于0，而且，網(wǎng)絡(luò)層數(shù)越深，這種現(xiàn)象就會(huì)越明顯，最終導(dǎo)致最開始的（也就是靠近輸入的）層沒(méi)有獲得有效的權(quán)重更新，甚至模型失效；

即梯度消失：假如每一處的梯度都小于1，由于我們使用的是反向傳播，當(dāng)梯度趨近于0時(shí)，那么權(quán)重得不到更新：，也就是說(shuō)離輸入近的塊沒(méi)辦法得到充分的訓(xùn)練。

解決方法：逐層訓(xùn)練，但層數(shù)過(guò)多會(huì)很難

ResNet采用了一個(gè)非常巧妙的方式解決了H(x)對(duì)x的偏導(dǎo)數(shù)的值分布在（0,1）之間這個(gè)問(wèn)題：

在以往的框架中，加入一個(gè)跳躍，再原有的網(wǎng)絡(luò)輸出F(x)的基礎(chǔ)上，將輸入x累加到上面，這樣一來(lái)，在最終輸出H(x)對(duì)輸入數(shù)據(jù)x求偏導(dǎo)數(shù)的時(shí)候，這個(gè)結(jié)果就會(huì)分布在（1,2）之間，這樣就不怕網(wǎng)絡(luò)在更新權(quán)重梯度累乘的過(guò)程中，出現(xiàn)乘積越來(lái)越趨于0而導(dǎo)致的梯度消失問(wèn)題；

與GoogLeNet類似，ResNet的Residual Block在搭建時(shí)，留了一個(gè)傳入?yún)?shù)的機(jī)會(huì)，這個(gè)參數(shù)留給了通道數(shù)channel，Residual Block的要求是輸入與輸出的C，W，H分別對(duì)應(yīng)相同，B是一定要相同的，所以就是說(shuō)，經(jīng)過(guò)殘差模塊Residual Block處理過(guò)的圖像，并不改變?cè)械某叽绾屯ǖ罃?shù)；(TBD)
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但是注意，因?yàn)橐蛒做加法，所以圖中的兩層輸出和輸入x 張量維度必須完全一樣，即通道高度寬度都要一樣

若輸出和輸入的維度不一樣，也可以做跳連接，可以將x過(guò)一個(gè)最大池化層轉(zhuǎn)換成同樣的大小，如下圖

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利用殘差結(jié)構(gòu)塊的網(wǎng)絡(luò)：

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先來(lái)看一下residual block的代碼實(shí)現(xiàn)：

為了保持輸入輸出的大小不變，所以要將padding設(shè)置為1，輸入通道和輸出通道都和x保持一致

注意第二個(gè)卷積之后，先做求和再激活

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MNIST數(shù)據(jù)集 代碼實(shí)現(xiàn)：

import torch
from torchvision import transforms
from torchvision import datasets
from torch.utils.data import DataLoader
import torch.nn.functional as F
import torch.optim as optimfrom torchvision import models
from torchsummary import summary
from torchviz import make_dot# 1、數(shù)據(jù)準(zhǔn)備
batch_size = 64
transform = transforms.Compose([transforms.ToTensor(),transforms.Normalize((0.1307,),(0.3081,))
])train_dataset = datasets.MNIST(root='../dataset/mnist',train=True,download=True,transform=transform)
train_loader = DataLoader(train_dataset,shuffle=True,batch_size=batch_size)test_dataset = datasets.MNIST(root='../dataset/mnist',train=False,download=True,transform=transform)
test_loader = DataLoader(test_dataset,shuffle=False,batch_size=batch_size)# 2、構(gòu)建模型
class InceptionA(torch.nn.Module):def __init__(self,in_channels):super(InceptionA,self).__init__()self.branch1x1 = torch.nn.Conv2d(in_channels,16,kernel_size=1)self.branch5x5_1 = torch.nn.Conv2d(in_channels,16,kernel_size=1)self.branch5x5_2 = torch.nn.Conv2d(16, 24, kernel_size=5,padding=2)self.branch3x3_1 = torch.nn.Conv2d(in_channels,16,kernel_size=1)self.branch3x3_2 = torch.nn.Conv2d(16, 24,kernel_size=3,padding=1)self.branch3x3_3 = torch.nn.Conv2d(24, 24, kernel_size=3, padding=1)self.branch_pool = torch.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 ResidualBlock(torch.nn.Module):def __init__(self,channels):super(ResidualBlock,self).__init__()self.channels = channelsself.conv1 = torch.nn.Conv2d(channels,channels,kernel_size=3,padding=1)self.conv2 = torch.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(torch.nn.Module):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.rblock1 = ResidualBlock(16)self.rblock2 = ResidualBlock(32)self.mp = torch.nn.MaxPool2d(2)self.fc = torch.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 xmodel = Net()
#x = torch.randn(1,1,28,28)
#y = model(x)
#vise=make_dot(y, params=dict(model.named_parameters()))
#vise.view()
#print(model)
#summary(model,(1,28,28),device='cpu')# 3、損失函數(shù)和優(yōu)化器
criterion = torch.nn.CrossEntropyLoss()
optimizer = optim.SGD(model.parameters(),lr=0.01,momentum=0.5)# 4、訓(xùn)練和測(cè)試
def train(epoch):running_loss = 0.0for batch_idx,data in enumerate(train_loader,0):inputs,target = dataoptimizer.zero_grad()outputs = model(inputs)loss = criterion(outputs,target)loss.backward()optimizer.step()running_loss += loss.item()if batch_idx % 300 == 299: # 每三百次迭代輸出一次print('[%d , %5d] loss: %.3f' % (epoch + 1 ,batch_idx + 1,running_loss / 300))running_loss = 0.0def test():correct = 0total = 0with torch.no_grad():for data in test_loader:images,labels = dataoutputs = model(images) # 輸出為一個(gè)矩陣，下面要求每一行最大值(即分類)的下標(biāo)_,predicted = torch.max(outputs.data,dim=1)total += labels.size(0)correct += (predicted == labels).sum().item()print('Accuracy on test set: %d %%' % (100 * correct / total))if __name__ == '__main__':for epoch in range(10):train(epoch)test()

?實(shí)驗(yàn)結(jié)果：

?????????

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課程最后劉老師推薦了兩篇論文：

??? Identity Mappings in Deep Residual Networks：

??? He K, Zhang X, Ren S, et al. Identity Mappings in Deep Residual Networks[C]

????????其中給出了很多不同種類的Residual Block變化的構(gòu)造形式；

?????????

??? Densely Connected Convolutional Networks：

??? Huang G, Liu Z, Laurens V D M, et al. Densely Connected Convolutional Networks[J]. 2016:2261-2269.?

?????????

????????大名鼎鼎的DenseNet，這個(gè)網(wǎng)絡(luò)結(jié)構(gòu)基于ResNet跳躍傳遞的思想，實(shí)現(xiàn)了多次跳躍的網(wǎng)絡(luò)結(jié)構(gòu)，以后很多通過(guò)神經(jīng)網(wǎng)絡(luò)提取多尺度、多層級(jí)的特征，都在利用這種方式，通過(guò)Encoder對(duì)不同層級(jí)的語(yǔ)義特征進(jìn)行逐步提取，在穿插著傳遞到Decoder過(guò)程中不同的層級(jí)上去，旨在融合不同層級(jí)的特征，盡可能地挖掘圖像全部的特征；

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學(xué)習(xí)方法

????????

全文資料及部分文字來(lái)源于 ——?

【Pytorch深度學(xué)習(xí)實(shí)踐】B站up劉二大人之BasicCNN & Advanced CNN -代碼理解與實(shí)現(xiàn)(9/9)_b站講神經(jīng)網(wǎng)絡(luò)的up土堆-CSDN博客

11.卷積神經(jīng)網(wǎng)絡(luò)（高級(jí)篇）_嗶哩嗶哩_bilibili

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