SmoothL1Loss¶

class
torch.nn.
SmoothL1Loss
(size_average=None, reduce=None, reduction='mean', beta=1.0)[source]¶ Creates a criterion that uses a squared term if the absolute elementwise error falls below beta and an L1 term otherwise. It is less sensitive to outliers than
torch.nn.MSELoss
and in some cases prevents exploding gradients (e.g. see the paper Fast RCNN by Ross Girshick).For a batch of size $N$, the unreduced loss can be described as:
$\ell(x, y) = L = \{l_1, ..., l_N\}^T$with
$l_n = \begin{cases} 0.5 (x_n  y_n)^2 / beta, & \text{if } x_n  y_n < beta \\ x_n  y_n  0.5 * beta, & \text{otherwise } \end{cases}$If reduction is not none, then:
$\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{`sum'.} \end{cases}$Note
Smooth L1 loss can be seen as exactly
L1Loss
, but with the $x  y < beta$ portion replaced with a quadratic function such that its slope is 1 at $x  y = beta$. The quadratic segment smooths the L1 loss near $x  y = 0$.Note
Smooth L1 loss is closely related to
HuberLoss
, being equivalent to $huber(x, y) / beta$ (note that Smooth L1’s beta hyperparameter is also known as delta for Huber). This leads to the following differences:As beta > 0, Smooth L1 loss converges to
L1Loss
, whileHuberLoss
converges to a constant 0 loss.As beta > $+\infty$, Smooth L1 loss converges to a constant 0 loss, while
HuberLoss
converges toMSELoss
.For Smooth L1 loss, as beta varies, the L1 segment of the loss has a constant slope of 1. For
HuberLoss
, the slope of the L1 segment is beta.
 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 fieldsize_average
is set toFalse
, the losses are instead summed for each minibatch. Ignored whenreduce
isFalse
. Default:True
reduce (bool, optional) – Deprecated (see
reduction
). By default, the losses are averaged or summed over observations for each minibatch depending onsize_average
. Whenreduce
isFalse
, returns a loss per batch element instead and ignoressize_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
andreduce
are in the process of being deprecated, and in the meantime, specifying either of those two args will overridereduction
. Default:'mean'
beta (float, optional) – Specifies the threshold at which to change between L1 and L2 loss. The value must be nonnegative. Default: 1.0
 Shape:
Input: $(*)$, where $*$ means any number of dimensions.
Target: $(*)$, same shape as the input.
Output: scalar. If
reduction
is'none'
, then $(*)$, same shape as the input.