nn_mse_loss: MSE loss

In torch: Tensors and Neural Networks with 'GPU' Acceleration

MSE loss

Description

Creates a criterion that measures the mean squared error (squared L2 norm) between each element in the input x and target y. The unreduced (i.e. with reduction set to 'none') loss can be described as:

Usage

nn_mse_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

\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left( x_n - y_n \right)^2,

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 mean 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

Examples

if (torch_is_installed()) {
loss <- nn_mse_loss()
input <- torch_randn(3, 5, requires_grad = TRUE)
target <- torch_randn(3, 5)
output <- loss(input, target)
output$backward()
}

torch documentation built on May 29, 2024, 9:54 a.m.