Understanding PyTorch's BCE Notation According to the PyTorch documentation for the Binary Cross Entropy Loss, we can write it as follows:
$$l_{n} = -w_{n}\cdot \left[y_{n}\cdot \log \left(x_{n}\right) + \left( 1-y_{n}\right)\cdot \log\left( 1-x_{n}\right) \right].$$
What do the $w_{n}$, $x_{n}$ and $y_{n}$ mean?
If you look at the documentation of the BCELoss you will the that they mean the following:

$w$ is the weight to use, by which the loss will be rescaled.
$x$ is the output value, which is the value that is predicted by the model.
$y$ is the target value, which is the ground truth value.