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

## Usage

nn_bce_loss(weight = NULL, reduction = "mean")

## 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()
}