论文标题
张量的算法网络收缩顺序
Algorithms for Tensor Network Contraction Ordering
论文作者
论文摘要
收缩张量网络通常在计算上要求。精心设计的收缩序列可以大大降低收缩成本。我们探索了模拟退火和遗传算法的性能，这是两种常见的离散优化技术，用于此订购问题。我们基于对物理相关的张量网络的常见贪婪搜索进行基准测试。在计算可行的地方，我们还将它们与通过详尽搜索获得的最佳收缩序列进行了比较。我们发现，在给定相等的计算资源的情况下，我们考虑的算法始终超过贪婪的搜索，其优势具有张量的网络大小。我们比较获得的收缩序列并确定高度非本地优化的迹象，并在收缩的早期牺牲了运行时间，以提高整体性能。
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.
