  We study the machine learning techniques applied to the lattice gauge
theory's critical behavior, particularly to the confinement/deconfinement phase
transition in the SU(2) and SU(3) gauge theories. We find that the neural
network, trained on lattice configurations of gauge fields at an unphysical
value of the lattice parameters as an input, builds up a gauge-invariant
function, and finds correlations with the target observable that is valid in
the physical region of the parameter space. In particular, if the algorithm
aimed to predict the Polyakov loop as the deconfining order parameter, it
builds a trace of the gauge group matrices along a closed loop in the time
direction. As a result, the neural network, trained at one unphysical value of
the lattice coupling $\beta$ predicts the order parameter in the whole region
of the $\beta$ values with good precision. We thus demonstrate that the machine
learning techniques may be used as a numerical analog of the analytical
continuation from easily accessible but physically uninteresting regions of the
coupling space to the interesting but potentially not accessible regions.
