Efficient construction of tensor ring representations from sampling

Yuehaw Khoo; Jianfeng Lu; Lexing Ying

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arXiv · 1711.00954

Efficient construction of tensor ring representations from sampling

Yuehaw Khoo·Jianfeng Lu·Lexing Ying

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Abstract

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.

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Yuehaw Khoo, Jianfeng Lu, Lexing Ying. 2017-11-02. Efficient construction of tensor ring representations from sampling. https://arxiv.org/abs/1711.00954

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