Softmax

# import needed package
%matplotlib inline
from IPython import display
import matplotlib.pyplot as plt

import torch
import torchvision
import torchvision.transforms as transforms
import time

import sys
sys.path.append("/home/kesci/input")
import d2lzh1981 as d2l

print(torch.__version__)
print(torchvision.__version__)
1.3.0
0.4.1a0+d94043a
get dataset
mnist_train = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True, transform=transforms.ToTensor())
mnist_test = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=False, download=True, transform=transforms.ToTensor())
class torchvision.datasets.FashionMNIST(root, train=True, transform=None, target_transform=None, download=False)

root（string）– 数据集的根目录，其中存放processed/training.pt和processed/test.pt文件。
train（bool, 可选）– 如果设置为True，从training.pt创建数据集，否则从test.pt创建。
download（bool, 可选）– 如果设置为True，从互联网下载数据并放到root文件夹下。如果root目录下已经存在数据，不会再次下载。
transform（可被调用 , 可选）– 一种函数或变换，输入PIL图片，返回变换之后的数据。如：transforms.RandomCrop。
target_transform（可被调用 , 可选）– 一种函数或变换，输入目标，进行变换。
# show result 
print(type(mnist_train))
print(len(mnist_train), len(mnist_test))
<class 'torchvision.datasets.mnist.FashionMNIST'>
60000 10000
# 我们可以通过下标来访问任意一个样本
feature, label = mnist_train[0]
print(feature.shape, label)  # Channel x Height x Width
torch.Size([1, 28, 28]) 9
如果不做变换输入的数据是图像，我们可以看一下图片的类型参数：

mnist_PIL = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True)
PIL_feature, label = mnist_PIL[0]
print(PIL_feature)
<PIL.Image.Image image mode=L size=28x28 at 0x7F57E8736F28>
# 本函数已保存在d2lzh包中方便以后使用
def get_fashion_mnist_labels(labels):
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]
def show_fashion_mnist(images, labels):
    d2l.use_svg_display()
    # 这里的_表示我们忽略（不使用）的变量
    _, figs = plt.subplots(1, len(images), figsize=(12, 12))
    for f, img, lbl in zip(figs, images, labels):
        f.imshow(img.view((28, 28)).numpy())
        f.set_title(lbl)
        f.axes.get_xaxis().set_visible(False)
        f.axes.get_yaxis().set_visible(False)
    plt.show()
X, y = [], []
for i in range(10):
    X.append(mnist_train[i][0]) # 将第i个feature加到X中
    y.append(mnist_train[i][1]) # 将第i个label加到y中
show_fashion_mnist(X, get_fashion_mnist_labels(y))

# 读取数据
batch_size = 256
num_workers = 4
train_iter = torch.utils.data.DataLoader(mnist_train, batch_size=batch_size, shuffle=True, num_workers=num_workers)
test_iter = torch.utils.data.DataLoader(mnist_test, batch_size=batch_size, shuffle=False, num_workers=num_workers)
start = time.time()
for X, y in train_iter:
    continue
print('%.2f sec' % (time.time() - start))
4.89 sec
softmax从零开始的实现
import torch
import torchvision
import numpy as np
import sys
sys.path.append("/home/kesci/input")
import d2lzh1981 as d2l

print(torch.__version__)
print(torchvision.__version__)
1.3.0
0.4.1a0+d94043a
获取训练集数据和测试集数据
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
模型参数初始化
num_inputs = 784
print(28*28)
num_outputs = 10

W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float)
b = torch.zeros(num_outputs, dtype=torch.float)
784
W.requires_grad_(requires_grad=True)
b.requires_grad_(requires_grad=True)
tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], requires_grad=True)
对多维Tensor按维度操作
X = torch.tensor([[1, 2, 3], [4, 5, 6]])
print(X.sum(dim=0, keepdim=True))  # dim为0，按照相同的列求和，并在结果中保留列特征
print(X.sum(dim=1, keepdim=True))  # dim为1，按照相同的行求和，并在结果中保留行特征
print(X.sum(dim=0, keepdim=False)) # dim为0，按照相同的列求和，不在结果中保留列特征
print(X.sum(dim=1, keepdim=False)) # dim为1，按照相同的行求和，不在结果中保留行特征
tensor([[5, 7, 9]])
tensor([[ 6],
        [15]])
tensor([5, 7, 9])
tensor([ 6, 15])
定义softmax操作
y^j=exp(oj)∑3i=1exp(oi)
 
def softmax(X):
    X_exp = X.exp()
    partition = X_exp.sum(dim=1, keepdim=True)
    # print("X size is ", X_exp.size())
    # print("partition size is ", partition, partition.size())
    return X_exp / partition  # 这里应用了广播机制
X = torch.rand((2, 5))
X_prob = softmax(X)
print(X_prob, '\n', X_prob.sum(dim=1))
tensor([[0.1927, 0.2009, 0.1823, 0.1887, 0.2355],
        [0.1274, 0.1843, 0.2536, 0.2251, 0.2096]]) 
 tensor([1., 1.])
softmax回归模型
o(i)y^(i)=x(i)W+b,=softmax(o(i)).
 
def net(X):
    return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)
定义损失函数
H(y(i),y^(i))=−∑j=1qy(i)jlogy^(i)j,
 
ℓ(Θ)=1n∑i=1nH(y(i),y^(i)),
 
ℓ(Θ)=−(1/n)∑i=1nlogy^(i)y(i)
 
y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])
y = torch.LongTensor([0, 2])
y_hat.gather(1, y.view(-1, 1))
tensor([[0.1000],
        [0.5000]])
def cross_entropy(y_hat, y):
    return - torch.log(y_hat.gather(1, y.view(-1, 1)))
定义准确率
我们模型训练完了进行模型预测的时候，会用到我们这里定义的准确率。
def accuracy(y_hat, y):
    return (y_hat.argmax(dim=1) == y).float().mean().item()
print(accuracy(y_hat, y))
0.5
# 本函数已保存在d2lzh_pytorch包中方便以后使用。该函数将被逐步改进：它的完整实现将在“图像增广”一节中描述
def evaluate_accuracy(data_iter, net):
    acc_sum, n = 0.0, 0
    for X, y in data_iter:
        acc_sum += (net(X).argmax(dim=1) == y).float().sum().item()
        n += y.shape[0]
    return acc_sum / n
print(evaluate_accuracy(test_iter, net))
0.1457
训练模型
num_epochs, lr = 5, 0.1

# 本函数已保存在d2lzh_pytorch包中方便以后使用
def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,
              params=None, lr=None, optimizer=None):
    for epoch in range(num_epochs):
        train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
        for X, y in train_iter:
            y_hat = net(X)
            l = loss(y_hat, y).sum()
            
            # 梯度清零
            if optimizer is not None:
                optimizer.zero_grad()
            elif params is not None and params[0].grad is not None:
                for param in params:
                    param.grad.data.zero_()
            
            l.backward()
            if optimizer is None:
                d2l.sgd(params, lr, batch_size)
            else:
                optimizer.step() 
            
            
            train_l_sum += l.item()
            train_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()
            n += y.shape[0]
        test_acc = evaluate_accuracy(test_iter, net)
        print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'
              % (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))

train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, batch_size, [W, b], lr)
epoch 1, loss 0.7870, train acc 0.751, test acc 0.794
epoch 2, loss 0.5702, train acc 0.813, test acc 0.809
epoch 3, loss 0.5254, train acc 0.826, test acc 0.814
epoch 4, loss 0.5009, train acc 0.832, test acc 0.822
epoch 5, loss 0.4853, train acc 0.837, test acc 0.828
模型预测
现在我们的模型训练完了，可以进行一下预测，我们的这个模型训练的到底准确不准确。 现在就可以演示如何对图像进行分类了。给定一系列图像（第三行图像输出），我们比较一下它们的真实标签（第一行文本输出）和模型预测结果（第二行文本输出）。

X, y = iter(test_iter).next()

true_labels = d2l.get_fashion_mnist_labels(y.numpy())
pred_labels = d2l.get_fashion_mnist_labels(net(X).argmax(dim=1).numpy())
titles = [true + '\n' + pred for true, pred in zip(true_labels, pred_labels)]

d2l.show_fashion_mnist(X[0:9], titles[0:9])

softmax的简洁实现
# 加载各种包或者模块
import torch
from torch import nn
from torch.nn import init
import numpy as np
import sys
sys.path.append("/home/kesci/input")
import d2lzh1981 as d2l

print(torch.__version__)
1.3.0
初始化参数和获取数据
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
定义网络模型
num_inputs = 784
num_outputs = 10

class LinearNet(nn.Module):
    def __init__(self, num_inputs, num_outputs):
        super(LinearNet, self).__init__()
        self.linear = nn.Linear(num_inputs, num_outputs)
    def forward(self, x): # x 的形状: (batch, 1, 28, 28)
        y = self.linear(x.view(x.shape[0], -1))
        return y
    
# net = LinearNet(num_inputs, num_outputs)

class FlattenLayer(nn.Module):
    def __init__(self):
        super(FlattenLayer, self).__init__()
    def forward(self, x): # x 的形状: (batch, *, *, ...)
        return x.view(x.shape[0], -1)

from collections import OrderedDict
net = nn.Sequential(
        # FlattenLayer(),
        # LinearNet(num_inputs, num_outputs) 
        OrderedDict([
           ('flatten', FlattenLayer()),
           ('linear', nn.Linear(num_inputs, num_outputs))]) # 或者写成我们自己定义的 LinearNet(num_inputs, num_outputs) 也可以
        )
初始化模型参数
init.normal_(net.linear.weight, mean=0, std=0.01)
init.constant_(net.linear.bias, val=0)
Parameter containing:
tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], requires_grad=True)
定义损失函数
loss = nn.CrossEntropyLoss() # 下面是他的函数原型
# class torch.nn.CrossEntropyLoss(weight=None, size_average=None, ignore_index=-100, reduce=None, reduction='mean')
定义优化函数
optimizer = torch.optim.SGD(net.parameters(), lr=0.1) # 下面是函数原型
# class torch.optim.SGD(params, lr=, momentum=0, dampening=0, weight_decay=0, nesterov=False)
训练
num_epochs = 5
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, optimizer)
epoch 1, loss 0.0031, train acc 0.749, test acc 0.794
epoch 2, loss 0.0022, train acc 0.814, test acc 0.800
epoch 3, loss 0.0021, train acc 0.826, test acc 0.811
epoch 4, loss 0.0020, train acc 0.833, test acc 0.826
epoch 5, loss 0.0019, train acc 0.837, test acc 0.825