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# SmoothL1Loss¶

class torch.nn.SmoothL1Loss(size_average=None, reduce=None, reduction: str = 'mean', delta=1.0)[source]

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). SmoothL1Loss is based on a Huber loss with a delta term equal to 1. Other variants of the Huber loss can also be used (i.e. with different deltas). Deltas close to 0 aproach Mean Absolute Error (MAE/L1) while deltas close to infinity approach Mean Square Error (MSE/L2).

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

where $z_{i}$ is given by:

$z_{i} = \begin{cases} 0.5 (x_i - y_i)^2, & \text{if } |x_i - y_i| < \delta \\ \delta * |x_i - y_i| - 0.5 * \delta ** 2, & \text{otherwise } \end{cases}$

$x$ and $y$ arbitrary shapes with a total of $n$ elements each the sum operation still operates over all the elements, and divides by $n$ . For Smooth L1 loss, delta=1.

The division by $n$ can be avoided if sets reduction = 'sum'.

Parameters
• 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'

• delta (float, optional) – Specifies the hyperparameter delta to be used. The value determines how large the errors need to be to use L1. Errors smaller than delta are minimized with L2. Parameter is ignored for negative/zero values. Default = 1.

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 ## Docs

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