  Tensor decomposition methods have proven effective in various applications,
including compression and acceleration of neural networks. At the same time,
the problem of determining optimal decomposition ranks, which present the
crucial parameter controlling the compression-accuracy trade-off, is still
acute. In this paper, we introduce MARS -- a new efficient method for the
automatic selection of ranks in general tensor decompositions. During training,
the procedure learns binary masks over decomposition cores that "select" the
optimal tensor structure. The learning is performed via relaxed maximum a
posteriori (MAP) estimation in a specific Bayesian model and can be naturally
embedded into the standard neural network training routine. Diverse experiments
demonstrate that MARS achieves better results compared to previous works in
various tasks.
