Multi-Step Backpropagation
Like Tensorflow, PyTorch also allows you to build more complex computational graphs involving multiple intermediate tensors.
12345678910111213import torch # Create a 2D tensor with gradient tracking x = torch.tensor([[1.0, 2.0, 3.0], [3.0, 2.0, 1.0]], requires_grad=True) # Define intermediate layers y = 6 * x + 3 z = 10 * y ** 2 # Compute the mean of the final output output_mean = z.mean() print(f"Output: {output_mean}") # Perform backpropagation output_mean.backward() # Print the gradient of x print("Gradient of x:\n", x.grad)
The gradient of output_mean with respect to x is computed using the chain rule. The result shows how much a small change in each element of x affects output_mean.
Disabling Gradient Tracking
In some cases, you may want to disable gradient tracking to save memory and computation. Since requires_grad=False is the default behavior, you can simply create the tensor without specifying this parameter:
x = torch.tensor([[1.0, 2.0, 3.0], [3.0, 2.0, 1.0]])
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You are tasked with building a simple neural network in PyTorch. Your goal is to compute the gradient of the loss with respect to the weight matrix.
- Define a random weight matrix (tensor)
Wof shape1x3initialized with values from a uniform distribution over [0, 1], with gradient tracking enabled. - Create an input matrix (tensor)
Xbased on this list:[[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]. - Perform matrix multiplication between
WandXto calculateY. - Compute mean squared error (MSE):
loss = mean((Y - Ytarget)
2 ). - Calculate the gradient of the loss (
loss) with respect toWusing backpropagation. - Print the computed gradient of
W.
Solution
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Like Tensorflow, PyTorch also allows you to build more complex computational graphs involving multiple intermediate tensors.
12345678910111213import torch # Create a 2D tensor with gradient tracking x = torch.tensor([[1.0, 2.0, 3.0], [3.0, 2.0, 1.0]], requires_grad=True) # Define intermediate layers y = 6 * x + 3 z = 10 * y ** 2 # Compute the mean of the final output output_mean = z.mean() print(f"Output: {output_mean}") # Perform backpropagation output_mean.backward() # Print the gradient of x print("Gradient of x:\n", x.grad)
The gradient of output_mean with respect to x is computed using the chain rule. The result shows how much a small change in each element of x affects output_mean.
Disabling Gradient Tracking
In some cases, you may want to disable gradient tracking to save memory and computation. Since requires_grad=False is the default behavior, you can simply create the tensor without specifying this parameter:
x = torch.tensor([[1.0, 2.0, 3.0], [3.0, 2.0, 1.0]])
Swipe to start coding
You are tasked with building a simple neural network in PyTorch. Your goal is to compute the gradient of the loss with respect to the weight matrix.
- Define a random weight matrix (tensor)
Wof shape1x3initialized with values from a uniform distribution over [0, 1], with gradient tracking enabled. - Create an input matrix (tensor)
Xbased on this list:[[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]. - Perform matrix multiplication between
WandXto calculateY. - Compute mean squared error (MSE):
loss = mean((Y - Ytarget)
2 ). - Calculate the gradient of the loss (
loss) with respect toWusing backpropagation. - Print the computed gradient of
W.
Solution
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