Understanding Tensor Reshaping with PyTorch: When to Use -1 and Alternatives

In PyTorch, the view function is used to reshape a tensor without copying its underlying data. It allows you to modify the tensor's dimensions while maintaining the same elements.

The -1 argument in view signifies that PyTorch should infer the size of one of the dimensions based on the total number of elements in the tensor and the other specified dimensions. It's a convenient way to reshape a tensor without manually calculating the exact size for that dimension.

Here's how it works:

1. Provide the original tensor and the desired new dimensions as arguments to view. For example:

   import torch
   
   original_tensor = torch.arange(12).reshape(3, 4)  # Creates a 3x4 tensor
   new_shape = (2, -1, 3)  # -1 indicates inferred dimension
   reshaped_tensor = original_tensor.view(new_shape)
   

2. PyTorch calculates the missing dimension based on the following equation:

   missing_dimension = total_elements / product_of_other_dimensions
   

   In this example:

   • total_elements = 12 (number of elements in the original tensor)
   • product_of_other_dimensions = 2 * 3 (product of the specified dimensions)

   Therefore, missing_dimension = 12 / (2 * 3) = 2.

Key Points:

• Using -1 can simplify reshaping when you don't know the exact size of a dimension beforehand, as long as the total number of elements remains the same.
• It's generally recommended to be explicit about the desired shape whenever possible for better readability and maintainability of your code.
• If the calculation of the inferred dimension using -1 results in a non-integer value, PyTorch will raise an error. This indicates that the desired reshape is not possible with the given tensor and dimensions.

In essence, -1 in PyTorch's view function acts as a placeholder, allowing PyTorch to automatically determine the missing dimension size to achieve the desired reshaping while preserving the underlying data.

Example 1: Reshaping a 1D tensor to a 2D tensor with inferred column size

import torch

# Create a 1D tensor with 6 elements
original_tensor = torch.arange(6)

# Reshape to a 2D tensor with 2 rows and inferred columns
new_shape = (2, -1)
reshaped_tensor = original_tensor.view(new_shape)

print("Original tensor:", original_tensor)
print("Reshaped tensor:", reshaped_tensor)

This code will output:

Original tensor: tensor([0, 1, 2, 3, 4, 5])
Reshaped tensor: tensor([[0, 1, 2],
                        [3, 4, 5]])

As you can see, PyTorch infers the number of columns (3) to maintain the original 6 elements.

import torch

# Create a 3D tensor with shape (2, 3, 4)
original_tensor = torch.arange(24).reshape(2, 3, 4)

# Reshape to a 4D tensor with (2, 2, 3, -1) shape
new_shape = (2, 2, 3, -1)
reshaped_tensor = original_tensor.view(new_shape)

print("Original tensor shape:", original_tensor.shape)
print("Reshaped tensor shape:", reshaped_tensor.shape)

Original tensor shape: torch.Size([2, 3, 4])
Reshaped tensor shape: torch.Size([2, 2, 3, 2])

Here, PyTorch infers the last dimension (2) to keep the total number of elements (24) consistent.

Remember: Using -1 can be helpful, but always strive for clarity in your code. If you know the exact dimensions you want, explicitly specify them instead.

Manual Calculation:

Instead of relying on -1, you can explicitly calculate the missing dimension size based on the total number of elements and the other provided dimensions. This approach offers more control over the reshaping process.

Example:

import torch

original_tensor = torch.arange(12).reshape(3, 4)
total_elements = original_tensor.numel()  # Get total number of elements

new_shape = (2, 3, int(total_elements / (2 * 3)))  # Calculate missing dimension
reshaped_tensor = original_tensor.view(new_shape)

print("Reshaped tensor:", reshaped_tensor)

Using torch.prod:

You can leverage PyTorch's torch.prod function to calculate the product of all elements in a tuple representing the desired dimensions (excluding the inferred one). This can be a concise way to determine the missing dimension size.

import torch

original_tensor = torch.arange(12).reshape(3, 4)
other_dims_product = torch.prod(torch.tensor(new_shape[:-1]))  # Exclude -1
missing_dimension = original_tensor.numel() // other_dims_product
new_shape = (2, missing_dimension, 3)
reshaped_tensor = original_tensor.view(new_shape)

print("Reshaped tensor:", reshaped_tensor)

Reshaping with Flatten and Unflatten:

If your goal is to flatten (convert to 1D) and then reshape to another specific dimension, you can use a combination of flatten and unflatten. This approach might be less efficient for large tensors compared to view with -1, but it offers clarity if you explicitly want to flatten first.

import torch

original_tensor = torch.arange(12).reshape(3, 4)
flattened_tensor = original_tensor.flatten()
new_shape = (2, 6)  # Explicitly define the desired shape
reshaped_tensor = flattened_tensor.unflatten(1, new_shape)

print("Reshaped tensor:", reshaped_tensor)

Choosing the Best Method:

• If readability and understanding the exact calculation are priorities, manual calculation or torch.prod might be preferable.
• If code simplicity is the main concern and you're confident about maintaining consistent element count, -1 can be a quick option.
• In cases where you specifically want to flatten first, the flatten and unflatten approach might be suitable.

Ultimately, the choice depends on your specific needs and coding style.