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# BCEWithLogitsLoss¶

class torch.nn.BCEWithLogitsLoss(weight=None, size_average=None, reduce=None, reduction='mean', pos_weight=None)[source]

This loss combines a Sigmoid layer and the BCELoss in one single class. This version is more numerically stable than using a plain Sigmoid followed by a BCELoss as, by combining the operations into one layer, we take advantage of the log-sum-exp trick for numerical stability.

The unreduced (i.e. with reduction set to 'none') loss can be described as:

$\ell(x, y) = L = \{l_1,\dots,l_N\}^\top, \quad l_n = - w_n \left[ y_n \cdot \log \sigma(x_n) + (1 - y_n) \cdot \log (1 - \sigma(x_n)) \right],$

where $N$ is the batch size. If reduction is not 'none' (default 'mean'), then

$\ell(x, y) = \begin{cases} \operatorname{mean}(L), & \text{if reduction} = \text{mean';}\\ \operatorname{sum}(L), & \text{if reduction} = \text{sum'.} \end{cases}$

This is used for measuring the error of a reconstruction in for example an auto-encoder. Note that the targets t[i] should be numbers between 0 and 1.

It’s possible to trade off recall and precision by adding weights to positive examples. In the case of multi-label classification the loss can be described as:

$\ell_c(x, y) = L_c = \{l_{1,c},\dots,l_{N,c}\}^\top, \quad l_{n,c} = - w_{n,c} \left[ p_c y_{n,c} \cdot \log \sigma(x_{n,c}) + (1 - y_{n,c}) \cdot \log (1 - \sigma(x_{n,c})) \right],$

where $c$ is the class number ($c > 1$ for multi-label binary classification, $c = 1$ for single-label binary classification), $n$ is the number of the sample in the batch and $p_c$ is the weight of the positive answer for the class $c$.

$p_c > 1$ increases the recall, $p_c < 1$ increases the precision.

For example, if a dataset contains 100 positive and 300 negative examples of a single class, then pos_weight for the class should be equal to $\frac{300}{100}=3$. The loss would act as if the dataset contains $3\times 100=300$ positive examples.

Examples:

>>> target = torch.ones([10, 64], dtype=torch.float32)  # 64 classes, batch size = 10
>>> output = torch.full([10, 64], 1.5)  # A prediction (logit)
>>> pos_weight = torch.ones()  # All weights are equal to 1
>>> criterion = torch.nn.BCEWithLogitsLoss(pos_weight=pos_weight)
>>> criterion(output, target)  # -log(sigmoid(1.5))
tensor(0.2014)

Parameters
• weight (Tensor, optional) – a manual rescaling weight given to the loss of each batch element. If given, has to be a Tensor of size nbatch.

• 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 (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. 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'

• pos_weight (Tensor, optional) – a weight of positive examples. Must be a vector with length equal to the number of classes.

Shape:
• Input: $(*)$, where $*$ means any number of dimensions.

• Target: $(*)$, same shape as the input.

• Output: scalar. If reduction is 'none', then $(*)$, same shape as input.

Examples:

>>> loss = nn.BCEWithLogitsLoss()
>>> target = torch.empty(3).random_(2)
>>> output = loss(input, target)
>>> output.backward() ## Docs

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