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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:


nn_mse_loss(reduction = "mean")



(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.


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

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'.


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

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


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)