MARS: Masked Automatic Ranks Selection in Tensor Decompositions

TL;DR

MARS is an automatic, Bayesian-based method for selecting optimal tensor decomposition ranks during neural network training, improving compression and accuracy trade-offs across various tasks.

Contribution

Introduces MARS, a novel Bayesian approach for automatic rank selection in tensor decompositions integrated into neural network training.

Findings

MARS outperforms previous methods in multiple tasks.

It effectively balances compression and accuracy.

The method is computationally efficient and easy to embed.

Abstract

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.