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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:

$$ \mbox{loss}(x, y) = \frac{\sum_i \max(0, w[y] * (\mbox{margin} - x[y] + x[i]))^p)}{\mbox{x.size}(0)} $$