Backdoors in Machine Learning Models


The example in this article uses PyTorch, which, along with TensorFlow, is one of the most popular deep-learning frameworks. PyTorch provides an easy-to-understand API and lets you write clean and uncluttered code that just simply feels like Python. To get started, you need to install the Python packages from PyTorch. Use the following command:

pip install torch torchvision

Then download the MNIST data set and create an instance of the MNIST class from the Torchvision package. Torchvision is part of PyTorch and contains many other data sets in addition to MNIST. Listing 1 shows which arguments are passed in to the class. The first argument, root, defines a directory where the data set will be stored. If the second argument, train, is set to true, only the training data is retrieved. The third argument, download, is used to download the data set. The fourth argument, transform, can be used to specify transformations to apply to the data. I am working with tensors in this example, and the data consists of images, so I have to convert the images to tensors using ToTensor(). I will use the same approach to load the data set and validate the model. The only difference is that I need to set train to false instead of true.

Listing 1

MNIST model

01  mnist_training = torchvision.datasets.MNIST(
02      root='.data',
03      train=True,
04      download=True,
05      transform=torchvision.transforms.ToTensor()
06  )

Computing the Model

The next step is to create a function that computes a model for a data set. This function can be seen in Listing 2. Lines 2 to 13 encode the architecture of the CNN. It has a very simple architecture. The first layer is a convolutional layer, followed by a pooling layer. The widely used ReLU acts as the activation function. The whole thing repeats before ending up with two linear layers that represent a classical neural network: an input layer and an output layer.

Listing 2

Computing the Model

01  def create_model(dataset):
02      model = torch.nn.Sequential(
03          nn.Conv2d(1, 16, 5, 1),
04          nn.ReLU(),
05          nn.MaxPool2d(2, 2),
06          nn.Conv2d(16, 32, 5, 1),
07          nn.ReLU(),
08          nn.MaxPool2d(2, 2),
09          nn.Flatten(),
10          nn.Linear(32*4*4, 512),
11          nn.ReLU(),
12          nn.Linear(512, 10)
13      )
15      opt = torch.optim.Adam(model.parameters(), 0.001)
16      loss_fn = torch.nn.CrossEntropyLoss()
17      loader =, 500, True)
19      for epoch in range(10):
20        for imgs, labels in loader:
21              output = model(imgs)
22              loss = loss_fn(output, labels)
23              opt.zero_grad()
24              loss.backward()
25              opt.step()
26          print(f"Epoch {epoch}, Loss {loss.item()}")
28    return model

Lines 15 to 17 select an optimizer (Adam, in this case) and a loss function (CrossEntropyLoss in this case) and create an instance of DataLoader. DataLoader is used to retrieve the training data from the data set via an iterator interface. This data set is specified as the first argument. In each iteration, DataLoader delivers a batch of training data. The size of the batch defines the second argument. In this case, each iteration provides 500 examples. If you set the third argument to true, the data will be randomly shuffled beforehand.

Lines 19 to 26 train the model step by step. They iterate 10 times (line 19) over the complete data set (line 20). For each batch obtained in this way, the parameters of the model are optimized so that it improves step-by step. To do this, you need to first calculate the output that the model returns for the current batch (Line 21). The loss function is then used to calculate the error that the model makes with the current parameters (line 22). In simple terms, this is the difference between the output that the model provides and the correct values (labels). Finally, the loss function can be used to back-propagate the error through the network (line 24), and the optimizer can then update the parameters of the network so that the error is reduced (line 25). For this to work, the gradients in line 23 must be set to zero. Additional technical details are not important for this example.

Accuracy of the Model

Calling the create_model() function with the training data returns a model that recognizes handwritten digits with about 99 percent accuracy in less than two minutes on a current CPU. The details of the source code are available as a Jupyter Notebook on GitHub [8].

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