Efficient construction of tensor ring representations from sampling

In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least squares (ALS). Since the function has size exponential in d, where d is the number of dimensions, we propose an efficient sampling scheme to obtain O(d) important samples in order to learn the tensor ring. Furthermore, we devise an initialization method for ALS that allows fast convergence in practice. Numerical examples show that to approximate a function with similar accuracy, the tensor ring format provided by the proposed method has fewer parameters than the tensor-train format and also better respects the structure of the original function.

Duke Scholars

Author Jianfeng Lu Mathematics