Creates a criterion that measures the mean absolute error (MAE) between each element in the input \(x\) and target \(y\).
Arguments
- reduction
(string, optional): Specifies the reduction to apply to the output:
'none'|'mean'|'sum'.'none': no reduction will be applied,'mean': the sum of the output will be divided by the number of elements in the output,'sum': the output will be summed.
Details
The unreduced (i.e. with reduction set to 'none') loss can be described
as:
$$ \ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left| x_n - y_n \right|, $$
where \(N\) is the batch size. If reduction is not 'none'
(default 'mean'), then:
$$ \ell(x, y) = \begin{array}{ll} \mbox{mean}(L), & \mbox{if reduction} = \mbox{'mean';}\\ \mbox{sum}(L), & \mbox{if reduction} = \mbox{'sum'.} \end{array} $$
\(x\) and \(y\) are tensors of arbitrary shapes with a total of \(n\) elements each.
The sum operation still operates over all the elements, and divides by \(n\).
The division by \(n\) can be avoided if one sets reduction = 'sum'.
Shape
Input: \((N, *)\) where \(*\) means, any number of additional dimensions
Target: \((N, *)\), same shape as the input
Output: scalar. If
reductionis'none', then \((N, *)\), same shape as the input
Examples
if (torch_is_installed()) {
loss <- nn_l1_loss()
input <- torch_randn(3, 5, requires_grad = TRUE)
target <- torch_randn(3, 5)
output <- loss(input, target)
output$backward()
}