Multi margin loss — nn_multi_margin

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

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

where $x \in {0, \dots, x.size (0) - 1}$ 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:

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