Consider a neural network with one output,
hidden neurons and
inputs. For two-class classification problems with classes
and
we want the neural network to compute the probability
that an input vector
belongs to class
(and so
). For this case we often use the *cross-entropy error function* (where
is the network's prediction for
and
):

Derive the backpropagation update of the weights in both layers for the

Haeusler Stefan 2010-01-19