  We present a procedure for reconstructing the decision function of an
artificial neural network as a simple function of the input, provided the
decision function is sufficiently symmetric. In this case one can easily deduce
the quantity by which the neural network classifies the input. The procedure is
embedded into a pipeline of machine learning algorithms able to detect the
existence of different phases of matter, to determine the position of phase
transitions and to find explicit expressions of the physical quantities by
which the algorithm distinguishes between phases. We assume no prior knowledge
about the Hamiltonian or the order parameters except Monte Carlo-sampled
configurations. The method is applied to the Ising Model and SU(2) lattice
gauge theory. In both systems we deduce the explicit expressions of the known
order parameters from the decision functions of the neural networks.
