  Recently, machine learning has been applied successfully for identifying
phases and phase transitions of the Ising models. The continuous phase
transition is characterized by spontaneous symmetry breaking, which can not be
detected in general from a single spin configuration. To investigate if neural
networks can extract correlations among spin snapshots, we propose a new test
using the random-gauge Ising model. We show that neural networks can extract
the order parameter or the energy of the random-gauge model as in the
ferromagnetic case. We also discuss how and where the information of random
gauge is encoded in neural networks and attempt to reconstruct the gauge from
the neural network parameters. We find that the fully connected network encodes
the effect of random gauge to its weights naturally. In contrast, the
convolutional network copes with the randomness by assigning different network
parts to local gauge patterns. This observation indicates that although the
latter demonstrates higher performance than the former for the present
randomized-gauge test, the former is more effective and suitable for dealing
with models with spatial randomness.
