softmax的基本概念
- 分类问题
softmax函数主要是用于分类问题，一般在全连接层后面使用。 - 权重矢量
因此softmax运算不改变预测类别输出。softmax回归对样本分类的矢量计算表达式为
交叉熵损失函数
模型训练与预测
获取Fashion-MNIST训练集和读取数据
图像分类数据集中最常用的是手写数字识别数据集MNIST[1]。但大部分模型在MNIST上的分类精度都超过了95%。为了更直观地观察算法之间的差异，我们将使用一个图像内容更加复杂的数据集Fashion-MNIST[2]。
我这里我们会使用torchvision包，主要用来构建计算机视觉模型。torchvision主要由以下几部分构成：
- torchvision.datasets: 一些加载数据的函数及常用的数据集接口；
- torchvision.models: 包含常用的模型结构（含预训练模型），例如AlexNet、VGG、ResNet等；
- torchvision.transforms: 常用的图片变换，例如裁剪、旋转等；
- torchvision.utils: 其他的一些有用的方法。
%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/input") import d2lzh1981 as d2l #获取数据 mnist_train = torchvision.datasets.FashionMNIST(root='/home/input/FashionMNIST2065', train=True, download=True, transform=transforms.ToTensor()) mnist_test = torchvision.datasets.FashionMNIST(root='/home/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。
#显示结果 print(type(mnist_train)) print(len(mnist_train), len(mnist_test))
输出：<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 输出torch.Size([1, 28, 28]) 9 mnist_PIL = torchvision.datasets.FashionMNIST(root='/home/kesci/input/FashionMNIST2065', train=True, download=True) PIL_feature, label = mnist_PIL[0] # 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))
输出：
# 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)
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 #获取数据 batch_size = 256 train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, root='/home/input/FashionMNIST2065') #模型参数初始化 num_inputs = 784 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) W.requires_grad_(requires_grad=True) b.requires_grad_(requires_grad=True)
输出：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
输出：tensor([[5, 7, 9]]) tensor([[ 6], [15]]) tensor([5, 7, 9]) tensor([ 6, 15])
定义softmax操作
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))
输出：tensor([[0.2767, 0.1386, 0.1364, 0.1738, 0.2746], [0.1855, 0.1690, 0.1513, 0.3168, 0.1774]]) tensor([1.0000, 1.0000])
softmax回归模型
def net(X): return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)
定义损失函数
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)) #1表示按行相加 def cross_entropy(y_hat, y): return - torch.log(y_hat.gather(1, y.view(-1, 1)))
定义准确率
def accuracy(y_hat, y): return (y_hat.argmax(dim=1) == y).float().mean().item() #y_hat按行取最大的值与y比较 # 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): #data_iter是取数据的，net是网络 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
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)
模型预测
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/input") import d2lzh1981 as d2l #初始化 batch_size = 256 train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size, root='/home/input/FashionMNIST2065') #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) loss = nn.CrossEntropyLoss() optimizer = torch.optim.SGD(net.parameters(), lr=0.1) num_epochs = 5 d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size, None, None, optimizer)
参考文献
[1]《动手深度学习》李沐
[2]伯禹教育课程
![Pytorch教程[07]损失函数](https://ucc.alicdn.com/pic/developer-ecology/5bc1c18e60eb4e468cdd38975a3aab61.png?x-oss-process=image/resize,h_160,m_lfit)
