In this paper, we suggest a new method for a given tensor to find CP decompositions using a less number of rank $1$ tensors. The main ingredient is the Least Absolute Shrinkage and Selection Operator (LASSO) by considering the decomposition problem as a sparse optimization problem. As applications, we design experiments to find some CP decompositions of the matrix multiplication and determinant tensors. In particular, we find a new formula for the $4 \times 4$ determinant tensor as a sum of $12$ rank $1$ tensors.

翻译：本文提出了一种新方法，通过利用较少数量的秩$1$张量来求解给定张量的CP分解。核心思想是将分解问题视为稀疏优化问题，并采用最小绝对收缩与选择算子（LASSO）进行处理。作为应用，我们设计了实验来寻找矩阵乘法张量和行列式张量的CP分解。特别地，我们发现了$4 \times 4$行列式张量的一个新表达式，即将其表示为$12$个秩$1$张量之和。