Tensor network (TN) representation is a powerful technique for data analysis and machine learning. It practically involves a challenging TN structure search (TN-SS) problem, which aims to search for the optimal structure to achieve a compact representation. Existing TN-SS methods mainly adopt a bi-level optimization method that leads to excessive computational costs due to repeated structure evaluations. To address this issue, we propose an efficient integrated (single-level) method named SVD-inspired TN decomposition (SVDinsTN), eliminating the need for repeated tedious structure evaluation. By inserting a diagonal factor for each edge of the fully-connected TN, we calculate TN cores and diagonal factors simultaneously, with factor sparsity revealing the most compact TN structure. Experimental results on real-world data demonstrate that SVDinsTN achieves approximately $10\sim{}10^3$ times acceleration in runtime compared to the existing TN-SS methods while maintaining a comparable level of representation ability.

翻译：张量网络表示是数据分析和机器学习中的强大技术。它实际涉及一个具有挑战性的张量网络结构搜索问题，旨在搜索最优结构以实现紧凑表示。现有张量网络结构搜索方法主要采用双层优化方法，因重复结构评估导致计算成本过高。针对此问题，我们提出一种名为SVD启发张量网络分解的高效集成（单层）方法，消除了重复繁琐结构评估的需要。通过在完全连接张量网络的每条边上插入对角因子，我们同时计算张量网络核和对角因子，因子稀疏性揭示了最紧凑的张量网络结构。在实际数据上的实验结果表明，SVDinsTN在保持相当表示能力的同时，相比现有张量网络结构搜索方法实现了约$10\sim{}10^3$倍的运行时间加速。