Quantum Neural Networks and Topological Quantum Field Theories.

Journal: Neural networks : the official journal of the International Neural Network Society
Published Date: Jun 7, 2022

Abstract

Our work intends to show that: (1) Quantum Neural Networks (QNNs) can be mapped onto spin-networks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theory (TQFT); (2) A number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNNs, relating it to the topological features of the graph structures involved.

Authors

  • Antonino Marcianò
    Center for Field Theory and Particle Physics & Department of Physics, Fudan University, Jingwan campus, Jingsan Rd, 200433 Shanghai, China; Laboratori Nazionali di Frascati INFN, Via Enrico Fermi, 54, 00044, Frascati (Rome), Italy. Electronic address: marciano@fudan.edu.cn.
  • Deen Chen
    College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China. Electronic address: deenchen@tongji.edu.cn.
  • Filippo Fabrocini
    College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China; Institute for Computing Applications "Mario Picone", Italy National Research Council, Via dei Taurini, 19, 00185, Rome, Italy. Electronic address: fabrocini@tongji.edu.cn.
  • Chris Fields
    Allen Discovery Center, Tufts University, 200 College Avenue, 02155 Medford, MA, USA. Electronic address: fieldsres@gmail.com.
  • Enrico Greco
    Department of Chemical and Pharmaceutical Sciences, University of Trieste, Via Giorgieri, 1, 34127 Trieste, Italy. Electronic address: enrico.greco@live.it.
  • Niels Gresnigt
    Department of Physics, Xi'an Jiaotong-Liverpool University, 111 Ren'ai Rd, 215123 Suzhou, China. Electronic address: niels.gresnigt@xjtlu.edu.cn.
  • Krid Jinklub
    College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China. Electronic address: jinklub_krid@tongji.edu.cn.
  • Matteo Lulli
    Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, 1088 Xueyuan Avenue, 518055 Shenzhen, China. Electronic address: lulli@sustech.edu.cn.
  • Kostas Terzidis
    College of Design and Innovation, Tongji University, 281 Fuxin Rd, 200092 Shanghai, China. Electronic address: kostas@tongji.edu.cn.
  • Emanuele Zappala
    Yale School of Medicine, Yale University, New Haven, 06510 CT, USA. Electronic address: emanuele.zappala@yale.edu.

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