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

## Arguments

- 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`

.- 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.

## Details

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

$$ \ell(x, y) = \left\{ \begin{array}{ll} \mbox{mean}(L), & \mbox{if reduction} = \mbox{'mean';}\\ \mbox{sum}(L), & \mbox{if reduction} = \mbox{'sum'.} \end{array} \right. $$

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.

## Shape

Input: \((N, *)\) where \(*\) means, any number of additional dimensions

Target: \((N, *)\), same shape as the input

Output: scalar. If

`reduction`

is`'none'`

, then \((N, *)\), same shape as input.

## Examples

```
if (torch_is_installed()) {
m <- nn_sigmoid()
loss <- nn_bce_loss()
input <- torch_randn(3, requires_grad = TRUE)
target <- torch_rand(3)
output <- loss(m(input), target)
output$backward()
}
```