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# MultiMarginLoss¶

class torch.nn.MultiMarginLoss(p=1, margin=1.0, weight=None, size_average=None, reduce=None, reduction='mean')[source]

Creates a criterion that optimizes a multi-class classification hinge loss (margin-based loss) between input $x$ (a 2D mini-batch Tensor) and output $y$ (which is a 1D tensor of target class indices, $0 \leq y \leq \text{x.size}(1)-1$):

For each mini-batch sample, the loss in terms of the 1D input $x$ and scalar output $y$ is:

$\text{loss}(x, y) = \frac{\sum_i \max(0, \text{margin} - x[y] + x[i])^p}{\text{x.size}(0)}$

where $i \in \left\{0, \; \cdots , \; \text{x.size}(0) - 1\right\}$ and $i \neq y$.

Optionally, you can give non-equal weighting on the classes by passing a 1D weight tensor into the constructor.

The loss function then becomes:

$\text{loss}(x, y) = \frac{\sum_i w[y] * \max(0, \text{margin} - x[y] + x[i])^p}{\text{x.size}(0)}$
Parameters
• p (int, optional) – Has a default value of $1$. $1$ and $2$ are the only supported values.

• margin (float, optional) – Has a default value of $1$.

• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, it has to be a Tensor of size C. Otherwise, it is treated as if having all ones.

• size_average (bool, optional) – Deprecated (see reduction). By default, the losses are averaged over each loss element in the batch. Note that for some losses, there are multiple elements per sample. If the field size_average is set to False, the losses are instead summed for each minibatch. Ignored when reduce is False. Default: True

• reduce (bool, optional) – Deprecated (see reduction). By default, the losses are averaged or summed over observations for each minibatch depending on size_average. When reduce is False, returns a loss per batch element instead and ignores size_average. Default: True

• reduction (str, 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. Note: size_average and reduce are in the process of being deprecated, and in the meantime, specifying either of those two args will override reduction. Default: 'mean'

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

• Target: $(N)$ or $()$, where each value is $0 \leq \text{targets}[i] \leq C-1$.

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

Examples:

>>> loss = nn.MultiMarginLoss()
>>> x = torch.tensor([[0.1, 0.2, 0.4, 0.8]])
>>> y = torch.tensor([3])
>>> # 0.25 * ((1-(0.8-0.1)) + (1-(0.8-0.2)) + (1-(0.8-0.4)))
>>> loss(x, y)
tensor(0.32...)


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