  Symmetries built into a neural network have appeared to be very beneficial
for a wide range of tasks as it saves the data to learn them. We depart from
the position that when symmetries are not built into a model a priori, it is
advantageous for robust networks to learn symmetries directly from the data to
fit a task function. In this paper, we present a method to extract symmetries
learned by a neural network and to evaluate the degree to which a network is
invariant to them. With our method, we are able to explicitly retrieve learned
invariances in a form of the generators of corresponding Lie-groups without
prior knowledge of symmetries in the data. We use the proposed method to study
how symmetrical properties depend on a neural network's parameterization and
configuration. We found that the ability of a network to learn symmetries
generalizes over a range of architectures. However, the quality of learned
symmetries depends on the depth and the number of parameters.

Machine Learning