论文标题
作为索引交互功能给出的张紧器的建设性TT代理与应用
Constructive TT-representation of the tensors given as index interaction functions with applications
论文作者
论文摘要
本文提出了一种构建明确张量训练（TT）表示的方法。我们表明，可以用稀疏的TT核显式地表示一类张量，在许多情况下，可以获得最佳的TT量表。数值实验表明，我们的方法在包括游戏理论问题在内的几种实际应用中优于现有的实验。对操作数量的理论估计表明，在某些问题（例如永久计算）中，我们的方法接近已知的最佳渐近线，这些方法是通过完全不同类型的方法获得的。
This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments show that our method outperforms the existing ones in several practical applications, including game theory problems. Theoretical estimations of the number of operations show that in some problems, such as permanent calculation, our methods are close to the known optimal asymptotics, which are obtained by a completely different type of methods.
