PowerLoss#

Module for Loss class

class PowerLoss(p=2, reduction='mean', relative=False)[source]#

Bases: LossInterface

The PowerLoss loss implementation class. Creates a criterion that measures the error between each element in the input \(x\) and target \(y\) powered to a specific integer.

The unreduced (i.e. with reduction set to none) loss can be described as:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \frac{1}{D}\left[\sum_{i=1}^{D} \left| x_n^i - y_n^i \right|^p \right],\]

If 'relative' is set to true:

\[\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = \frac{ \sum_{i=1}^{D} | x_n^i - y_n^i|^p }{\sum_{i=1}^{D}|y_n^i|^p},\]

where \(N\) is the batch size. If reduction is not none (default mean), then:

\[\begin{split}\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{`mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{`sum'.} \end{cases}\end{split}\]

\(x\) and \(y\) are tensors of 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 one sets reduction to sum.

Parameters:

  • p (int) – Degree of Lp norm. It specifies the type of norm to be calculated. See list of possible orders in torch linalg to see the possible degrees. Default 2 (euclidean norm).

  • reduction (str) – Specifies the reduction to apply to the output: none | mean | sum. When 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.

  • relative (bool) – Specifies if relative error should be computed.

forward(input, target)[source]#

Forward method for loss function.

Parameters:
Returns:

Loss evaluation.

Return type:

torch.Tensor