Efficient construction of tensor ring representations from sampling

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In this note 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.







Jianfeng Lu

Professor of Mathematics

Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.

More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.

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