feed-forward neural networks we can take logarithm operation on both sides to arrive at the followingn log log xi xi yi which simplifies to the following expressionn log yi log xi yi log xi instead of maximizing the rhswe minimize its negative value as followsn yi log xi yi log xi this leads us to the following binary cross-entropy functionn yi log xi yi log xi  thusthe idea of maximum likelihood enables us to derive the binary cross-entropy functionwhich can be used as loss function in the context of binary classification cross-entropy building on the idea of binary cross-entropylet' now consider deriving the cross-entropy loss function to be used in the context of multiclassification let' assume that { }where { kare the classes we also denote nk to be the observed counts of each of the classes observe that ni in this casetoolet us assume that we