python - 用于学习 10 位分类的 Pytorch MNIST 自动编码器

Question

我正在尝试为 MNIST 构建一个简单的自动编码器，其中中间层只有 10 个神经元。我希望它能学会对 10 位数字进行分类，我认为这最终会导致最低的错误(wrt 再现原始图像)。

我有以下代码，我已经使用了相当多的代码。如果我运行它多达 100 个 epoch，损失并没有真正低于 1.0，如果我评估它，它显然不起作用。我错过了什么？

训练:

import torch
import torchvision as tv
import torchvision.transforms as transforms
import torch.nn as nn
import torch.nn.functional as F
from torch.autograd import Variable
from torchvision.utils import save_image

num_epochs = 100
batch_size = 64

transform = transforms.Compose([
    transforms.ToTensor(),
    transforms.Normalize((0.1307,), (0.3081,))
])
trainset = tv.datasets.MNIST(root='./data',  train=True, download=True, transform=transform)
dataloader = torch.utils.data.DataLoader(trainset, batch_size=batch_size, shuffle=True, num_workers=4)

class Autoencoder(nn.Module):
    def __init__(self):
        super(Autoencoder,self).__init__()
        self.encoder = nn.Sequential(
            # 28 x 28
            nn.Conv2d(1, 4, kernel_size=5),
            nn.Dropout2d(p=0.2),
            # 4 x 24 x 24
            nn.ReLU(True),
            nn.Conv2d(4, 8, kernel_size=5),
            nn.Dropout2d(p=0.2),
            # 8 x 20 x 20 = 3200
            nn.ReLU(True),
            nn.Flatten(),
            nn.Linear(3200, 10),
            nn.ReLU(True),
            # 10
            nn.Softmax(),
            # 10
            )
        self.decoder = nn.Sequential(
            # 10
            nn.Linear(10, 400),
            nn.ReLU(True),
            # 400
            nn.Unflatten(1, (1, 20, 20)),
            # 20 x 20
            nn.Dropout2d(p=0.2),
            nn.ConvTranspose2d(1, 10, kernel_size=5),
            # 24 x 24
            nn.ReLU(True),
            nn.Dropout2d(p=0.2),
            nn.ConvTranspose2d(10, 1, kernel_size=5),
            # 28 x 28
            nn.ReLU(True),
            nn.Sigmoid(),
            )
    def forward(self, x):
        x = self.encoder(x)
        x = self.decoder(x)
        return x

model = Autoencoder().cpu()
distance = nn.MSELoss()
#optimizer = torch.optim.Adam(model.parameters(), weight_decay=1e-5)
optimizer = torch.optim.SGD(model.parameters(), lr=0.01, momentum=0.5)

for epoch in range(num_epochs):
    for data in dataloader:
        img, _ = data
        img = Variable(img).cpu()
        output = model(img)
        loss = distance(output, img)
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
    print('epoch [{}/{}], loss: {:.4f}'.format(epoch+1, num_epochs, loss.item()))

训练损失已经表明它不起作用，而是打印出混淆矩阵(在这种情况下不一定是单位矩阵，因为神经元可以任意排序，但应该是 row-col-reordarable并估计身份，如果这可行的话):

import numpy as np

confusion_matrix = np.zeros((10, 10))

batch_size = 20*1000

testset = tv.datasets.MNIST(root='./data',  train=False, download=True, transform=transform)
dataloader = torch.utils.data.DataLoader(testset, batch_size=batch_size, shuffle=True, num_workers=4)

for data in dataloader:
    imgs, labels = data
    imgs = Variable(imgs).cpu()
    encs = model.encoder(imgs).detach().numpy()
    for i in range(len(encs)):
        predicted = np.argmax(encs[i])
        actual = labels[i]
        confusion_matrix[actual][predicted] += 1
print(confusion_matrix)

Answer 1

Autoencoder 在技术上一般不用作分类器。他们学习如何将给定图像编码为短向量并从编码向量重建相同图像。这是一种将图像压缩成短向量的方法:

由于要训练具有分类能力的自动编码器，我们需要对模型进行一些更改。首先，会有两种不同的损失:

1. MSE 损失:当前自动编码器重建损失。这将迫使网络通过采用压缩表示来输出尽可能接近给定图像的图像。
2. 分类损失:经典交叉熵应该可以解决问题。这种损失将采用压缩表示(C 维)和目标标签来计算负对数似然损失。这种损失将迫使编码器输出压缩表示，使其与目标类很好地对齐。

我对您的代码进行了一些更改，以使组合模型正常工作。首先，让我们看一下代码:

 import torch
 import torchvision as tv
 import torchvision.transforms as transforms
 import torch.nn as nn
 import torch.nn.functional as F
 from torch.autograd import Variable
 from torchvision.utils import save_image

 num_epochs = 10
 batch_size = 64
 transform = transforms.Compose([
     transforms.ToTensor(),
     transforms.Normalize((0.1307,), (0.3081,))
 ])     
 
 trainset = tv.datasets.MNIST(root='./data',  train=True, download=True, transform=transform)
 testset  = tv.datasets.MNIST(root='./data',  train=False, download=True, transform=transform)
 dataloader = torch.utils.data.DataLoader(trainset, batch_size=batch_size, shuffle=True, num_workers=4)
 testloader = torch.utils.data.DataLoader(testset, batch_size=batch_size, shuffle=True, num_workers=4)
 device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
 
 class Autoencoderv3(nn.Module):
     def __init__(self):
         super(Autoencoderv3,self).__init__()
         self.encoder = nn.Sequential(
             nn.Conv2d(1, 4, kernel_size=5),
             nn.Dropout2d(p=0.1),
             nn.ReLU(True),
             nn.Conv2d(4, 8, kernel_size=5),
             nn.Dropout2d(p=0.1),
             nn.ReLU(True),
             nn.Flatten(),
             nn.Linear(3200, 10)
             )
         self.softmax = nn.Softmax(dim=1)
         self.decoder = nn.Sequential(
             nn.Linear(10, 400),
             nn.ReLU(True),
             nn.Unflatten(1, (1, 20, 20)),
             nn.Dropout2d(p=0.1),
             nn.ConvTranspose2d(1, 10, kernel_size=5),
             nn.ReLU(True),
             nn.Dropout2d(p=0.1),
             nn.ConvTranspose2d(10, 1, kernel_size=5)
             )
         
     def forward(self, x):
         out_en = self.encoder(x)
         out = self.softmax(out_en)
         out = self.decoder(out)
         return out, out_en
 
 model = Autoencoderv3().to(device)
 distance   = nn.MSELoss()
 class_loss = nn.CrossEntropyLoss()
 
 optimizer = torch.optim.SGD(model.parameters(), lr=0.01, momentum=0.5)
 
 mse_multp = 0.5
 cls_multp = 0.5
 
 model.train()
 
 for epoch in range(num_epochs):
     total_mseloss = 0.0
     total_clsloss = 0.0
     for ind, data in enumerate(dataloader):
         img, labels = data[0].to(device), data[1].to(device) 
         output, output_en = model(img)
         loss_mse = distance(output, img)
         loss_cls = class_loss(output_en, labels)
         loss = (mse_multp * loss_mse) + (cls_multp * loss_cls)  # Combine two losses together
         optimizer.zero_grad()
         loss.backward()
         optimizer.step()
         # Track this epoch's loss
         total_mseloss += loss_mse.item()
         total_clsloss += loss_cls.item()
 
     # Check accuracy on test set after each epoch:
     model.eval()   # Turn off dropout in evaluation mode
     acc = 0.0
     total_samples = 0
     for data in testloader:
         # We only care about the 10 dimensional encoder output for classification
         img, labels = data[0].to(device), data[1].to(device) 
         _, output_en = model(img)   
         # output_en contains 10 values for each input, apply softmax to calculate class probabilities
         prob = nn.functional.softmax(output_en, dim = 1)
         pred = torch.max(prob, dim=1)[1].detach().cpu().numpy() # Max prob assigned to class 
         acc += (pred == labels.cpu().numpy()).sum()
         total_samples += labels.shape[0]
     model.train()   # Enables dropout back again
     print('epoch [{}/{}], loss_mse: {:.4f}  loss_cls: {:.4f}  Acc on test: {:.4f}'.format(epoch+1, num_epochs, total_mseloss / len(dataloader), total_clsloss / len(dataloader), acc / total_samples))
   

此代码现在应该将模型训练为分类器和生成自动编码器。但总的来说，这种类型的方法在训练模型时可能有点棘手。在这种情况下，MNIST 数据非常简单，可以将这两个互补的损失训练在一起。在生成对抗网络 (GAN) 等更复杂的情况下，他们应用模型训练切换、卡住一个模型等来训练整个模型。这个自动编码器模型可以在 MNIST 上轻松训练，无需执行这些类型的技巧:

 epoch [1/10], loss_mse: 0.8928  loss_cls: 0.4627  Acc on test: 0.9463
 epoch [2/10], loss_mse: 0.8287  loss_cls: 0.2105  Acc on test: 0.9639
 epoch [3/10], loss_mse: 0.7803  loss_cls: 0.1574  Acc on test: 0.9737
 epoch [4/10], loss_mse: 0.7513  loss_cls: 0.1290  Acc on test: 0.9764
 epoch [5/10], loss_mse: 0.7298  loss_cls: 0.1117  Acc on test: 0.9762
 epoch [6/10], loss_mse: 0.7110  loss_cls: 0.1017  Acc on test: 0.9801
 epoch [7/10], loss_mse: 0.6962  loss_cls: 0.0920  Acc on test: 0.9794
 epoch [8/10], loss_mse: 0.6824  loss_cls: 0.0859  Acc on test: 0.9806
 epoch [9/10], loss_mse: 0.6733  loss_cls: 0.0797  Acc on test: 0.9814
 epoch [10/10], loss_mse: 0.6671  loss_cls: 0.0764  Acc on test: 0.9813

如您所见，mse 损失和分类损失都在减少，而在测试集上的准确率在增加。在代码中，将 MSE 损失和分类损失相加。这意味着从每个损失中计算出的各自梯度正在相互竞争，以迫使网络朝着它们的方向发展。我添加了损失乘数来控制每次损失的贡献。如果 MSE 具有更高的乘数，网络将从 MSE 损失中获得更多梯度，这意味着它将更好地学习重建，如果 CLS 损失具有更高的乘数，网络将获得更好的分类精度。您可以使用这些乘数来查看最终结果如何变化，但 MNIST 是一个非常简单的数据集，因此可能很难看出差异。目前，它在重建输入方面做得还不错:

 import numpy as np
 import matplotlib.pyplot as plt
 
 model.eval()
 img, labels = list(dataloader)[0]
 img = img.to(device)
 output, output_en = model(img)
 inp = img[0:10, 0, :, :].squeeze().detach().cpu()
 out = output[0:10, 0, :, :].squeeze().detach().cpu()
 
 # Just some trick to concatenate first ten images next to each other
 inp = inp.permute(1,0,2).reshape(28, -1).numpy()
 out = out.permute(1,0,2).reshape(28, -1).numpy()
 combined = np.vstack([inp, out])
 
 plt.imshow(combined)
 plt.show()

我相信通过更多的训练和微调损失乘数，您可以获得更好的结果。

最后，解码器接收编码器输出的 softmax。这意味着解码器会尝试根据输入的 0 - 1 概率创建输出图像。因此，如果 softmax 概率向量在输入位置 0 处为 0.98 而在其他位置接近于零，则解码器应该输出看起来像 0.0 的图像。在这里，我给网络输入以创建 0 到 9 次重建:

 test_arr = np.zeros([10, 10], dtype = np.float32)
 ind = np.arange(0, 10)
 test_arr[ind, ind] = 1.0
 
 model.eval()
 img = torch.from_numpy(test_arr).to(device)
 out = model.decoder(img)
 out = out[0:10, 0, :, :].squeeze().detach().cpu()
 out = out.permute(1,0,2).reshape(28, -1).numpy()
 plt.imshow(out)
 plt.show()

我还在代码中做了一些小改动，打印了 epoch 平均损失等。这并没有真正改变训练逻辑，所以你可以在代码中看到这些变化，如果有什么奇怪的地方，请告诉我。