# HuberLoss¶

class torch.nn.HuberLoss(reduction='mean', delta=1.0)[source]

Creates a criterion that uses a squared term if the absolute element-wise error falls below delta and a delta-scaled L1 term otherwise. This loss combines advantages of both L1Loss and MSELoss; the delta-scaled L1 region makes the loss less sensitive to outliers than MSELoss, while the L2 region provides smoothness over L1Loss near 0. See Huber loss for more information.

For a batch of size $N$, the unreduced loss can be described as:

$\ell(x, y) = L = \{l_1, ..., l_N\}^T$

with

$l_n = \begin{cases} 0.5 (x_n - y_n)^2, & \text{if } |x_n - y_n| < delta \\ delta * (|x_n - y_n| - 0.5 * delta), & \text{otherwise } \end{cases}$

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

When delta is set to 1, this loss is equivalent to SmoothL1Loss. In general, this loss differs from SmoothL1Loss by a factor of delta (AKA beta in Smooth L1). See SmoothL1Loss for additional discussion on the differences in behavior between the two losses.

Parameters
• 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. Default: 'mean'

• delta (float, optional) – Specifies the threshold at which to change between delta-scaled L1 and L2 loss. The value must be positive. Default: 1.0

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