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 structures for TN decomposition, since the number of candidate solutions exponentially grows with increasing the order of a tensor. In this paper, we claim that the issue can be practically tackled by evolutionary algorithms in an affordable manner. We encode the complex topological structures into binary strings, and develop a simple genetic meta-algorithm to search the optimal topology on Hamming space. The experimental results by both synthetic and real-world data demonstrate that our method can effectively discover the ground-truth topology or even better structures with a small number of generations, and significantly boost the representational power of TN decomposition compared with well-known tensor-train (TT) or tensor-ring (TR) models.