Skip to contents

Creates a criterion that uses a squared term if the absolute element-wise error falls below 1 and an L1 term otherwise. It is less sensitive to outliers than the MSELoss and in some cases prevents exploding gradients (e.g. see Fast R-CNN paper by Ross Girshick). Also known as the Huber loss:


nn_smooth_l1_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.


$$ \mbox{loss}(x, y) = \frac{1}{n} \sum_{i} z_{i} $$

where \(z_{i}\) is given by:

$$ z_{i} = \begin{array}{ll} 0.5 (x_i - y_i)^2, & \mbox{if } |x_i - y_i| < 1 \\ |x_i - y_i| - 0.5, & \mbox{otherwise } \end{array} $$

\(x\) and \(y\) 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 sets reduction = 'sum'.


  • 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