nn_smooth_l1_loss function

Smooth L1 loss

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")

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

where $z_{i}$ is given by:

$x$ 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'.

Shape

• 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