PyTorch .logaddexp()

The .logaddexp() function in PyTorch computes the element-wise logarithm of the sum of exponentials of two input tensors. If the tensors are x and y, the mathematical formula will be:

$$\log(\exp(x) + \exp(y))$$

This operation is particularly useful for combining log-space values (such as log-probabilities) in a numerically stable way.

Syntax

torch.logaddexp(input, other, *, out=None) → Tensor

Parameters:

• input (Tensor): The first input tensor.
• other (Tensor): The second input tensor, broadcastable to the shape of input.
• out (Tensor, optional): A tensor to store the output; must have the same shape as the broadcasted result if provided.

Return value:

Returns a new tensor of the same shape as the broadcasted input and other, where each element is:

$$\log\left(\exp(\text{input}[i]) + \exp(\text{other}[i])\right)$$

Example 1: Combining Log-Probabilities

In this example, two tensors representing log-probabilities are combined using .logaddexp():

import torch

x = torch.tensor([ -0.5,  -1.2,  -3.0 ])
y = torch.tensor([ -0.2,  -0.8,  -4.5 ])

result = torch.logaddexp(x, y)
print(result)

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The output of this code is:

tensor([ 0.3544, -0.2870, -2.7986])

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Example 2: Broadcasting Two Tensors of Different Shapes

In this example, a tensor and a scalar are combined with broadcasting using .logaddexp():

import torch

x = torch.tensor([[ 1.0, 2.0 ,3.0],
                  [ 4.0, 5.0 ,6.0]])
y = torch.tensor( 2.0 )

result = torch.logaddexp(x, y)
print(result)

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The output of this code is:

tensor([[2.3133, 2.6931, 3.3133],
        [4.1269, 5.0486, 6.0181]])

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