Evolutionary Topology Search for Tensor Network Decomposition

Chao Li, Zhun Sun
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5947-5957, 2020.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-li20l, title = {Evolutionary Topology Search for Tensor Network Decomposition}, author = {Li, Chao and Sun, Zhun}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5947--5957}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/li20l/li20l.pdf}, url = {https://proceedings.mlr.press/v119/li20l.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Evolutionary Topology Search for Tensor Network Decomposition %A Chao Li %A Zhun Sun %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-li20l %I PMLR %P 5947--5957 %U https://proceedings.mlr.press/v119/li20l.html %V 119 %X 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.
APA
Li, C. & Sun, Z.. (2020). Evolutionary Topology Search for Tensor Network Decomposition. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5947-5957 Available from https://proceedings.mlr.press/v119/li20l.html.

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