2017/11/02 by Yuehaw Khoo, Khoo, Yuehaw, Jianfeng Lu +3 · 2 citations
Computer Science · Mathematics · #15A69 #33F05 #65D15 #Algorithms and Data Compression #Digital Filter Design and Implementation #FOS: Mathematics #G.1.10 #G.1.3 #Numerical Analysis (math.NA) #Tensor decomposition and applications #acm:15A69 #acm:33F05 #acm:65D15 #cs.NA #math.NA #msc:15A69 #msc:33F05 #msc:65D15
paper · pdf · doi:10.48550/arxiv.1711.00954
openalex publication_date 2017/11/02 · arxiv created 2019/06/27 · arxiv updated 2019/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 less parameters than tensor-train format and also better respects the structure of the original function.