torch (version 0.14.2)

nn_hinge_embedding_loss: Hinge embedding loss

Description

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

Usage

nn_hinge_embedding_loss(margin = 1, reduction = "mean")

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.

Shape

• Input: $(\ast )$ where $\ast$ means, any number of dimensions. The sum operation operates over all the elements.

• Target: $(\ast )$, same shape as the input

• Output: scalar. If reduction is 'none', then same shape as the input

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

$$l_n=\begin{array}{ll}{x}_n,& \text{if}{y}_n=1,\\ max\{0,\mathrm{\Delta }-x_n\},& \text{if}{y}_n=-1,\end{array}$$

and the total loss functions is

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

where $L=\{l_1,\dots ,l_N{\}}^{\mathrm{\top }}$.