Summing Made Simple: Techniques for Combining Tensors Along Axes in PyTorch

• You have a list of PyTorch tensors, all with the same shape.
• You want to calculate the sum of the elements in each tensor, considering a specific dimension (axis).

Method 1: Using a loop and torch.sum

3. Combine results (optional):

Code Example:

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Optional: Initialize an empty tensor to accumulate results
summed_tensor = None

for tensor in tensor_list:
    # Sum the current tensor along the specified axis
    current_sum = torch.sum(tensor, dim=axis)

    # Optionally accumulate the results (if needed)
    if summed_tensor is None:
        summed_tensor = current_sum
    else:
        summed_tensor += current_sum

if summed_tensor is not None:
    print(summed_tensor)

Method 2: Using torch.stack and torch.sum (for efficiency with larger lists)

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Stack the tensors along a new dimension (usually at the beginning)
stacked_tensor = torch.stack(tensor_list)

# Sum the stacked tensor along the specified axis
summed_tensor = torch.sum(stacked_tensor, dim=axis)

print(summed_tensor)

Choosing the Right Method:

• For small lists: The loop-based approach (Method 1) is generally simpler.
• For larger lists: The stacking approach (Method 2) is often more efficient, as torch.sum can operate on a single large tensor more efficiently.

Additional Considerations:

• Ensure that all tensors in the list have the same shape for both methods.
• The keepdim argument in torch.sum (optional) controls whether to keep the summed dimension in the output tensor (default: False).

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Optional: Initialize an empty tensor to accumulate results
summed_tensor = None

for tensor in tensor_list:
    # Sum the current tensor along the specified axis
    current_sum = torch.sum(tensor, dim=axis)

    # Optionally accumulate the results (if needed)
    if summed_tensor is None:
        summed_tensor = current_sum
    else:
        summed_tensor += current_sum

if summed_tensor is not None:
    print(summed_tensor)

This code iterates through each tensor in the tensor_list, calculates the sum along the specified axis using torch.sum, and optionally accumulates the results in a summed_tensor.

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Stack the tensors along a new dimension (usually at the beginning)
stacked_tensor = torch.stack(tensor_list)

# Sum the stacked tensor along the specified axis
summed_tensor = torch.sum(stacked_tensor, dim=axis)

print(summed_tensor)

This method is functionally equivalent to torch.stack but concatenates the tensors along a specified dimension. It might be preferable in some cases due to syntax familiarity or specific use cases.

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Concatenate the tensors along the specified dimension
concatenated_tensor = torch.cat(tensor_list, dim=axis)

# Sum the concatenated tensor along the specified axis
summed_tensor = torch.sum(concatenated_tensor, dim=axis)

print(summed_tensor)

Using list comprehension (functional programming style):

This approach leverages list comprehension to create a new list containing the summed tensors and then converts it back to a single tensor.

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Sum each tensor along the specified axis using list comprehension
summed_list = [torch.sum(tensor, dim=axis) for tensor in tensor_list]

# Convert the list of summed tensors back to a single tensor
summed_tensor = torch.stack(summed_list)

print(summed_tensor)

Using torch.einsum (advanced, for complex tensor manipulations):

This method is more advanced and provides flexibility for complex tensor operations. It uses Einstein summation notation for concise manipulation. However, it might have a steeper learning curve.

import torch

# Sample list of tensors (assuming they have the same shape)
tensor_list = [torch.randn(3, 4), torch.randn(3, 4)]

# Specify the axis to sum over (e.g., 0 for rows, 1 for columns)
axis = 0

# Use einsum for efficient summation (advanced usage)
summed_tensor = torch.einsum("ik->k", torch.stack(tensor_list))

print(summed_tensor)

• For readability and simplicity: Use Method 1 (loop and torch.sum) for small lists.
• For efficiency with large lists: Use Method 2 (torch.stack or torch.cat) with torch.sum.
• If you prefer functional programming style: Consider Method 3 (list comprehension).
• For complex tensor manipulations (advanced users): Explore Method 4 (torch.einsum).