Multilabel margin loss

Creates a criterion that optimizes a multi-class multi-classification hinge loss (margin-based loss) between input \(x\) (a 2D mini-batch Tensor) and output \(y\) (which is a 2D Tensor of target class indices). For each sample in the mini-batch:

Usage

nn_multilabel_margin_loss(reduction = "mean")

Arguments

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

$$ \mbox{loss}(x, y) = \sum_{ij}\frac{\max(0, 1 - (x[y[j]] - x[i]))}{\mbox{x.size}(0)} $$

where \(x \in \left\{0, \; \cdots , \; \mbox{x.size}(0) - 1\right\}\), \ \(y \in \left\{0, \; \cdots , \; \mbox{y.size}(0) - 1\right\}\), \ \(0 \leq y[j] \leq \mbox{x.size}(0)-1\), \ and \(i \neq y[j]\) for all \(i\) and \(j\). \(y\) and \(x\) must have the same size.

The criterion only considers a contiguous block of non-negative targets that starts at the front. This allows for different samples to have variable amounts of target classes.

Shape

• Input: \((C)\) or \((N, C)\) where N is the batch size and C is the number of classes.

• Target: \((C)\) or \((N, C)\), label targets padded by -1 ensuring same shape as the input.

• Output: scalar. If reduction is 'none', then \((N)\).

Examples

if (torch_is_installed()) {
loss <- nn_multilabel_margin_loss()
x <- torch_tensor(c(0.1, 0.2, 0.4, 0.8))$view(c(1, 4))
# for target y, only consider labels 4 and 1, not after label -1
y <- torch_tensor(c(4, 1, -1, 2), dtype = torch_long())$view(c(1, 4))
loss(x, y)
}
#> torch_tensor
#> 0.85
#> [ CPUFloatType{} ]