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# BCELoss¶

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

Creates a criterion that measures the Binary Cross Entropy between the target and the input probabilities:

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

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

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 $y$ should be numbers between 0 and 1.

Notice that if $x_n$ is either 0 or 1, one of the log terms would be mathematically undefined in the above loss equation. PyTorch chooses to set $\log (0) = -\infty$, since $\lim_{x\to 0} \log (x) = -\infty$. However, an infinite term in the loss equation is not desirable for several reasons.

For one, if either $y_n = 0$ or $(1 - y_n) = 0$, then we would be multiplying 0 with infinity. Secondly, if we have an infinite loss value, then we would also have an infinite term in our gradient, since $\lim_{x\to 0} \frac{d}{dx} \log (x) = \infty$. This would make BCELoss’s backward method nonlinear with respect to $x_n$, and using it for things like linear regression would not be straight-forward.

Our solution is that BCELoss clamps its log function outputs to be greater than or equal to -100. This way, we can always have a finite loss value and a linear backward method.

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'

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:

>>> m = nn.Sigmoid()
>>> loss = nn.BCELoss()
>>> target = torch.empty(3).random_(2)
>>> output = loss(m(input), target)
>>> output.backward()


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