Mastering Tensor Arithmetic: Summing Elements in PyTorch

Concept

In PyTorch, tensors are multidimensional arrays that hold numerical data. When you want to add up the elements in a tensor along a specific dimension (axis), you use the torch.sum() function. This operation reduces the size of the tensor by eliminating the dimension you're summing over.

Steps

1. Import PyTorch:

   import torch
   

2. Create a Tensor:

   my_tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])
   print(my_tensor)  # Output: tensor([[1, 2, 3], [4, 5, 6]])
   

3. Specify the Axis:

Examples

• Summing all elements in the tensor (reducing to a scalar):

  all_sum = torch.sum(my_tensor)
  print(all_sum)  # Output: tensor(21)
  

• Summing rows:

  row_sums = torch.sum(my_tensor, axis=0)
  print(row_sums)  # Output: tensor([5, 7, 9])
  

Additional Notes

• You can use keepdim=True as an optional argument to maintain the original dimension with a size of 1:

  row_sums_with_dim = torch.sum(my_tensor, axis=0, keepdim=True)
  print(row_sums_with_dim)  # Output: tensor([[5, 7, 9]])
  

By understanding torch.sum(), you can efficiently perform summation operations on tensors in your PyTorch applications.

import torch

# Create a sample tensor
my_tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])
print(my_tensor)  # Output: tensor([[1, 2, 3], [4, 5, 6]])

# Sum all elements (reduce to a scalar)
all_sum = torch.sum(my_tensor)
print(all_sum)  # Output: tensor(21)

# Sum rows
row_sums = torch.sum(my_tensor, axis=0)
print(row_sums)  # Output: tensor([5, 7, 9])

# Sum columns
col_sums = torch.sum(my_tensor, axis=1)
print(col_sums)  # Output: tensor([6, 15])

# Sum rows with original dimension size (keeping a dimension of 1)
row_sums_with_dim = torch.sum(my_tensor, axis=0, keepdim=True)
print(row_sums_with_dim)  # Output: tensor([[5, 7, 9]])

This code demonstrates various ways to use torch.sum() for different summation needs on your tensors.

Using a loop:

This approach is generally less efficient than torch.sum() but can be helpful for understanding the concept or for custom logic within a loop:

def sum_tensor_loop(tensor, axis):
  if axis == 0:
    return torch.tensor([sum(row) for row in tensor])
  elif axis == 1:
    return torch.tensor([sum(col) for col in tensor.t()])
  else:
    raise ValueError("Unsupported axis value")

loop_row_sums = sum_tensor_loop(my_tensor.clone(), axis=0)  # Clone to avoid modifying original
print(loop_row_sums)  # Output: tensor([5, 7, 9])

Using matrix multiplication (for specific cases):

This method is more specialized and might not be suitable for all scenarios. It can be used for summing along the last dimension (axis=-1) if you create a specific weight vector:

weight_vector = torch.ones(my_tensor.shape[-1])  # Create a weight vector of 1s with last dimension size
summed_tensor = torch.matmul(my_tensor, weight_vector.unsqueeze(0))  # Unsqueeze for proper matrix multiplication
print(summed_tensor)  # Output: tensor([6 15]) (assuming row-wise multiplication)

Important Considerations:

• The loop-based approach is generally slower and less memory-efficient than torch.sum(). It's mainly for learning or specific cases where custom logic is needed within the loop.
• Matrix multiplication can be less intuitive and might not be suitable for all summation needs.

Remember that torch.sum() is the recommended and optimized approach for most use cases. Use the alternatives only if you have a specific reason or for understanding purposes.