If you are asking the neural network to make a discrete classification or discrete prediction about some set of input data, you are almost by definition asking

If you are asking the neural network to make a discrete classification or discrete prediction about some set of input data, you are almost by definition asking it a Hamiltonian class of question. By way of a counter example, you could say “but it depends whether the person walked or took the bus!” In that case either you need to provide the data on whether they walked or took the bus (in which case your question collapses to a simple Hamiltonian form with the additional data) or you don’t provide the data and the question is fundamentally unanswerable in a simple discrete way.