  We examine here what type of predictive modelling, classification, or
regression, using neural networks (NN), fits better the task of soft-demapping
based post-processing in coherent optical communications, where the
transmission channel is nonlinear and dispersive. For the first time, we
present possible drawbacks in using each type of predictive task in a machine
learning context, considering the nonlinear coherent optical channel
equalization/soft-demapping problem. We study two types of equalizers based on
the feed-forward and recurrent NNs, for several transmission scenarios, in
linear and nonlinear regimes of the optical channel. We point out that even
though from the information theory perspective the cross-entropy loss
(classification) is the most suitable option for our problem, the NN models
based on the cross-entropy loss function can severely suffer from learning
problems. The latter translates into the fact that regression-based learning is
typically superior in terms of delivering higher Q-factor and achievable
information rates. In short, we show by empirical evidence that loss functions
based on cross-entropy may not be necessarily the most suitable option for
training communication systems in practical scenarios when overfitting- and
vanishing gradients-related problems come into play.
