# 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.