Creates a criterion that measures the triplet loss given an input tensors $$x1$$, $$x2$$, $$x3$$ and a margin with a value greater than $$0$$. This is used for measuring a relative similarity between samples. A triplet is composed by a, p and n (i.e., anchor, positive examples and negative examples respectively). The shapes of all input tensors should be $$(N, D)$$.

## Usage

nn_triplet_margin_loss(
margin = 1,
p = 2,
eps = 1e-06,
swap = FALSE,
reduction = "mean"
)

## Arguments

margin

(float, optional): Default: $$1$$.

p

(int, optional): The norm degree for pairwise distance. Default: $$2$$.

eps

constant to avoid NaN's

swap

(bool, optional): The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al. Default: FALSE.

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

The distance swap is described in detail in the paper Learning shallow convolutional feature descriptors with triplet losses by V. Balntas, E. Riba et al.

The loss function for each sample in the mini-batch is:

$$L(a, p, n) = \max \{d(a_i, p_i) - d(a_i, n_i) + {\rm margin}, 0\}$$

where

$$d(x_i, y_i) = | {\bf x}_i - {\bf y}_i |_p$$

See also nn_triplet_margin_with_distance_loss(), which computes the triplet margin loss for input tensors using a custom distance function.

## Shape

• Input: $$(N, D)$$ where $$D$$ is the vector dimension.

• Output: A Tensor of shape $$(N)$$ if reduction is 'none', or a scalar otherwise.

## Examples

if (torch_is_installed()) {
triplet_loss <- nn_triplet_margin_loss(margin = 1, p = 2)
anchor <- torch_randn(100, 128, requires_grad = TRUE)
positive <- torch_randn(100, 128, requires_grad = TRUE)
negative <- torch_randn(100, 128, requires_grad = TRUE)
output <- triplet_loss(anchor, positive, negative)
output\$backward()
}