  The logcosh loss function for neural networks has been developed to combine
the advantage of the absolute error loss function of not overweighting outliers
with the advantage of the mean square error of continuous derivative near the
mean, which makes the last phase of learning easier. It is clear, and one
experiences it soon, that in the case of clustered data, an artificial neural
network with logcosh loss learns the bigger cluster rather than the mean of the
two. Even more so, the ANN, when used for regression of a set-valued function,
will learn a value close to one of the choices, in other words, one branch of
the set-valued function, while a mean-square-error NN will learn the value in
between. This work suggests a method that uses artificial neural networks with
logcosh loss to find the branches of set-valued mappings in parameter-outcome
sample sets and classifies the samples according to those branches.
