深度学习--全连接层、高阶应用、GPU加速

MSE均方差
Cross Entropy Loss：交叉熵损失

Entropy 熵：

1948年，香农将统计物理中熵的概念，引申到信道通信的过程中，从而开创了信息论这门学科，把信息中排除了冗余后的平均信息量称为“信息熵”。香农定义的“熵”又被称为香农熵或信息熵，即

其中标记概率空间中所有可能的样本，表示该样本的出现几率，是和单位选取相关的任意常数。

针对此问题，熵越大，不确定程度就越大，对于其中信息量的讨论参考知乎。

在信息学里信息量大代表着数据离散范围小，不确定性小。香农作为一个信息学家，他关心的是信息的正确传递，所以信息熵代表着信息传递的不确定性的大小。所以在信息学上，使用香农公式算出来的这个值，在信息学上叫做信息熵值，在熵权法中叫做冗余度值或者叫偏离度值，它的本来含义是指一个确定无疑的信息源发送出来的信息，受到干扰以后，衡量偏离了原始精确信息的程度。离散度越大，计算得这个值越小，则收到的信息越不可靠，得到的信息越小。这个值越大，则收到的信息越可靠，得到的信息越多。

在统计学里，就完全不是这样。统计学家不认为存在仅有一个的确定无疑的原始信息。而是认为收到的统计数字都是确信无疑的，只是由于发送主体可能是很多主体，或者是同一主体不同时间，不同地点，或者是统计渠道不同等等原因，得到了一组具有离散性的数值。在这种情况下，离散性越大，熵值越小，代表着信息量越大，所以权重越大。

 a=torch.full([4],1/4)
#tensor([0.2500, 0.2500, 0.2500, 0.2500])
 
#计算交叉熵
-(a*torch.log2(a)).sum()
#tensor(2.)

交叉熵在神经网络中作为损失函数，p表示真实标记的分布，q则为训练后的模型的预测标记分布，交叉熵损失函数可以衡量p与q的相似性。交叉熵作为损失函数还有一个好处是使用sigmoid函数在梯度下降时能避免均方误差损失函数学习速率降低的问题，因为学习速率可以被输出的误差所控制。

交叉熵计算：H(p,q)=

MNIST再实现

 import  torch
import  torch.nn as nn
import  torch.nn.functional as F
import  torch.optim as optim
from    torchvision import datasets, transforms
 
 
batch_size=200
learning_rate=0.01
epochs=10
 
#加载数据集DataLoader(数据位置，batch_size,shuffle是否打乱，num_workers=4:4线程处理）
    #torchvision.datasets.MNIST(root,train,transform,download)   root指下载到的位置，train指是否下载训练集，transform指对图片进行转换后返回，download指是否下载
        #torchvision.transforms([transforms.ToTensor(),transforms.Normalize((mean),(std))])
            #transforms.ToTensor()做了三件事：1.归一化/255 2.数据类型转为torch.FloatTensor  3.shape(H,W,C)->(C,H,W)
            #transforms.Normalize((mean),(std)) :用均值和标准差对张量图像进行归一化
 
train_loader = torch.utils.data.DataLoader(
    datasets.MNIST('../data', train=True, download=True,
                   transform=transforms.Compose([
                       transforms.ToTensor(),
                       transforms.Normalize((0.1307,), (0.3081,))
                   ])),
    batch_size=batch_size, shuffle=True)
test_loader = torch.utils.data.DataLoader(
    datasets.MNIST('../data', train=False, transform=transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
    ])),
    batch_size=batch_size, shuffle=True)
 
 
 
w1, b1 = torch.randn(200, 784, requires_grad=True),\
         torch.zeros(200, requires_grad=True)
w2, b2 = torch.randn(200, 200, requires_grad=True),\
         torch.zeros(200, requires_grad=True)
w3, b3 = torch.randn(10, 200, requires_grad=True),\
         torch.zeros(10, requires_grad=True)
 
torch.nn.init.kaiming_normal_(w1)
torch.nn.init.kaiming_normal_(w2)
torch.nn.init.kaiming_normal_(w3)
 
 
def forward(x):
    x = x@w1.t() + b1
    x = F.relu(x)
    x = x@w2.t() + b2
    x = F.relu(x)
    x = x@w3.t() + b3
    x = F.relu(x)
    return x
 
 
 
optimizer = optim.SGD([w1, b1, w2, b2, w3, b3], lr=learning_rate)
criteon = nn.CrossEntropyLoss()
 
for epoch in range(epochs):
 
    for batch_idx, (data, target) in enumerate(train_loader):
        data = data.view(-1, 28*28)
 
        logits = forward(data)
#        print(data.shape, target.shape,logits.shape)
 
        loss = criteon(logits, target)
 
        optimizer.zero_grad()
        loss.backward()
        # print(w1.grad.norm(), w2.grad.norm())
        optimizer.step()
 
        if batch_idx % 100 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                       100. * batch_idx / len(train_loader), loss.item()))
 
 
    test_loss = 0
    correct = 0
    for data, target in test_loader:
        data = data.view(-1, 28 * 28)
        logits = forward(data)
        test_loss += criteon(logits, target).item()
 
        pred = logits.data.max(1)[1]
        #print(pred)
        correct += pred.eq(target.data).sum()
 
    test_loss /= len(test_loader.dataset)
    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

全连接层

 import torch
import torch.nn as nn
import torch.nn.functional as F
 
x=torch.randn(1,784)
x.shape
#torch.Size([1, 784])
 
# nn.Linear(输入、输出）
layer1 = nn.Linear(784,200)
layer2 = nn.Linear(200,200)
layer3 = nn.Linear(200,10)
 
x=layer1(x)
x=F.relu(x,inplace=True)
x.shape
#torch.Size([1, 200])
 
x=layer2(x)
x=F.relu(x,inplace=True)
x.shape
#torch.Size([1, 200])
 
x=layer3(x)
x=F.relu(x,inplace=True)
x.shape
#torch.Size([1, 10])

网络定义的高阶用法

 import torch
import torch.nn as nn
import torch.nn.functional as F
import  torch.optim as optim
 
class MLP(nn.Module):
    
    def __init__(self):
        super(MLP,self).__init__()
        
        self.model = nn.Sequential(
            nn.Linear(784,200),
            nn.ReLU(inplace=True),
            nn.Linear(200,200),
            nn.ReLU(inplace=True),
            nn.Linear(200,10),
            nn.ReLU(inplace=True),
        )
 
    def forward(self,x):
        x=self.model(x)
        return x
 
net= MLP()
optimizer = optim.SGD(net.parameters(),lr=learning_rate)
criteon = nn.CrossEntropyLoss()

其他的激活函数 SELU、softplus、

GPU加速

 import  torch
import  torch.nn as nn
import  torch.nn.functional as F
import  torch.optim as optim
from    torchvision import datasets, transforms
 
 
batch_size=200
learning_rate=0.01
epochs=10
 
#加载数据集DataLoader(数据位置，batch_size,shuffle是否打乱，num_workers=4:4线程处理）
    #torchvision.datasets.MNIST(root,train,transform,download)   root指下载到的位置，train指是否下载训练集，transform指对图片进行转换后返回，download指是否下载
        #torchvision.transforms([transforms.ToTensor(),transforms.Normalize((mean),(std))])
            #transforms.ToTensor()做了三件事：1.归一化/255 2.数据类型转为torch.FloatTensor  3.shape(H,W,C)->(C,H,W)
            #transforms.Normalize((mean),(std)) :用均值和标准差对张量图像进行归一化
 
train_loader = torch.utils.data.DataLoader(
    datasets.MNIST('../data', train=True, download=True,
                   transform=transforms.Compose([
                       transforms.ToTensor(),
                       transforms.Normalize((0.1307,), (0.3081,))
                   ])),
    batch_size=batch_size, shuffle=True)
test_loader = torch.utils.data.DataLoader(
    datasets.MNIST('../data', train=False, transform=transforms.Compose([
        transforms.ToTensor(),
        transforms.Normalize((0.1307,), (0.3081,))
    ])),
    batch_size=batch_size, shuffle=True)
 
 
class MLP(nn.Module):
 
    def __init__(self):
        super(MLP, self).__init__()
 
        self.model = nn.Sequential(
            nn.Linear(784, 200),
            nn.LeakyReLU(inplace=True),
            nn.Linear(200, 200),
            nn.LeakyReLU(inplace=True),
            nn.Linear(200, 10),
            nn.LeakyReLU(inplace=True),
        )
 
    def forward(self,x):
        x=self.model(x)
        return x
 
    
##重点重点！！！ 
 
device=torch.device('cuda:0')
net = MLP().to(device)
optimizer = optim.SGD(net.parameters(),lr=learning_rate)
criteon = nn.CrossEntropyLoss().to(device)
 
 
for epoch in range(epochs):
 
    for batch_idx, (data, target) in enumerate(train_loader):
        data = data.view(-1, 28*28)
        data,target = data.to(device),target.to(device)
 
 
        logits = net(data)
#        print(data.shape, target.shape,logits.shape)
 
        loss = criteon(logits, target)
 
        optimizer.zero_grad()
        loss.backward()
        # print(w1.grad.norm(), w2.grad.norm())
        optimizer.step()
 
        if batch_idx % 100 == 0:
            print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
                epoch, batch_idx * len(data), len(train_loader.dataset),
                       100. * batch_idx / len(train_loader), loss.item()))
 
 
    test_loss = 0
    correct = 0
    for data, target in test_loader:
        data = data.view(-1, 28 * 28)
        data, target = data.to(device), target.to(device)
        logits = net(data)
        test_loss += criteon(logits, target).item()
 
        pred = logits.data.max(1)[1]
        #print(pred)
        correct += pred.eq(target.data).sum()
 
    test_loss /= len(test_loader.dataset)
    print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
        test_loss, correct, len(test_loader.dataset),
        100. * correct / len(test_loader.dataset)))

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原文地址：https://www.cnblogs.com/ssl-study/p/17343719.html

	a=torch.full([4],1/4)
	#tensor([0.2500, 0.2500, 0.2500, 0.2500])

	#计算交叉熵
	-(a*torch.log2(a)).sum()
	#tensor(2.)

	import torch
	import torch.nn as nn
	import torch.nn.functional as F
	import torch.optim as optim
	from torchvision import datasets, transforms


	batch_size=200
	learning_rate=0.01
	epochs=10

	#加载数据集DataLoader(数据位置，batch_size,shuffle是否打乱，num_workers=4:4线程处理）
	#torchvision.datasets.MNIST(root,train,transform,download) root指下载到的位置，train指是否下载训练集，transform指对图片进行转换后返回，download指是否下载
	#torchvision.transforms([transforms.ToTensor(),transforms.Normalize((mean),(std))])
	#transforms.ToTensor()做了三件事：1.归一化/255 2.数据类型转为torch.FloatTensor 3.shape(H,W,C)->(C,H,W)
	#transforms.Normalize((mean),(std)) :用均值和标准差对张量图像进行归一化

	train_loader = torch.utils.data.DataLoader(
	datasets.MNIST('../data', train=True, download=True,
	transform=transforms.Compose([
	transforms.ToTensor(),
	transforms.Normalize((0.1307,), (0.3081,))
	])),
	batch_size=batch_size, shuffle=True)
	test_loader = torch.utils.data.DataLoader(
	datasets.MNIST('../data', train=False, transform=transforms.Compose([
	transforms.ToTensor(),
	transforms.Normalize((0.1307,), (0.3081,))
	])),
	batch_size=batch_size, shuffle=True)



	w1, b1 = torch.randn(200, 784, requires_grad=True),\
	torch.zeros(200, requires_grad=True)
	w2, b2 = torch.randn(200, 200, requires_grad=True),\
	torch.zeros(200, requires_grad=True)
	w3, b3 = torch.randn(10, 200, requires_grad=True),\
	torch.zeros(10, requires_grad=True)

	torch.nn.init.kaiming_normal_(w1)
	torch.nn.init.kaiming_normal_(w2)
	torch.nn.init.kaiming_normal_(w3)


	def forward(x):
	x = x@w1.t() + b1
	x = F.relu(x)
	x = x@w2.t() + b2
	x = F.relu(x)
	x = x@w3.t() + b3
	x = F.relu(x)
	return x



	optimizer = optim.SGD([w1, b1, w2, b2, w3, b3], lr=learning_rate)
	criteon = nn.CrossEntropyLoss()

	for epoch in range(epochs):

	for batch_idx, (data, target) in enumerate(train_loader):
	data = data.view(-1, 28*28)

	logits = forward(data)
	# print(data.shape, target.shape,logits.shape)

	loss = criteon(logits, target)

	optimizer.zero_grad()
	loss.backward()
	# print(w1.grad.norm(), w2.grad.norm())
	optimizer.step()

	if batch_idx % 100 == 0:
	print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format(
	epoch, batch_idx * len(data), len(train_loader.dataset),
	100. * batch_idx / len(train_loader), loss.item()))


	test_loss = 0
	correct = 0
	for data, target in test_loader:
	data = data.view(-1, 28 * 28)
	logits = forward(data)
	test_loss += criteon(logits, target).item()

	pred = logits.data.max(1)[1]
	#print(pred)
	correct += pred.eq(target.data).sum()

	test_loss /= len(test_loader.dataset)
	print('\nTest set: Average loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
	test_loss, correct, len(test_loader.dataset),
	100. * correct / len(test_loader.dataset)))