torch (version 0.8.1)

nn_multi_margin_loss: Multi margin loss

Description

Creates a criterion that optimizes a multi-class classification hinge loss (margin-based loss) between input $x$ (a 2D mini-batch Tensor) and output $y$ (which is a 1D tensor of target class indices, $0\le y\le \text{x.size}(1)-1$):

Usage

nn_multi_margin_loss(p = 1, margin = 1, weight = NULL, reduction = "mean")

Arguments

p

(int, optional): Has a default value of $1$. $1$ and $2$ are the only supported values.

margin

(float, optional): Has a default value of $1$.

weight

(Tensor, optional): a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.

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.

Details

For each mini-batch sample, the loss in terms of the 1D input $x$ and scalar output $y$ is: $$\text{loss}(x,y)=\frac{\sum _{i}max(0,\text{margin}-x[y]+x[i]){)}^p}{\text{x.size}(0)}$$

where $x\in \{0,\cdots ,\text{x.size}(0)-1\}$ and $i\ne y$.

Optionally, you can give non-equal weighting on the classes by passing a 1D weight tensor into the constructor. The loss function then becomes:

$$\text{loss}(x,y)=\frac{\sum _{i}max(0,w[y]\ast (\text{margin}-x[y]+x[i]){)}^p)}{\text{x.size}(0)}$$