Tensor Networks Meet Neural Networks: A Survey and Future Perspectives

By M. Wang et al

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Table of Contents

1. Introduction
2. Tensor Basis
3. Tensor Notations
4. Tensor Diagrams
5. Tensor Unfolding
6. Tensor Contraction
7. Dummy Tensor
8. Hyperedge
9. Super-diagonal Tensor

Summary

This paper presents a survey on the integration of Tensor Networks (TNs) and Neural Networks (NNs) through Tensorial Neural Networks (TNNs). The paper discusses the fundamental concepts of tensors, tensor diagrams, and various TN formats. It explores the application of TNs in building compact TNNs, efficient information fusion, quantum circuit simulation, training techniques, and toolboxes for processing TNNs. The combination of TNs and NNs in TNNs offers advantages in network compression, information fusion, and quantum circuit simulation, leading to promising future directions in data modeling and network applications.