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Deep learning in neural networks has drawn great attentions from physics communities in recent years. Due to the similarity of their goals, the two fields are learning from each other. The way of thinking and techniques developed so far in industry begin to play a role in studying physics, and at the meanwile, the basic ideas and concepts in physics helps to deepen our understanding of deep learning. In this talk, I will talk about our recent work in this intersection field, especially the interplay between tensor networks in physics and neural networks in deep learning. On one hand, we proved that in the framework of tensor networks, the backward iteration used in the second renormalization group (SRG) in tensor networks are equivalent to the backpropagation algorithm used in the training of neural networks in deep learnning, thus the automatic differentiation technique can be used to realize the SRG method effectively which can significantly improve the performance of conventional tensor network methods. On the other hand, using the concept of entanglement entropy, we proposed to use the matrix product operators to represent the linear mappings in neural networks, and constructed a new kind of network structure, MPO-Net, which can drastically reduce the number of parameters in modern deep neural networks and helps to improve the explainability and generalization power. I will focus on the first part, and briefly talk about the second part.
Refs: PRB 101, 220409(R) (2020), PRResearch 2, 023300 (2020), PRL 103, 160601 (2009)
I obtained my PhD degree in Institute of Theoretical Physics, Chinese Academy of Sciences (CAS), in 2012. After PhD, I worked as a postdoctor in Institute of Physics, CAS for 3 years, and then joined the Department of Physics, Renmin University of China, in 2015. I major in theoretical condensed matter physics, especially in developing effetive numerical quantum many-body computaional methods in strongly correlated systems. Together with my collaborators, I have developed several effective tensor network methods, such as second renormalization group (SRG), higher-order tensor renormalization group (HOTRG), projected entanglement simplex state (PESS) ansatz, nested tensor network (NTN) methods, etc.