Measures the loss given an input tensor \(x\) and a labels tensor \(y\) (containing 1 or -1).

## Arguments

- margin
(float, optional): Has a default value of

`1`

.- 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

This is usually used for measuring whether two inputs are similar or dissimilar, e.g. using the L1 pairwise distance as \(x\), and is typically used for learning nonlinear embeddings or semi-supervised learning. The loss function for \(n\)-th sample in the mini-batch is

$$ l_n = \begin{array}{ll} x_n, & \mbox{if}\; y_n = 1,\\ \max \{0, \Delta - x_n\}, & \mbox{if}\; y_n = -1, \end{array} $$

and the total loss functions is

$$ \ell(x, y) = \begin{array}{ll} \mbox{mean}(L), & \mbox{if reduction} = \mbox{'mean';}\\ \mbox{sum}(L), & \mbox{if reduction} = \mbox{'sum'.} \end{array} $$

where \(L = \{l_1,\dots,l_N\}^\top\).