Triplet margin loss — nn_triplet_margin

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 doi:10.5244/C.30.119 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()
}