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We study the machine learning techniques applied to the lattice gaugetheory's critical behavior, particularly to the confinement/deconfinement phasetransition in the SU(2) and SU(3) gauge theories. We find that the neuralnetwork, trained on lattice configurations of gauge fields at an unphysicalvalue of the lattice parameters as an input, builds up a gauge-invariantfunction, and finds correlations with the target observable that is valid inthe physical region of the parameter space. In particular, if the algorithmaimed to predict the Polyakov loop as the deconfining order parameter, itbuilds a trace of the gauge group matrices along a closed loop in the timedirection. As a result, the neural network, trained at one unphysical value ofthe lattice coupling $\beta$ predicts the order parameter in the whole regionof the $\beta$ values with good precision. We thus demonstrate that the machinelearning techniques may be used as a numerical analog of the analyticalcontinuation from easily accessible but physically uninteresting regions of thecoupling space to the interesting but potentially not accessible regions.

Machine-learning physics from unphysics: Finding deconfinement temperature in lattice Yang-Mills theories from outside the scaling window