CNN案例：手写数字识别

1. 超参数定义

import torch
import torchvision
from torch.utils.data import DataLoader

# 训练次数
n_epochs = 3
# 一次训练的图片数
batch_size_train = 64
# 一次测试的图片数
batch_size_test = 1000
# 学习率
learning_rate = 0.01

momentum = 0.5
log_interval = 10
# 随机数种子，保证了实验的可复现
random_seed = 1
torch.manual_seed(random_seed)

2. 数据加载与标准化裁剪

为了便于训练，图像需要进行标准化处理。TorchVision库提供了许多方便的图像转化功能。

# 获取训练集
train_loader = torch.utils.data.DataLoader(
  torchvision.datasets.MNIST('./data/', train=True, download=True,
                             transform=torchvision.transforms.Compose([
                               torchvision.transforms.ToTensor(),
                               torchvision.transforms.Normalize(
                                 (0.1307,), (0.3081,))
                             ])),
  batch_size=batch_size_train, shuffle=True)
# 获取测试集
test_loader = torch.utils.data.DataLoader(
  torchvision.datasets.MNIST('./data/', train=False, download=True,
                             transform=torchvision.transforms.Compose([
                               torchvision.transforms.ToTensor(),
                               torchvision.transforms.Normalize(
                                 (0.1307,), (0.3081,))
                             ])),
  batch_size=batch_size_test, shuffle=True)

下面我们可以看看数据集的样貌，以测试集为例。

examples = enumerate(test_loader)
batch_idx, (example_data, example_targets) = next(examples)
# 目标值，0-9之间的数字
print(example_targets)
# 数据集的格式 batch_size=1000,channels = 1, width = height = 28
print(example_data.shape)

tensor([7, 6, 7, 5, 6, 7, 8, 1, 1, 2, 4, 1, 0, 8, 4, 4, 4, 9, 8, 1, 3, 3, 8, 6,
        2, 7, 5, 1, 6, 5, 6, 2, 9, 2, 8, 4, 9, 4, 8, 6, 7, 7, 9, 8, 4, 9, 5, 3,
        1, 0, 9, 1, 7, 3, 7, 0, 9, 2, 5, 1, 8, 9, 3, 7, 8, 4, 1, 9, 0, 3, 1, 2,
        3, 6, 2, 9, 9, 0, 3, 8, 3, 0, 8, 8, 5, 3, 8, 2, 8, 5, 5, 7, 1, 5, 5, 1,
        0, 9, 7, 5, 2, 0, 7, 6, 1, 2, 2, 7, 5, 4, 7, 3, 0, 6, 7, 5, 1, 7, 6, 7,
        2, 1, 9, 1, 9, 2, 7, 6, 8, 8, 8, 4, 6, 0, 0, 2, 3, 0, 1, 7, 8, 7, 4, 1,
        3, 8, 3, 5, 5, 9, 6, 0, 5, 3, 3, 9, 4, 0, 1, 9, 9, 1, 5, 6, 2, 0, 4, 7,
        3, 5, 8, 8, 2, 5, 9, 5, 0, 7, 8, 9, 3, 8, 5, 3, 2, 4, 4, 6, 3, 0, 8, 2,
        7, 0, 5, 2, 0, 6, 2, 6, 3, 6, 6, 7, 9, 3, 4, 1, 6, 2, 8, 4, 7, 7, 2, 7,
        4, 2, 4, 9, 7, 7, 5, 9, 1, 3, 0, 4, 4, 8, 9, 6, 6, 5, 3, 3, 2, 3, 9, 1,
        1, 4, 4, 8, 1, 5, 1, 8, 8, 0, 7, 5, 8, 4, 0, 0, 0, 6, 3, 0, 9, 0, 6, 6,
        9, 8, 1, 2, 3, 7, 6, 1, 5, 9, 3, 9, 3, 2, 5, 9, 9, 5, 4, 9, 3, 9, 6, 0,
        3, 3, 8, 3, 1, 4, 1, 4, 7, 3, 1, 6, 8, 4, 7, 7, 3, 3, 6, 1, 3, 2, 3, 5,
        9, 9, 9, 2, 9, 0, 2, 7, 0, 7, 5, 0, 2, 6, 7, 3, 7, 1, 4, 6, 4, 0, 0, 3,
        2, 1, 9, 3, 5, 5, 1, 6, 4, 7, 4, 6, 4, 4, 9, 7, 4, 1, 5, 4, 8, 7, 5, 9,
        2, 9, 4, 0, 8, 7, 3, 4, 2, 7, 9, 4, 4, 0, 1, 4, 1, 2, 5, 2, 8, 5, 3, 9,
        1, 3, 5, 1, 9, 5, 3, 6, 8, 1, 7, 9, 9, 9, 9, 9, 2, 3, 5, 1, 4, 2, 3, 1,
        1, 3, 8, 2, 8, 1, 9, 2, 9, 0, 7, 3, 5, 8, 3, 7, 8, 5, 6, 4, 1, 9, 7, 1,
        7, 1, 1, 8, 6, 7, 5, 6, 7, 4, 9, 5, 8, 6, 5, 6, 8, 4, 1, 0, 9, 1, 4, 3,
        5, 1, 8, 7, 5, 4, 6, 6, 0, 2, 4, 2, 9, 5, 9, 8, 1, 4, 8, 1, 1, 6, 7, 5,
        9, 1, 1, 7, 8, 7, 5, 5, 2, 6, 5, 8, 1, 0, 7, 2, 2, 4, 3, 9, 7, 3, 5, 7,
        6, 9, 5, 9, 6, 5, 7, 2, 3, 7, 2, 9, 7, 4, 8, 4, 9, 3, 8, 7, 5, 0, 0, 3,
        4, 3, 3, 6, 0, 1, 7, 7, 4, 6, 3, 0, 8, 0, 9, 8, 2, 4, 2, 9, 4, 9, 9, 9,
        7, 7, 6, 8, 2, 4, 9, 3, 0, 4, 4, 1, 5, 7, 7, 6, 9, 7, 0, 2, 4, 2, 1, 4,
        7, 4, 5, 1, 4, 7, 3, 1, 7, 6, 9, 0, 0, 7, 3, 6, 3, 3, 6, 5, 8, 1, 7, 1,
        6, 1, 2, 3, 1, 6, 8, 8, 7, 4, 3, 7, 7, 1, 8, 9, 2, 6, 6, 6, 2, 8, 8, 1,
        6, 0, 3, 0, 5, 1, 3, 2, 4, 1, 5, 5, 7, 3, 5, 6, 2, 1, 8, 0, 2, 0, 8, 4,
        4, 5, 0, 0, 1, 5, 0, 7, 4, 0, 9, 2, 5, 7, 4, 0, 3, 7, 0, 3, 5, 1, 0, 6,
        4, 7, 6, 4, 7, 0, 0, 5, 8, 2, 0, 6, 2, 4, 2, 3, 2, 7, 7, 6, 9, 8, 5, 9,
        7, 1, 3, 4, 3, 1, 8, 0, 3, 0, 7, 4, 9, 0, 8, 1, 5, 7, 3, 2, 2, 0, 7, 3,
        1, 8, 8, 2, 2, 6, 2, 7, 6, 6, 9, 4, 9, 3, 7, 0, 4, 6, 1, 9, 7, 4, 4, 5,
        8, 2, 3, 2, 4, 9, 1, 9, 6, 7, 1, 2, 1, 1, 2, 6, 9, 7, 1, 0, 1, 4, 2, 7,
        7, 8, 3, 2, 8, 2, 7, 6, 1, 1, 9, 1, 0, 9, 1, 3, 9, 3, 7, 6, 5, 6, 2, 0,
        0, 3, 9, 4, 7, 3, 2, 9, 0, 9, 5, 2, 2, 4, 1, 6, 3, 4, 0, 1, 6, 9, 1, 7,
        0, 8, 0, 0, 9, 8, 5, 9, 4, 4, 7, 1, 9, 0, 0, 2, 4, 3, 5, 0, 4, 0, 1, 0,
        5, 8, 1, 8, 3, 3, 2, 1, 2, 6, 8, 2, 5, 3, 7, 9, 3, 6, 2, 2, 6, 2, 7, 7,
        6, 1, 8, 0, 3, 5, 7, 5, 0, 8, 6, 7, 2, 4, 1, 4, 3, 7, 7, 2, 9, 3, 5, 5,
        9, 4, 8, 7, 6, 7, 4, 9, 2, 7, 7, 1, 0, 7, 2, 8, 0, 3, 5, 4, 5, 1, 5, 7,
        6, 7, 3, 5, 3, 4, 5, 3, 4, 3, 2, 3, 1, 7, 4, 4, 8, 5, 5, 3, 2, 2, 9, 5,
        8, 2, 0, 6, 0, 7, 9, 9, 6, 1, 6, 6, 2, 3, 7, 4, 7, 5, 2, 9, 4, 2, 9, 0,
        8, 1, 7, 5, 5, 7, 0, 5, 2, 9, 5, 2, 3, 4, 6, 0, 0, 2, 9, 2, 0, 5, 4, 8,
        9, 0, 9, 1, 3, 4, 1, 8, 0, 0, 4, 0, 8, 5, 9, 8])
torch.Size([1000, 1, 28, 28])

下面用matplotlib还原几个图像

import matplotlib.pyplot as plt
fig = plt.figure()
for i in range(6):
  plt.subplot(2,3,i+1)
  plt.tight_layout()
  plt.imshow(example_data[i][0], cmap='gray', interpolation='none')
  plt.title("Ground Truth: {}".format(example_targets[i]))
  plt.xticks([])
  plt.yticks([])
plt.show()

3. 卷积神经网络模型构建

import torch.nn as nn
import torch.nn.functional as F

class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        # 输入1通道，输出10通道，卷积核10个1*5*5
        self.conv1 = nn.Conv2d(1, 10, kernel_size=5)
        # 输入10通道，输出20通道，卷积核20个10*5*5
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        # 下采样
        self.conv2_drop = nn.Dropout2d()
        # 全连接层，输入320由计算得出
        self.fc1 = nn.Linear(320, 50)
        self.fc2 = nn.Linear(50, 10)
    def forward(self, x):
        # 池化核大小为2*2
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2))
        x = x.view(-1, 320)
        x = F.relu(self.fc1(x))
        x = F.dropout(x, training=self.training)
        x = self.fc2(x)
        return F.log_softmax(x)

4. 初始化网络、优化器

import torch.optim as optim

network = Net()
# momentum是一种采用动量思想的SGD优化算法，即积累了之前转化为动能的重力势能，加快训练，又不容易陷入局部最小
optimizer = optim.SGD(network.parameters(), lr=learning_rate, momentum=momentum)

# 检测是否有N卡
device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')
network.to(device)

Net(
  (conv1): Conv2d(1, 10, kernel_size=(5, 5), stride=(1, 1))
  (conv2): Conv2d(10, 20, kernel_size=(5, 5), stride=(1, 1))
  (conv2_drop): Dropout2d(p=0.5, inplace=False)
  (fc1): Linear(in_features=320, out_features=50, bias=True)
  (fc2): Linear(in_features=50, out_features=10, bias=True)
)

5. 模型训练

# 用于记录loss下降的过程
train_losses = []
train_counter = []
test_counter = [i*len(train_loader.dataset) for i in range(n_epochs + 1)]

def train(epoch):
  network.train()
  for batch_idx, (data, target) in enumerate(train_loader):
    data = data.to(device)
    target = target.to(device)
    optimizer.zero_grad()
    output = network(data)
    loss = F.nll_loss(output, target)
    loss.backward()
    optimizer.step()
    if batch_idx % log_interval == 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()))
      train_losses.append(loss.item())
      train_counter.append(
        (batch_idx*64) + ((epoch-1)*len(train_loader.dataset)))
      torch.save(network.state_dict(), './model.pth')
      torch.save(optimizer.state_dict(), './optimizer.pth')

train(1)

D:\Anaconda3\lib\site-packages\ipykernel_launcher.py:24: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.


Train Epoch: 1 [0/60000 (0%)]	Loss: 2.342775
Train Epoch: 1 [640/60000 (1%)]	Loss: 2.301787
Train Epoch: 1 [1280/60000 (2%)]	Loss: 2.273638
Train Epoch: 1 [1920/60000 (3%)]	Loss: 2.215885
Train Epoch: 1 [2560/60000 (4%)]	Loss: 2.219636
Train Epoch: 1 [3200/60000 (5%)]	Loss: 2.182050
Train Epoch: 1 [3840/60000 (6%)]	Loss: 2.154599
Train Epoch: 1 [4480/60000 (7%)]	Loss: 2.109921
Train Epoch: 1 [5120/60000 (9%)]	Loss: 2.040787
Train Epoch: 1 [5760/60000 (10%)]	Loss: 1.918081
Train Epoch: 1 [6400/60000 (11%)]	Loss: 1.916582
Train Epoch: 1 [7040/60000 (12%)]	Loss: 1.752552
Train Epoch: 1 [7680/60000 (13%)]	Loss: 1.654067
Train Epoch: 1 [8320/60000 (14%)]	Loss: 1.799136
Train Epoch: 1 [8960/60000 (15%)]	Loss: 1.734123
Train Epoch: 1 [9600/60000 (16%)]	Loss: 1.306920
Train Epoch: 1 [10240/60000 (17%)]	Loss: 1.465809
Train Epoch: 1 [10880/60000 (18%)]	Loss: 1.182047
Train Epoch: 1 [11520/60000 (19%)]	Loss: 1.411433
Train Epoch: 1 [12160/60000 (20%)]	Loss: 1.196440
Train Epoch: 1 [12800/60000 (21%)]	Loss: 1.151352
Train Epoch: 1 [13440/60000 (22%)]	Loss: 0.999309
Train Epoch: 1 [14080/60000 (23%)]	Loss: 1.099866
Train Epoch: 1 [14720/60000 (25%)]	Loss: 1.343900
Train Epoch: 1 [15360/60000 (26%)]	Loss: 1.035041
Train Epoch: 1 [16000/60000 (27%)]	Loss: 1.200880
Train Epoch: 1 [16640/60000 (28%)]	Loss: 1.073424
Train Epoch: 1 [17280/60000 (29%)]	Loss: 0.992197
Train Epoch: 1 [17920/60000 (30%)]	Loss: 0.889907
Train Epoch: 1 [18560/60000 (31%)]	Loss: 0.791340
Train Epoch: 1 [19200/60000 (32%)]	Loss: 0.929186
Train Epoch: 1 [19840/60000 (33%)]	Loss: 0.779179
Train Epoch: 1 [20480/60000 (34%)]	Loss: 0.822259
Train Epoch: 1 [21120/60000 (35%)]	Loss: 0.800306
Train Epoch: 1 [21760/60000 (36%)]	Loss: 1.106641
Train Epoch: 1 [22400/60000 (37%)]	Loss: 0.866425
Train Epoch: 1 [23040/60000 (38%)]	Loss: 0.680763
Train Epoch: 1 [23680/60000 (39%)]	Loss: 0.738366
Train Epoch: 1 [24320/60000 (41%)]	Loss: 0.724880
Train Epoch: 1 [24960/60000 (42%)]	Loss: 0.657511
Train Epoch: 1 [25600/60000 (43%)]	Loss: 0.858225
Train Epoch: 1 [26240/60000 (44%)]	Loss: 0.733906
Train Epoch: 1 [26880/60000 (45%)]	Loss: 0.921771
Train Epoch: 1 [27520/60000 (46%)]	Loss: 0.743885
Train Epoch: 1 [28160/60000 (47%)]	Loss: 0.652919
Train Epoch: 1 [28800/60000 (48%)]	Loss: 0.791037
Train Epoch: 1 [29440/60000 (49%)]	Loss: 0.587879
Train Epoch: 1 [30080/60000 (50%)]	Loss: 0.465844
Train Epoch: 1 [30720/60000 (51%)]	Loss: 0.340918
Train Epoch: 1 [31360/60000 (52%)]	Loss: 0.679137
Train Epoch: 1 [32000/60000 (53%)]	Loss: 0.695010
Train Epoch: 1 [32640/60000 (54%)]	Loss: 0.616460
Train Epoch: 1 [33280/60000 (55%)]	Loss: 0.592633
Train Epoch: 1 [33920/60000 (57%)]	Loss: 0.617049
Train Epoch: 1 [34560/60000 (58%)]	Loss: 0.550085
Train Epoch: 1 [35200/60000 (59%)]	Loss: 0.801612
Train Epoch: 1 [35840/60000 (60%)]	Loss: 0.454174
Train Epoch: 1 [36480/60000 (61%)]	Loss: 0.588209
Train Epoch: 1 [37120/60000 (62%)]	Loss: 0.671104
Train Epoch: 1 [37760/60000 (63%)]	Loss: 0.798899
Train Epoch: 1 [38400/60000 (64%)]	Loss: 0.637726
Train Epoch: 1 [39040/60000 (65%)]	Loss: 0.656208
Train Epoch: 1 [39680/60000 (66%)]	Loss: 0.542938
Train Epoch: 1 [40320/60000 (67%)]	Loss: 0.541254
Train Epoch: 1 [40960/60000 (68%)]	Loss: 0.551119
Train Epoch: 1 [41600/60000 (69%)]	Loss: 0.646996
Train Epoch: 1 [42240/60000 (70%)]	Loss: 0.639059
Train Epoch: 1 [42880/60000 (71%)]	Loss: 0.523870
Train Epoch: 1 [43520/60000 (72%)]	Loss: 0.537203
Train Epoch: 1 [44160/60000 (74%)]	Loss: 0.279806
Train Epoch: 1 [44800/60000 (75%)]	Loss: 0.609367
Train Epoch: 1 [45440/60000 (76%)]	Loss: 0.662970
Train Epoch: 1 [46080/60000 (77%)]	Loss: 0.637495
Train Epoch: 1 [46720/60000 (78%)]	Loss: 0.405338
Train Epoch: 1 [47360/60000 (79%)]	Loss: 0.496160
Train Epoch: 1 [48000/60000 (80%)]	Loss: 0.428567
Train Epoch: 1 [48640/60000 (81%)]	Loss: 0.475516
Train Epoch: 1 [49280/60000 (82%)]	Loss: 0.443161
Train Epoch: 1 [49920/60000 (83%)]	Loss: 0.474389
Train Epoch: 1 [50560/60000 (84%)]	Loss: 0.480269
Train Epoch: 1 [51200/60000 (85%)]	Loss: 0.431389
Train Epoch: 1 [51840/60000 (86%)]	Loss: 0.422643
Train Epoch: 1 [52480/60000 (87%)]	Loss: 0.510923
Train Epoch: 1 [53120/60000 (88%)]	Loss: 0.335113
Train Epoch: 1 [53760/60000 (90%)]	Loss: 0.722130
Train Epoch: 1 [54400/60000 (91%)]	Loss: 0.362313
Train Epoch: 1 [55040/60000 (92%)]	Loss: 0.456559
Train Epoch: 1 [55680/60000 (93%)]	Loss: 0.491410
Train Epoch: 1 [56320/60000 (94%)]	Loss: 0.517430
Train Epoch: 1 [56960/60000 (95%)]	Loss: 0.417551
Train Epoch: 1 [57600/60000 (96%)]	Loss: 0.554161
Train Epoch: 1 [58240/60000 (97%)]	Loss: 0.481269
Train Epoch: 1 [58880/60000 (98%)]	Loss: 0.512804
Train Epoch: 1 [59520/60000 (99%)]	Loss: 0.526870

6. 测试环节

def test():
  test_losses = []
  network.eval()
  test_loss = 0
  correct = 0
  with torch.no_grad():
    for data, target in test_loader:
      data = data.to(device)
      target = target.to(device)
      output = network(data)
      test_loss += F.nll_loss(output, target, size_average=False).item()
      pred = output.data.max(1, keepdim=True)[1]
      correct += pred.eq(target.data.view_as(pred)).sum()
  test_loss /= len(test_loader.dataset)
  test_losses.append(test_loss)
  print('\nTest set: Avg. loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format(
    test_loss, correct, len(test_loader.dataset),
    100. * correct / len(test_loader.dataset)))

test()

D:\Anaconda3\lib\site-packages\ipykernel_launcher.py:24: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.

​

Test set: Avg. loss: 0.0402, Accuracy: 9881/10000 (99%)

​

for epoch in range(1, n_epochs + 1):
  train(epoch)
  test()

D:\Anaconda3\lib\site-packages\ipykernel_launcher.py:24: UserWarning: Implicit dimension choice for log_softmax has been deprecated. Change the call to include dim=X as an argument.
D:\Anaconda3\lib\site-packages\torch\nn\_reduction.py:43: UserWarning: size_average and reduce args will be deprecated, please use reduction='sum' instead.
  warnings.warn(warning.format(ret))


Train Epoch: 1 [0/60000 (0%)]	Loss: 0.156632
Train Epoch: 1 [640/60000 (1%)]	Loss: 0.192664
Train Epoch: 1 [1280/60000 (2%)]	Loss: 0.151135
Train Epoch: 1 [1920/60000 (3%)]	Loss: 0.103477
Train Epoch: 1 [2560/60000 (4%)]	Loss: 0.064784
Train Epoch: 1 [3200/60000 (5%)]	Loss: 0.051481
Train Epoch: 1 [3840/60000 (6%)]	Loss: 0.441348
Train Epoch: 1 [4480/60000 (7%)]	Loss: 0.104150
Train Epoch: 1 [5120/60000 (9%)]	Loss: 0.179621
Train Epoch: 1 [5760/60000 (10%)]	Loss: 0.041205
Train Epoch: 1 [6400/60000 (11%)]	Loss: 0.194008
Train Epoch: 1 [7040/60000 (12%)]	Loss: 0.157087
Train Epoch: 1 [7680/60000 (13%)]	Loss: 0.124243
Train Epoch: 1 [8320/60000 (14%)]	Loss: 0.157707
Train Epoch: 1 [8960/60000 (15%)]	Loss: 0.246198
Train Epoch: 1 [9600/60000 (16%)]	Loss: 0.069816
Train Epoch: 1 [10240/60000 (17%)]	Loss: 0.108673
Train Epoch: 1 [10880/60000 (18%)]	Loss: 0.057313
Train Epoch: 1 [11520/60000 (19%)]	Loss: 0.048674
Train Epoch: 1 [12160/60000 (20%)]	Loss: 0.088004
Train Epoch: 1 [12800/60000 (21%)]	Loss: 0.306724
Train Epoch: 1 [13440/60000 (22%)]	Loss: 0.038037
Train Epoch: 1 [14080/60000 (23%)]	Loss: 0.065409
Train Epoch: 1 [14720/60000 (25%)]	Loss: 0.220334
Train Epoch: 1 [15360/60000 (26%)]	Loss: 0.275643
Train Epoch: 1 [16000/60000 (27%)]	Loss: 0.151600
Train Epoch: 1 [16640/60000 (28%)]	Loss: 0.081870
Train Epoch: 1 [17280/60000 (29%)]	Loss: 0.322228
Train Epoch: 1 [17920/60000 (30%)]	Loss: 0.075777
Train Epoch: 1 [18560/60000 (31%)]	Loss: 0.071830
Train Epoch: 1 [19200/60000 (32%)]	Loss: 0.154053
Train Epoch: 1 [19840/60000 (33%)]	Loss: 0.268226
Train Epoch: 1 [20480/60000 (34%)]	Loss: 0.277857
Train Epoch: 1 [21120/60000 (35%)]	Loss: 0.128731
Train Epoch: 1 [21760/60000 (36%)]	Loss: 0.216666
Train Epoch: 1 [22400/60000 (37%)]	Loss: 0.143428
Train Epoch: 1 [23040/60000 (38%)]	Loss: 0.049380
Train Epoch: 1 [23680/60000 (39%)]	Loss: 0.108051
Train Epoch: 1 [24320/60000 (41%)]	Loss: 0.126978
Train Epoch: 1 [24960/60000 (42%)]	Loss: 0.054452
Train Epoch: 1 [25600/60000 (43%)]	Loss: 0.232893
Train Epoch: 1 [26240/60000 (44%)]	Loss: 0.189157
Train Epoch: 1 [26880/60000 (45%)]	Loss: 0.118713
Train Epoch: 1 [27520/60000 (46%)]	Loss: 0.127154
Train Epoch: 1 [28160/60000 (47%)]	Loss: 0.042029
Train Epoch: 1 [28800/60000 (48%)]	Loss: 0.067848
Train Epoch: 1 [29440/60000 (49%)]	Loss: 0.080663
Train Epoch: 1 [30080/60000 (50%)]	Loss: 0.194574
Train Epoch: 1 [30720/60000 (51%)]	Loss: 0.085501
Train Epoch: 1 [31360/60000 (52%)]	Loss: 0.049935
Train Epoch: 1 [32000/60000 (53%)]	Loss: 0.132505
Train Epoch: 1 [32640/60000 (54%)]	Loss: 0.227582
Train Epoch: 1 [33280/60000 (55%)]	Loss: 0.019724
Train Epoch: 1 [33920/60000 (57%)]	Loss: 0.154131
Train Epoch: 1 [34560/60000 (58%)]	Loss: 0.304377
Train Epoch: 1 [35200/60000 (59%)]	Loss: 0.073455
Train Epoch: 1 [35840/60000 (60%)]	Loss: 0.053076
Train Epoch: 1 [36480/60000 (61%)]	Loss: 0.099523
Train Epoch: 1 [37120/60000 (62%)]	Loss: 0.116375
Train Epoch: 1 [37760/60000 (63%)]	Loss: 0.215245
Train Epoch: 1 [38400/60000 (64%)]	Loss: 0.146011
Train Epoch: 1 [39040/60000 (65%)]	Loss: 0.121127
Train Epoch: 1 [39680/60000 (66%)]	Loss: 0.156879
Train Epoch: 1 [40320/60000 (67%)]	Loss: 0.047265
Train Epoch: 1 [40960/60000 (68%)]	Loss: 0.139341
Train Epoch: 1 [41600/60000 (69%)]	Loss: 0.156220
Train Epoch: 1 [42240/60000 (70%)]	Loss: 0.116193
Train Epoch: 1 [42880/60000 (71%)]	Loss: 0.095791
Train Epoch: 1 [43520/60000 (72%)]	Loss: 0.189572
Train Epoch: 1 [44160/60000 (74%)]	Loss: 0.074131
Train Epoch: 1 [44800/60000 (75%)]	Loss: 0.101932
Train Epoch: 1 [45440/60000 (76%)]	Loss: 0.123666
Train Epoch: 1 [46080/60000 (77%)]	Loss: 0.153217
Train Epoch: 1 [46720/60000 (78%)]	Loss: 0.077803
Train Epoch: 1 [47360/60000 (79%)]	Loss: 0.283785
Train Epoch: 1 [48000/60000 (80%)]	Loss: 0.212793
Train Epoch: 1 [48640/60000 (81%)]	Loss: 0.142060
Train Epoch: 1 [49280/60000 (82%)]	Loss: 0.102382
Train Epoch: 1 [49920/60000 (83%)]	Loss: 0.221080
Train Epoch: 1 [50560/60000 (84%)]	Loss: 0.038571
Train Epoch: 1 [51200/60000 (85%)]	Loss: 0.123979
Train Epoch: 1 [51840/60000 (86%)]	Loss: 0.146767
Train Epoch: 1 [52480/60000 (87%)]	Loss: 0.436692
Train Epoch: 1 [53120/60000 (88%)]	Loss: 0.078703
Train Epoch: 1 [53760/60000 (90%)]	Loss: 0.083898
Train Epoch: 1 [54400/60000 (91%)]	Loss: 0.133949
Train Epoch: 1 [55040/60000 (92%)]	Loss: 0.102200
Train Epoch: 1 [55680/60000 (93%)]	Loss: 0.133427
Train Epoch: 1 [56320/60000 (94%)]	Loss: 0.077202
Train Epoch: 1 [56960/60000 (95%)]	Loss: 0.156647
Train Epoch: 1 [57600/60000 (96%)]	Loss: 0.037719
Train Epoch: 1 [58240/60000 (97%)]	Loss: 0.102780
Train Epoch: 1 [58880/60000 (98%)]	Loss: 0.052420
Train Epoch: 1 [59520/60000 (99%)]	Loss: 0.076627

Test set: Avg. loss: 0.0421, Accuracy: 9875/10000 (99%)

Train Epoch: 2 [0/60000 (0%)]	Loss: 0.081168
Train Epoch: 2 [640/60000 (1%)]	Loss: 0.224670
Train Epoch: 2 [1280/60000 (2%)]	Loss: 0.129191
Train Epoch: 2 [1920/60000 (3%)]	Loss: 0.247358
Train Epoch: 2 [2560/60000 (4%)]	Loss: 0.036171
Train Epoch: 2 [3200/60000 (5%)]	Loss: 0.077806
Train Epoch: 2 [3840/60000 (6%)]	Loss: 0.133592
Train Epoch: 2 [4480/60000 (7%)]	Loss: 0.103453
Train Epoch: 2 [5120/60000 (9%)]	Loss: 0.102922
Train Epoch: 2 [5760/60000 (10%)]	Loss: 0.060962
Train Epoch: 2 [6400/60000 (11%)]	Loss: 0.131838
Train Epoch: 2 [7040/60000 (12%)]	Loss: 0.189249
Train Epoch: 2 [7680/60000 (13%)]	Loss: 0.191448
Train Epoch: 2 [8320/60000 (14%)]	Loss: 0.190570
Train Epoch: 2 [8960/60000 (15%)]	Loss: 0.259936
Train Epoch: 2 [9600/60000 (16%)]	Loss: 0.118716
Train Epoch: 2 [10240/60000 (17%)]	Loss: 0.028625
Train Epoch: 2 [10880/60000 (18%)]	Loss: 0.044575
Train Epoch: 2 [11520/60000 (19%)]	Loss: 0.112197
Train Epoch: 2 [12160/60000 (20%)]	Loss: 0.143760
Train Epoch: 2 [12800/60000 (21%)]	Loss: 0.213565
Train Epoch: 2 [13440/60000 (22%)]	Loss: 0.067672
Train Epoch: 2 [14080/60000 (23%)]	Loss: 0.075030
Train Epoch: 2 [14720/60000 (25%)]	Loss: 0.173301
Train Epoch: 2 [15360/60000 (26%)]	Loss: 0.243791
Train Epoch: 2 [16000/60000 (27%)]	Loss: 0.509218
Train Epoch: 2 [16640/60000 (28%)]	Loss: 0.065029
Train Epoch: 2 [17280/60000 (29%)]	Loss: 0.064137
Train Epoch: 2 [17920/60000 (30%)]	Loss: 0.219690
Train Epoch: 2 [18560/60000 (31%)]	Loss: 0.068412
Train Epoch: 2 [19200/60000 (32%)]	Loss: 0.084879
Train Epoch: 2 [19840/60000 (33%)]	Loss: 0.118277
Train Epoch: 2 [20480/60000 (34%)]	Loss: 0.178690
Train Epoch: 2 [21120/60000 (35%)]	Loss: 0.138507
Train Epoch: 2 [21760/60000 (36%)]	Loss: 0.283177
Train Epoch: 2 [22400/60000 (37%)]	Loss: 0.111385
Train Epoch: 2 [23040/60000 (38%)]	Loss: 0.200256
Train Epoch: 2 [23680/60000 (39%)]	Loss: 0.091059
Train Epoch: 2 [24320/60000 (41%)]	Loss: 0.039519
Train Epoch: 2 [24960/60000 (42%)]	Loss: 0.117363
Train Epoch: 2 [25600/60000 (43%)]	Loss: 0.123654
Train Epoch: 2 [26240/60000 (44%)]	Loss: 0.224314
Train Epoch: 2 [26880/60000 (45%)]	Loss: 0.280589
Train Epoch: 2 [27520/60000 (46%)]	Loss: 0.052264
Train Epoch: 2 [28160/60000 (47%)]	Loss: 0.063365
Train Epoch: 2 [28800/60000 (48%)]	Loss: 0.064455
Train Epoch: 2 [29440/60000 (49%)]	Loss: 0.081827
Train Epoch: 2 [30080/60000 (50%)]	Loss: 0.089505
Train Epoch: 2 [30720/60000 (51%)]	Loss: 0.081288
Train Epoch: 2 [31360/60000 (52%)]	Loss: 0.160924
Train Epoch: 2 [32000/60000 (53%)]	Loss: 0.204062
Train Epoch: 2 [32640/60000 (54%)]	Loss: 0.033370
Train Epoch: 2 [33280/60000 (55%)]	Loss: 0.150454
Train Epoch: 2 [33920/60000 (57%)]	Loss: 0.092165
Train Epoch: 2 [34560/60000 (58%)]	Loss: 0.132951
Train Epoch: 2 [35200/60000 (59%)]	Loss: 0.111180
Train Epoch: 2 [35840/60000 (60%)]	Loss: 0.170439
Train Epoch: 2 [36480/60000 (61%)]	Loss: 0.272381
Train Epoch: 2 [37120/60000 (62%)]	Loss: 0.047448
Train Epoch: 2 [37760/60000 (63%)]	Loss: 0.205407
Train Epoch: 2 [38400/60000 (64%)]	Loss: 0.135557
Train Epoch: 2 [39040/60000 (65%)]	Loss: 0.101824
Train Epoch: 2 [39680/60000 (66%)]	Loss: 0.044439
Train Epoch: 2 [40320/60000 (67%)]	Loss: 0.086475
Train Epoch: 2 [40960/60000 (68%)]	Loss: 0.093398
Train Epoch: 2 [41600/60000 (69%)]	Loss: 0.139246
Train Epoch: 2 [42240/60000 (70%)]	Loss: 0.146613
Train Epoch: 2 [42880/60000 (71%)]	Loss: 0.128355
Train Epoch: 2 [43520/60000 (72%)]	Loss: 0.061965
Train Epoch: 2 [44160/60000 (74%)]	Loss: 0.112888
Train Epoch: 2 [44800/60000 (75%)]	Loss: 0.081551
Train Epoch: 2 [45440/60000 (76%)]	Loss: 0.170145
Train Epoch: 2 [46080/60000 (77%)]	Loss: 0.131782
Train Epoch: 2 [46720/60000 (78%)]	Loss: 0.167966
Train Epoch: 2 [47360/60000 (79%)]	Loss: 0.054064
Train Epoch: 2 [48000/60000 (80%)]	Loss: 0.133177
Train Epoch: 2 [48640/60000 (81%)]	Loss: 0.089363
Train Epoch: 2 [49280/60000 (82%)]	Loss: 0.097963
Train Epoch: 2 [49920/60000 (83%)]	Loss: 0.077683
Train Epoch: 2 [50560/60000 (84%)]	Loss: 0.175217
Train Epoch: 2 [51200/60000 (85%)]	Loss: 0.126265
Train Epoch: 2 [51840/60000 (86%)]	Loss: 0.213446
Train Epoch: 2 [52480/60000 (87%)]	Loss: 0.071028
Train Epoch: 2 [53120/60000 (88%)]	Loss: 0.045520
Train Epoch: 2 [53760/60000 (90%)]	Loss: 0.155648
Train Epoch: 2 [54400/60000 (91%)]	Loss: 0.065158
Train Epoch: 2 [55040/60000 (92%)]	Loss: 0.145879
Train Epoch: 2 [55680/60000 (93%)]	Loss: 0.167453
Train Epoch: 2 [56320/60000 (94%)]	Loss: 0.084260
Train Epoch: 2 [56960/60000 (95%)]	Loss: 0.325450
Train Epoch: 2 [57600/60000 (96%)]	Loss: 0.186134
Train Epoch: 2 [58240/60000 (97%)]	Loss: 0.028011
Train Epoch: 2 [58880/60000 (98%)]	Loss: 0.058806
Train Epoch: 2 [59520/60000 (99%)]	Loss: 0.163296

Test set: Avg. loss: 0.0399, Accuracy: 9878/10000 (99%)

Train Epoch: 3 [0/60000 (0%)]	Loss: 0.102998
Train Epoch: 3 [640/60000 (1%)]	Loss: 0.066535
Train Epoch: 3 [1280/60000 (2%)]	Loss: 0.051959
Train Epoch: 3 [1920/60000 (3%)]	Loss: 0.107484
Train Epoch: 3 [2560/60000 (4%)]	Loss: 0.087987
Train Epoch: 3 [3200/60000 (5%)]	Loss: 0.134019
Train Epoch: 3 [3840/60000 (6%)]	Loss: 0.144111
Train Epoch: 3 [4480/60000 (7%)]	Loss: 0.198046
Train Epoch: 3 [5120/60000 (9%)]	Loss: 0.049358
Train Epoch: 3 [5760/60000 (10%)]	Loss: 0.067649
Train Epoch: 3 [6400/60000 (11%)]	Loss: 0.177920
Train Epoch: 3 [7040/60000 (12%)]	Loss: 0.334545
Train Epoch: 3 [7680/60000 (13%)]	Loss: 0.124170
Train Epoch: 3 [8320/60000 (14%)]	Loss: 0.152111
Train Epoch: 3 [8960/60000 (15%)]	Loss: 0.061891
Train Epoch: 3 [9600/60000 (16%)]	Loss: 0.096038
Train Epoch: 3 [10240/60000 (17%)]	Loss: 0.128670
Train Epoch: 3 [10880/60000 (18%)]	Loss: 0.141426
Train Epoch: 3 [11520/60000 (19%)]	Loss: 0.098369
Train Epoch: 3 [12160/60000 (20%)]	Loss: 0.076490
Train Epoch: 3 [12800/60000 (21%)]	Loss: 0.024070
Train Epoch: 3 [13440/60000 (22%)]	Loss: 0.062902
Train Epoch: 3 [14080/60000 (23%)]	Loss: 0.111864
Train Epoch: 3 [14720/60000 (25%)]	Loss: 0.041554
Train Epoch: 3 [15360/60000 (26%)]	Loss: 0.176218
Train Epoch: 3 [16000/60000 (27%)]	Loss: 0.091784
Train Epoch: 3 [16640/60000 (28%)]	Loss: 0.099284
Train Epoch: 3 [17280/60000 (29%)]	Loss: 0.045067
Train Epoch: 3 [17920/60000 (30%)]	Loss: 0.163887
Train Epoch: 3 [18560/60000 (31%)]	Loss: 0.371201
Train Epoch: 3 [19200/60000 (32%)]	Loss: 0.132180
Train Epoch: 3 [19840/60000 (33%)]	Loss: 0.298130
Train Epoch: 3 [20480/60000 (34%)]	Loss: 0.188392
Train Epoch: 3 [21120/60000 (35%)]	Loss: 0.256692
Train Epoch: 3 [21760/60000 (36%)]	Loss: 0.333582
Train Epoch: 3 [22400/60000 (37%)]	Loss: 0.103843
Train Epoch: 3 [23040/60000 (38%)]	Loss: 0.054006
Train Epoch: 3 [23680/60000 (39%)]	Loss: 0.174218
Train Epoch: 3 [24320/60000 (41%)]	Loss: 0.109797
Train Epoch: 3 [24960/60000 (42%)]	Loss: 0.135606
Train Epoch: 3 [25600/60000 (43%)]	Loss: 0.208556
Train Epoch: 3 [26240/60000 (44%)]	Loss: 0.188399
Train Epoch: 3 [26880/60000 (45%)]	Loss: 0.216521
Train Epoch: 3 [27520/60000 (46%)]	Loss: 0.240275
Train Epoch: 3 [28160/60000 (47%)]	Loss: 0.046752
Train Epoch: 3 [28800/60000 (48%)]	Loss: 0.098208
Train Epoch: 3 [29440/60000 (49%)]	Loss: 0.145031
Train Epoch: 3 [30080/60000 (50%)]	Loss: 0.075472
Train Epoch: 3 [30720/60000 (51%)]	Loss: 0.060327
Train Epoch: 3 [31360/60000 (52%)]	Loss: 0.147099
Train Epoch: 3 [32000/60000 (53%)]	Loss: 0.071874
Train Epoch: 3 [32640/60000 (54%)]	Loss: 0.103185
Train Epoch: 3 [33280/60000 (55%)]	Loss: 0.042416
Train Epoch: 3 [33920/60000 (57%)]	Loss: 0.128803
Train Epoch: 3 [34560/60000 (58%)]	Loss: 0.070104
Train Epoch: 3 [35200/60000 (59%)]	Loss: 0.185671
Train Epoch: 3 [35840/60000 (60%)]	Loss: 0.109853
Train Epoch: 3 [36480/60000 (61%)]	Loss: 0.301363
Train Epoch: 3 [37120/60000 (62%)]	Loss: 0.012276
Train Epoch: 3 [37760/60000 (63%)]	Loss: 0.137707
Train Epoch: 3 [38400/60000 (64%)]	Loss: 0.111371
Train Epoch: 3 [39040/60000 (65%)]	Loss: 0.192704
Train Epoch: 3 [39680/60000 (66%)]	Loss: 0.118988
Train Epoch: 3 [40320/60000 (67%)]	Loss: 0.056389
Train Epoch: 3 [40960/60000 (68%)]	Loss: 0.069326
Train Epoch: 3 [41600/60000 (69%)]	Loss: 0.137394
Train Epoch: 3 [42240/60000 (70%)]	Loss: 0.113170
Train Epoch: 3 [42880/60000 (71%)]	Loss: 0.024602
Train Epoch: 3 [43520/60000 (72%)]	Loss: 0.108824
Train Epoch: 3 [44160/60000 (74%)]	Loss: 0.196626
Train Epoch: 3 [44800/60000 (75%)]	Loss: 0.149237
Train Epoch: 3 [45440/60000 (76%)]	Loss: 0.099488
Train Epoch: 3 [46080/60000 (77%)]	Loss: 0.262205
Train Epoch: 3 [46720/60000 (78%)]	Loss: 0.107861
Train Epoch: 3 [47360/60000 (79%)]	Loss: 0.081145
Train Epoch: 3 [48000/60000 (80%)]	Loss: 0.044981
Train Epoch: 3 [48640/60000 (81%)]	Loss: 0.092366
Train Epoch: 3 [49280/60000 (82%)]	Loss: 0.110018
Train Epoch: 3 [49920/60000 (83%)]	Loss: 0.104542
Train Epoch: 3 [50560/60000 (84%)]	Loss: 0.183242
Train Epoch: 3 [51200/60000 (85%)]	Loss: 0.166517
Train Epoch: 3 [51840/60000 (86%)]	Loss: 0.169112
Train Epoch: 3 [52480/60000 (87%)]	Loss: 0.097010
Train Epoch: 3 [53120/60000 (88%)]	Loss: 0.096146
Train Epoch: 3 [53760/60000 (90%)]	Loss: 0.085258
Train Epoch: 3 [54400/60000 (91%)]	Loss: 0.321822
Train Epoch: 3 [55040/60000 (92%)]	Loss: 0.215173
Train Epoch: 3 [55680/60000 (93%)]	Loss: 0.158387
Train Epoch: 3 [56320/60000 (94%)]	Loss: 0.048139
Train Epoch: 3 [56960/60000 (95%)]	Loss: 0.051018
Train Epoch: 3 [57600/60000 (96%)]	Loss: 0.141063
Train Epoch: 3 [58240/60000 (97%)]	Loss: 0.069343
Train Epoch: 3 [58880/60000 (98%)]	Loss: 0.113296
Train Epoch: 3 [59520/60000 (99%)]	Loss: 0.032219

Test set: Avg. loss: 0.0402, Accuracy: 9881/10000 (99%)

​

7.模型性能评估

import matplotlib.pyplot as plt
fig = plt.figure()
plt.plot(train_counter, train_losses, color='blue')
plt.scatter(test_counter, test_losses, color='red')
plt.legend(['Train Loss', 'Test Loss'], loc='upper right')
plt.xlabel('number of training examples seen')
plt.ylabel('negative log likelihood loss')
plt.show()