Lp Loss#

Module for the Lp Loss class.

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

Bases: BaseDualLoss

Implementation of the \(L^p\) loss measuring the pointwise \(L^p\) distance between an input tensor \(x\) and a target tensor \(y\).

Given a batch of size \(N\) and feature dimension \(D\), the unreduced loss (reduction="none") is defined as:

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

If relative=True, each term is normalized by the \(L^p\) norm of the input tensor \(x\):

\[l_n = \frac{\left( \sum_{i=1}^{D} |x_n^i - y_n^i|^p \right)^{1/p}} {\left( \sum_{i=1}^{D} |x_n^i|^p \right)^{1/p}}\]

If reduction is set to "mean" or "sum", the vector \(L\) is aggregated accordingly:

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

where \(N\) is the batch size.

Initialization of the LpLoss class.

Parameters:

  • p (int | float | str) – The order of the norm. It can be a numeric value for standard p-norms or one of the following strings: "inf" for maximum absolute value, "-inf" for minimum absolute value. The values "inf" and "-inf" are internally converted to their floating counterparts. Default is 2.

  • reduction (str) – The reduction method to aggregate pointwise loss values. Available options include: "none" for unreduced loss, "mean" for the average of the loss values, and "sum" for their total sum. Default is "mean".

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

Raises:
forward(input, target)[source]#

Forward method of the loss function.

Parameters:
Returns:

The computed loss.

Return type:

torch.Tensor