Evolutionary Topology Search for Tensor Network Decomposition
Evolutionary Topology Search for Tensor Network Decomposition
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发表时间：
2020-07
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通讯作者：
Chao Li;Zhun Sun
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作者：
Chao Li;Zhun Sun
在变量模型（Anandkumar et al., 2014）中，数据恢复-张量网络（TN）分解是一个很有前途的框架，可以用很少的参数表示极高的高维问题。然而，寻找TN分解的（接近）最优拓扑结构是一个挑战，因为候选解的数量随着张量阶数的增加呈指数增长。在本文中，我们声称这个问题可以通过进化算法以一种负担得起的方式实际解决。我们将复杂的拓扑结构编码为二进制字符串，并开发了一种简单的遗传元算法来搜索Hamming空间上的最优拓扑。合成数据和实际数据的实验结果表明，与已知的张量-列（TT）或张量-环（TR）模型相比，我们的方法可以有效地发现基真拓扑甚至更好的结构，并且显著提高了TN分解的表示能力。我们的代码可在https://github.com/ mingame /icml2020-TNGA获得。
tent variable model (Anandkumar et al., 2014), data restora-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. Our code is available at https://github.com/ minogame/icml2020-TNGA .