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Estimating the Interaction Between Sites of a System by Convolutional Neural Networks and Applying Renormalization Group Methods on the Network’s Density Matrix

Pourmohammad, Hamid | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54878 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rouhani, Shahin
  7. Abstract:
  8. In the last two decades, Convolutional Neural Networks (CNN) have shown significant capabilities in artificial intelligence. These networks are able to provide comprehensive conclusions about the overall behavior a system by analyzing the relationship between the components of that system; Clearly, these networks have been successful in performing categorization tasks. However, there are no coherent theories as to why they work, and how to optimize them. On the other hand, according to recent research on the relationship between deep networks (in computer science) and Renormalization Group (in physics), convolutional networks seem to use a method similar to the Density Matrix Renormalization Group (or DMRG.) The DMRG method can estimate the ground state energy of a statistical system by categorizing Hilbert space vectors. In this study, by first examining the relationship between convolutional networks and DMRG, we understand the reason for the use of convolutional networks from a physical point of view (focusing on one-dimensional problems, such as the Ising model); These networks are able to define a relationship between the system’s components (and related states) by considering an arbitrary interaction between the system’s sites. The interaction intends to perform the task of categorization in convolutional networks by examining blocks consisting of sites. This means that the interaction must be able to categorize the configurations of each block in a way that is appropriate for categorizing the data. In computer science, this data is usually images that each represent a group of objects (such as cats, cars, etc.); Therefore, the task of this interaction in the convolutional neural networks will be to discover the relationship between the pixels related to the cat category, the car category, and so on. This interaction is initially considered random (and multi-particle); It is then optimized by the gradient descent method. In this research, in addition to investigating these interactions and applying its renormalization methods in deep convolutional networks, we have also dealt with a new method; We have been able to introduce a new approach to these networks that works based on the relationship between the specific states of each block and the output of the neural network. Although the final confirmation of this new approach depends on the revision of artificial intelligence libraries, preliminary studies have shown a 25.3±10.5% increase compared to the performance of fully connected multilayer perceptrons
  9. Keywords:
  10. Deep Networks ; Ising model ; Classification ; Truncation ; Hilbert Space ; Convolutional Neural Network ; Density Matrix Renormalization Group

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