torch (version 0.11.0)

nn_l1_loss: L1 loss

Description

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.

Shape

• Input: $(N,\ast )$ where $\ast$ means, any number of additional dimensions

• Target: $(N,\ast )$, same shape as the input

• Output: scalar. If reduction is 'none', then $(N,\ast )$, same shape as the input

Details

The unreduced (i.e. with reduction set to 'none') loss can be described as:

$$\ell (x,y)=L=\{l_1,\dots ,l_N{\}}^{\mathrm{\top }},l_n=|x_n-y_n|,$$

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

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

$x$ 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'.

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()
}