How can "binary cross-entropy" be expressed in Mandarin Chinese?
I cannot find the Keras page you linked now. But I can still find the Keras document through search.

Binary cross entropy in the document is just a special case when the output can take only one of two classes. Make the context clear, there is no need to distinguish them in normal text. The mathematical formula of cross entropy just can deal with any number of classes (2 and above). So whether it is "binary" is implied in the problem you want to solve. There is no need to make it explicit.

So why the Keras documents explicitly distinguish them? This is because when the output can take only two classes, the input can take a different format than when there are multiple classes, and may save some space. So they have "binary_crossentropy" and "categorical_crossentropy", which deals with different input. Note that even you have only two classes, you can still use "categorical_crossentropy" by manipulating your input format to fit the requirements of "categorical_crossentropy".

As the translation, you may use "二类的交叉熵" and "多类的交叉熵". But these are only words that I coined up. There is no specific term for this, as this is only a software thing.