States of quantum many-body systems are defined in a high-dimensional Hilbert space, where rich and complex interactions among subsystems can be modelled. In machine learning, complex multiple multilinear correlations may also exist within input features. In this paper, we present a quantum-inspired multilinear model, named Residual Tensor Train (ResTT), to capture the multiple multilinear correlations of features, from low to high orders, within a single model. ResTT is able to build a robust decision boundary in a high-dimensional space for solving fitting and classification tasks. In particular, we prove that the fully-connected layer and the Volterra series can be taken as special cases of ResTT. Furthermore, we derive the rule for weight initialization that stabilizes the training of ResTT based on a mean-field analysis. We prove that such a rule is much more relaxed than that of TT, which means ResTT can easily address the vanishing and exploding gradient problem that exists in the existing TT models. Numerical experiments demonstrate that ResTT outperforms the state-of-the-art tensor network and benchmark deep learning models on MNIST and Fashion-MNIST datasets. Moreover, ResTT achieves better performance than other statistical methods on two practical examples with limited data which are known to have complex feature interactions.
Robust Residual Correction via Selective Deployment for Time Series Forecasting
University of New South Wales（新南威尔士大学）；University of Science and Technology of China（中国科学技术大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Hybrid Quantum-inspired Resnet and Densenet for Pattern Recognition
Institute for Brain Sciences（脑科学研究院）；Kuang Yaming Honors School, Nanjing University（南京大学匡杨荣誉学院）；National Laboratory of Solid State Microstructures（固态微结构国家实验室）；School of Physics, Collaborative Innovation Center of Advanced Microstructures（物理学院，先进微结构协同创新中心）；School of Physics（物理学院）；Beijing Key Laboratory of Opto-Electronic Functional Materials（北京光学材料重点实验室）；Micro-Nano Devices, Key Laboratory of Quantum State Construction（微纳器件，量子态构造重点实验室）；Manipulation(Ministry of Education), Renmin University of China（操控（教育部），中国人民大学）
