| 研究実績の概要 |
As the research mentioned in the progress report for the year 2020, we narrowed down the study to tensor network structure search (TN-SS). Based on the current work “Evolutionary topology search for tensor network decomposition,” funded by this project, we extended the targeted task towards a practically important variant, named tensor network permutation search (TN-PS). Unlike the previous work, TN-PS puts more effort into searching for the optimal “Mode-Vertex” mapping from data to tensor network models. As for the research result, we conduct a theoretical investigation of TN-PS and propose a practically-efficient algorithm to tackle the issue. Verified by extensive benchmark experiments, we claim that the new method can significantly improve the expressive power of tensor networks in learning tasks.
More specifically, on the theoretical side, we proved the counting and metric properties of the search spaces for TN-PS, analyzing for the first time the impact of TN structures on these unique properties, which differ from the original TN-SS. On the numerical side, we propose a novel meta-heuristic algorithm in which the searching is done by randomly sampling in a neighborhood established by our theory and then recurrently updating the neighborhood until convergence. Numerical results demonstrate that TN-PS can further improve the expressive power of TNs in various formats by the proposed algorithm, which requires less computational cost than the proposed methods in ICML 2020.
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