Chen Xi, Yang Dongliang, Hwang Geunwoo, Dong Yujiao, Cui Binbin, Wang Dingchen, Chen Hegan, Lin Ning, Zhang Wenqi, Li Huihan, Shao Ruiwen, Lin Peng, Hong Heemyoung, Yao Yugui, Sun Linfeng, Wang Zhongrui, Yang Heejun
Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China.
Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China.
ACS Nano. 2024 Apr 23;18(16):10758-10767. doi: 10.1021/acsnano.3c10559. Epub 2024 Apr 10.
Neural networks are increasingly used to solve optimization problems in various fields, including operations research, design automation, and gene sequencing. However, these networks face challenges due to the nondeterministic polynomial time (NP)-hard issue, which results in exponentially increasing computational complexity as the problem size grows. Conventional digital hardware struggles with the von Neumann bottleneck, the slowdown of Moore's law, and the complexity arising from heterogeneous system design. Two-dimensional (2D) memristors offer a potential solution to these hardware challenges, with their in-memory computing, decent scalability, and rich dynamic behaviors. In this study, we explore the use of nonvolatile 2D memristors to emulate synapses in a discrete-time Hopfield neural network, enabling the network to solve continuous optimization problems, like finding the minimum value of a quadratic polynomial, and tackle combinatorial optimization problems like Max-Cut. Additionally, we coupled volatile memristor-based oscillators with nonvolatile memristor synapses to create an oscillatory neural network-based Ising machine, a continuous-time analog dynamic system capable of solving combinatorial optimization problems including Max-Cut and map coloring through phase synchronization. Our findings demonstrate that 2D memristors have the potential to significantly enhance the efficiency, compactness, and homogeneity of integrated Ising machines, which is useful for future advances in neural networks for optimization problems.
神经网络越来越多地用于解决各个领域的优化问题，包括运筹学、设计自动化和基因测序。然而，由于非确定性多项式时间（NP）难题，这些网络面临挑战，随着问题规模的增大，计算复杂度呈指数级增长。传统数字硬件面临冯·诺依曼瓶颈、摩尔定律放缓以及异构系统设计带来的复杂性问题。二维（2D）忆阻器凭借其内存计算、良好的可扩展性和丰富的动态行为，为这些硬件挑战提供了一种潜在的解决方案。在本研究中，我们探索使用非易失性2D忆阻器在离散时间霍普菲尔德神经网络中模拟突触，使网络能够解决连续优化问题，如找到二次多项式的最小值，并处理诸如最大割等组合优化问题。此外，我们将基于易失性忆阻器的振荡器与非易失性忆阻器突触相结合，创建了一个基于振荡神经网络的伊辛机，这是一个连续时间模拟动态系统，能够通过相位同步解决包括最大割和地图着色在内的组合优化问题。我们的研究结果表明，二维忆阻器有潜力显著提高集成伊辛机的效率、紧凑性和同质性，这对神经网络在优化问题上的未来发展很有帮助。
