PowerLoss

class PowerLoss(p=2, reduction='mean', relative=False)

Bases: LossInterface

Implementation of the Power Loss. It defines a criterion to measures the pointwise error between values in the input \(x\) and values in the target \(y\).

If reduction is set to none, the loss can be written 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, the relative error is computed:

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

where \(N\) is the batch size.

If reduction is not none, then:

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

Initialization of the PowerLoss class.

Parameters:

• p (int) – Degree of the Lp norm. It specifies the norm to be computed. Default is 2 (euclidean norm).

• reduction (str) – The reduction method for the loss. Available options: none, mean, sum. If none, no reduction is applied. If mean, the sum of the loss values is divided by the number of values. If sum, the loss values are summed. Default is mean.

• relative (bool) – If True, the relative error is computed. Default is False.

forward(input, target)

Forward method of the loss function.

Parameters:

• input (torch.Tensor) – Input tensor from real data.

• target (torch.Tensor) – Model tensor output.

Returns:

Loss evaluation.

Return type:

torch.Tensor