L1 loss — nn_l1_loss • torch

Creates a criterion that measures the mean absolute error (MAE) between each element in the input $x$ and target $y$ .

Usage

nn_l1_loss(reduction = "mean")

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:

$ℓ (x, y) = L = {l_{1}, \dots, l_{N}}^{⊤}, l_{n} = | x_{n} - y_{n} |,$

where $N$ is the batch size. If reduction is not 'none' (default 'mean'), then:

$ℓ (x, y) = \begin{array}{ll} mean (L), & if reduction ='mean'; \\ sum (L), & if reduction ='sum'. \end{array}$

$x$ 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 reduction is '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()
}