Evolutionary Topology Search for Tensor Network Decomposition

Tensor network (TN) decomposition is a promising framework to represent extremely high-dimensional problems with few parameters. However, it is challenging to search the (near-)optimal topological structure for TN decomposition, since the number of possible solutions exponentially grows with increasing the order of tensor. In this paper, we claim that this issue can be practically tackled by evolutionary algorithms in an efficient manner. We encode the complex topological structures into binary string, and develop a simple yet efficient genetic-based algorithm (GA) to search the optimal topology on Hamming space. The experimental results by both synthetic and real-world data demonstrate that our method can efficiently discovers the groundtruth topology or even better structures with few number of generations, and significantly boost the representational power of TN decomposition compared with well-known tensor-train (TT) or tensor-ring (TR) models.