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.

翻译：张量分解方法已在多种应用中展现出有效性，包括神经网络的压缩与加速。然而，决定最优分解秩（控制压缩与精度权衡的关键参数）的问题仍悬而未决。本文提出MARS——一种针对通用张量分解中自动选择秩的高效新方法。在训练过程中，该过程通过分解核心上的二元掩码学习“选取”最优张量结构。该学习基于特定贝叶斯模型中的松弛最大后验（MAP）估计实现，并可自然嵌入标准神经网络训练流程。多项实验表明，MARS在各任务中均取得优于先前工作的结果。