nn_multi_margin_loss function

Multi margin loss

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, $0 \leq y \leq \mbox{x.size}(1)-1$):

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:

where $x \in \left\{0, \; \cdots , \; \mbox{x.size}(0) - 1\right\}$

and $i \neq y$.

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