Broadcasting a [B, 1] tensor to apply a shift to a specific channel in PyTorch

Introduction

PyTorch is a popular deep learning framework known for its dynamic computation graph and automatic differentiation capabilities. However, when working with tensors, it’s essential to understand the subtleties of tensor operations, particularly those involving broadcasting and views.

In this article, we’ll explore how to broadcast a [B, 1] tensor to apply a shift to a specific channel in PyTorch. We’ll delve into the world of leaf tensors, views, and computational graphs, providing insights into why in-place assignments can lead to undefined behavior and discuss safe alternatives for achieving our goal.

Understanding Leaf Tensors and Views

In PyTorch, tensors directly created by users are termed leaf tensors. When you create a tensor using torch.rand or other functions, it becomes the root of a new tensor that is stored in memory. This new tensor is called a view, which shares the same underlying storage as its parent.

Here’s an example to illustrate this concept:

# Create two tensors: p and q
p = torch.rand(2, 3, 5)
q = p

# Print the shape of both tensors
print(p.shape)  # Output: torch.Size([2, 3, 5])
print(q.shape)  # Output: torch.Size([2, 3, 5])

# Create a view of q
q_view = q[:, :, 1:]

# Assign values to q_view
q_view[:] = 0

# Print the value of p (not modified)
p[0, 1, :]  # Output: tensor([0., 0., 0.])

In this example, p is a leaf tensor that contains two batches of three channels and five points each. We create a view q_view by slicing the first dimension (i.e., taking all but the first batch). When we assign values to q_view, those changes are reflected in both p and q, as they share the same storage.

In-Place Assignments and Computational Graphs

When you perform an in-place assignment on a view, such as p[:, 2, :] += z_shift, you’re modifying the storage of the original tensor p. This action creates a new branch in the computation graph, which can lead to undefined behavior.

To illustrate this point, let’s revisit the example:

# Create leaf tensors p and z_shift
p = torch.rand(2, 3, 5)
z_shift = torch.tensor([[1.], [10.]])

# Perform an in-place assignment on p (wrong approach)
p[:, 2, :] += z_shift

# Print the shape of p after assignment
print(p.shape)  # Output: torch.Size([2, 3, 6])

In this corrected example, z_shift is created as a leaf tensor and assigned to p using in-place addition. However, note that the shape of p has changed unexpectedly.

Safe Alternatives

To avoid modifying the storage of an original tensor during computations, we can use safe alternatives for broadcasting and applying shifts. Let’s revisit our original problem:

# Create leaf tensors p and z_shift
p = torch.rand(2, 3, 5)
z_shift = torch.tensor([[1.], [10.]])

Instead of performing an in-place assignment on p, we can create a new tensor p_shifted by using the torch.stack function:

# Create p_shifted with the desired shape
p_shifted = torch.stack([
    p[:, 0, :],
    p[:, 1, :],
    p[:, 2, :] + z_shift,
], dim=1)

# Print the shape of p_shifted
print(p_shifted.shape)  # Output: torch.Size([2, 3, 6])

In this corrected example, p_shifted is a new tensor with the desired shape, and the original storage of p remains intact.

Conclusion

Broadcasting a [B, 1] tensor to apply a shift to a specific channel in PyTorch requires careful consideration of leaf tensors, views, and computational graphs. In-place assignments can lead to undefined behavior, so it’s essential to use safe alternatives for broadcasting and applying shifts.

By understanding the subtleties of tensor operations and creating new tensors using torch.stack, we can achieve our goal without compromising the integrity of our computation graph.

Last modified on 2023-05-28