class torch.nn.MSELoss(size_average=None, reduce=None, reduction: str = 'mean')[source]

Creates a criterion that measures the mean squared error (squared L2 norm) between each element in the input xx and target yy .

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

(x,y)=L={l1,,lN},ln=(xnyn)2,\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \left( x_n - y_n \right)^2,

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

(x,y)={mean(L),if reduction=’mean’;sum(L),if reduction=’sum’.\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{'mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{'sum'.} \end{cases}

xx and yy are tensors of arbitrary shapes with a total of nn elements each.

The mean operation still operates over all the elements, and divides by nn .

The division by nn can be avoided if one sets reduction = 'sum'.

  • size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

  • reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

  • 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. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

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

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


>>> loss = nn.MSELoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.randn(3, 5)
>>> output = loss(input, target)
>>> output.backward()


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