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# MultiMarginLoss

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

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

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

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

  where i∈{0, ⋯ , x.size(0)−1}i \in \left\{0, \; \cdots , \; \text{x.size}(0) - 1\right\}i∈{0,⋯,x.size(0)−1} and i≠y i \neq y i=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:

  loss(x,y)=∑i w[y]∗max⁡(0,margin−x[y]+x[i])p x.size(0)\text{loss}(x, y) = \frac{\sum_i w[y] * \max(0, \text{margin} - x[y] + x[i])^p}{\text{x.size}(0)} loss(x,y)=x.size(0)∑i​w[y]∗max(0,margin−x[y]+x[i])p​
  Parameters:

    - p (int, optional) – Has a default value of 1 1 1. 1 1 1 and 2 2 2 are the only supported values.

    - margin (float, optional) – Has a default value of 1 1 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)(N, C)(N,C) or (C)(C)(C), where N N N is the batch size and C C C is the number of classes.

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