Cosine embedding loss

Creates a criterion that measures the loss given input tensors \(x_1\), \(x_2\) and a Tensor label \(y\) with values 1 or -1. This is used for measuring whether two inputs are similar or dissimilar, using the cosine distance, and is typically used for learning nonlinear embeddings or semi-supervised learning. The loss function for each sample is:

Usage

nn_cosine_embedding_loss(margin = 0, reduction = "mean")

Arguments

margin

(float, optional): Should be a number from \(-1\) to \(1\), \(0\) to \(0.5\) is suggested. If margin is missing, the default value is \(0\).

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

$$ \mbox{loss}(x, y) = \begin{array}{ll} 1 - \cos(x_1, x_2), & \mbox{if } y = 1 \\ \max(0, \cos(x_1, x_2) - \mbox{margin}), & \mbox{if } y = -1 \end{array} $$