# CrossEntropyLoss¶

class torch.nn.CrossEntropyLoss(weight: Optional[torch.Tensor] = None, size_average=None, ignore_index: int = -100, reduce=None, reduction: str = 'mean')[source]

This criterion combines nn.LogSoftmax() and nn.NLLLoss() in one single class.

It is useful when training a classification problem with C classes. If provided, the optional argument weight should be a 1D Tensor assigning weight to each of the classes. This is particularly useful when you have an unbalanced training set.

The input is expected to contain raw, unnormalized scores for each class.

input has to be a Tensor of size either $(minibatch, C)$ or $(minibatch, C, d_1, d_2, ..., d_K)$ with $K \geq 1$ for the K-dimensional case (described later).

This criterion expects a class index in the range $[0, C-1]$ as the target for each value of a 1D tensor of size minibatch; if ignore_index is specified, this criterion also accepts this class index (this index may not necessarily be in the class range).

The loss can be described as:

$\text{loss}(x, class) = -\log\left(\frac{\exp(x[class])}{\sum_j \exp(x[j])}\right) = -x[class] + \log\left(\sum_j \exp(x[j])\right)$

or in the case of the weight argument being specified:

$\text{loss}(x, class) = weight[class] \left(-x[class] + \log\left(\sum_j \exp(x[j])\right)\right)$

The losses are averaged across observations for each minibatch. If the weight argument is specified then this is a weighted average:

$\text{loss} = \frac{\sum^{N}_{i=1} loss(i, class[i])}{\sum^{N}_{i=1} weight[class[i]]}$

Can also be used for higher dimension inputs, such as 2D images, by providing an input of size $(minibatch, C, d_1, d_2, ..., d_K)$ with $K \geq 1$ , where $K$ is the number of dimensions, and a target of appropriate shape (see below).

Parameters
• weight (Tensor, optional) – a manual rescaling weight given to each class. If given, has to be a Tensor of size C

• 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

• ignore_index (int, optional) – Specifies a target value that is ignored and does not contribute to the input gradient. When size_average is True, the loss is averaged over non-ignored targets.

• 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 (string, optional) – Specifies the reduction to apply to the output: 'none' | 'mean' | 'sum'. 'none': no reduction will be applied, 'mean': the weighted mean of the output is taken, '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: $(N, C)$ where C = number of classes, or $(N, C, d_1, d_2, ..., d_K)$ with $K \geq 1$ in the case of K-dimensional loss.

• Target: $(N)$ where each value is $0 \leq \text{targets}[i] \leq C-1$ , or $(N, d_1, d_2, ..., d_K)$ with $K \geq 1$ in the case of K-dimensional loss.

• Output: scalar. If reduction is 'none', then the same size as the target: $(N)$ , or $(N, d_1, d_2, ..., d_K)$ with $K \geq 1$ in the case of K-dimensional loss.

Examples:

>>> loss = nn.CrossEntropyLoss()
>>> input = torch.randn(3, 5, requires_grad=True)
>>> target = torch.empty(3, dtype=torch.long).random_(5)
>>> output = loss(input, target)
>>> output.backward()