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")(int, optional): Has a default value of \(1\). \(1\) and \(2\) are the only supported values.
(float, optional): Has a default value of \(1\).
(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.
(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.
For each mini-batch sample, the loss in terms of the 1D input \(x\) and scalar output \(y\) is: $$ \mbox{loss}(x, y) = \frac{\sum_i \max(0, \mbox{margin} - x[y] + x[i]))^p}{\mbox{x.size}(0)} $$
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:
$$ \mbox{loss}(x, y) = \frac{\sum_i \max(0, w[y] * (\mbox{margin} - x[y] + x[i]))^p)}{\mbox{x.size}(0)} $$