一、卷積神經網絡

卷積神經網絡（ConvolutionalNeuralNetwork，CNN）最初是為解決圖像識別等問題設計的，CNN現在的應用已經不限于圖像和視頻，也可用于時間序列信號，比如音頻信號和文本數據等。CNN作為一個深度學習架構被提出的最初訴求是降低對圖像數據預處理的要求，避免復雜的特征工程。在卷積神經網絡中，第一個卷積層會直接接受圖像像素級的輸入，每一層卷積（濾波器）都會提取數據中最有效的特征，這種方法可以提取到圖像中最基礎的特征，而后再進行組合和抽象形成更高階的特征，因此CNN在理論上具有對圖像縮放、平移和旋轉的不變性。

卷積神經網絡CNN的要點就是局部連接（LocalConnection）、權值共享（WeightsSharing）和池化層（Pooling）中的降采樣（Down-Sampling）。其中，局部連接和權值共享降低了參數量，使訓練復雜度大大下降并減輕了過擬合。同時權值共享還賦予了卷積網絡對平移的容忍性，池化層降采樣則進一步降低了輸出參數量并賦予模型對輕度形變的容忍性，提高了模型的泛化能力。可以把卷積層卷積操作理解為用少量參數在圖像的多個位置上提取相似特征的過程。

二、代碼實現

import torch import torch.nn as nn from torch.autograd import Variable import torch.utils.data as Data import torchvision import matplotlib.pyplot as plt  torch.manual_seed(1)  EPOCH = 1 BATCH_SIZE = 50 LR = 0.001 DOWNLOAD_MNIST = True  # 獲取訓練集dataset training_data = torchvision.datasets.MNIST(        root='./mnist/', # dataset存儲路徑        train=True, # True表示是train訓練集，False表示test測試集        transform=torchvision.transforms.ToTensor(), # 將原數據規范化到（0,1）區間        download=DOWNLOAD_MNIST,        )  # 打印MNIST數據集的訓練集及測試集的尺寸 print(training_data.train_data.size()) print(training_data.train_labels.size()) # torch.Size([60000, 28, 28]) # torch.Size([60000])  plt.imshow(training_data.train_data[0].numpy(), cmap='gray') plt.title('%i' % training_data.train_labels[0]) plt.show()  # 通過torchvision.datasets獲取的dataset格式可直接可置于DataLoader train_loader = Data.DataLoader(dataset=training_data, batch_size=BATCH_SIZE,                 shuffle=True)  # 獲取測試集dataset test_data = torchvision.datasets.MNIST(root='./mnist/', train=False) # 取前2000個測試集樣本 test_x = Variable(torch.unsqueeze(test_data.test_data, dim=1),          volatile=True).type(torch.FloatTensor)[:2000]/255 # (2000, 28, 28) to (2000, 1, 28, 28), in range(0,1) test_y = test_data.test_labels[:2000]  class CNN(nn.Module):   def __init__(self):     super(CNN, self).__init__()     self.conv1 = nn.Sequential( # (1,28,28)            nn.Conv2d(in_channels=1, out_channels=16, kernel_size=5,                 stride=1, padding=2), # (16,28,28)     # 想要con2d卷積出來的圖片尺寸沒有變化, padding=(kernel_size-1)/2            nn.ReLU(),            nn.MaxPool2d(kernel_size=2) # (16,14,14)            )     self.conv2 = nn.Sequential( # (16,14,14)            nn.Conv2d(16, 32, 5, 1, 2), # (32,14,14)            nn.ReLU(),            nn.MaxPool2d(2) # (32,7,7)            )     self.out = nn.Linear(32*7*7, 10)    def forward(self, x):     x = self.conv1(x)     x = self.conv2(x)     x = x.view(x.size(0), -1) # 將（batch，32,7,7）展平為（batch，32*7*7）     output = self.out(x)     return output  cnn = CNN() print(cnn) ''''' CNN (  (conv1): Sequential (   (0): Conv2d(1, 16, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))   (1): ReLU ()   (2): MaxPool2d (size=(2, 2), stride=(2, 2), dilation=(1, 1))  )  (conv2): Sequential (   (0): Conv2d(16, 32, kernel_size=(5, 5), stride=(1, 1), padding=(2, 2))   (1): ReLU ()   (2): MaxPool2d (size=(2, 2), stride=(2, 2), dilation=(1, 1))  )  (out): Linear (1568 -> 10) ) ''' optimizer = torch.optim.Adam(cnn.parameters(), lr=LR) loss_function = nn.CrossEntropyLoss()  for epoch in range(EPOCH):   for step, (x, y) in enumerate(train_loader):     b_x = Variable(x)     b_y = Variable(y)      output = cnn(b_x)     loss = loss_function(output, b_y)     optimizer.zero_grad()     loss.backward()     optimizer.step()      if step % 100 == 0:       test_output = cnn(test_x)       pred_y = torch.max(test_output, 1)[1].data.squeeze()       accuracy = sum(pred_y == test_y) / test_y.size(0)       print('Epoch:', epoch, '|Step:', step,          '|train loss:%.4f'%loss.data[0], '|test accuracy:%.4f'%accuracy)  test_output = cnn(test_x[:10]) pred_y = torch.max(test_output, 1)[1].data.numpy().squeeze() print(pred_y, 'prediction number') print(test_y[:10].numpy(), 'real number') ''''' Epoch: 0 |Step: 0 |train loss:2.3145 |test accuracy:0.1040 Epoch: 0 |Step: 100 |train loss:0.5857 |test accuracy:0.8865 Epoch: 0 |Step: 200 |train loss:0.0600 |test accuracy:0.9380 Epoch: 0 |Step: 300 |train loss:0.0996 |test accuracy:0.9345 Epoch: 0 |Step: 400 |train loss:0.0381 |test accuracy:0.9645 Epoch: 0 |Step: 500 |train loss:0.0266 |test accuracy:0.9620 Epoch: 0 |Step: 600 |train loss:0.0973 |test accuracy:0.9685 Epoch: 0 |Step: 700 |train loss:0.0421 |test accuracy:0.9725 Epoch: 0 |Step: 800 |train loss:0.0654 |test accuracy:0.9710 Epoch: 0 |Step: 900 |train loss:0.1333 |test accuracy:0.9740 Epoch: 0 |Step: 1000 |train loss:0.0289 |test accuracy:0.9720 Epoch: 0 |Step: 1100 |train loss:0.0429 |test accuracy:0.9770 [7 2 1 0 4 1 4 9 5 9] prediction number [7 2 1 0 4 1 4 9 5 9] real number '''