Graph-Constrained Structure Search for Tensor Network Representation

Chao Li, Junhua Zeng, Zerui Tao, Qibin Zhao

Keywords: Tensor network, structure search, tensor decomposition

TL;DR: This work is to study the task of structure search of tensor network decomposition under graph-constraints from the both theoretical and practical aspects.

Abstract: Recent works paid effort on the structure search issue for tensor network (TN) representation, of which the aim is to select the optimal network for TN contraction to fit a tensor. In practice, however, it is more inclined to solve its sub-problem: searching TN structures from candidates with a similar topology like a cycle or lattice. We name this problem the graph-constrained structure search, and it remains open to this date. In this work, we conduct a thorough investigation of this issue from both the theoretical and practical aspects. Theoretically, we prove that the TN structures are generally irregular under graph constraints yet can be universally embedded into a low-dimensional regular discrete space. Guided by the theoretical results, we propose a simple algorithm, which can encode the graph-constrained TN structures into fixed-length strings for practical purposes by a ` “random-key" trick, and empirical results demonstrate the effectiveness and efficiency of the proposed coding method on extensive benchmark TN representation tasks.

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