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Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

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Communications on Applied mathematics and Computation 2024年第2期6卷 1175-1188页

作者： Wes Whiting Bao Wang Jack Xin Department of mathematics University of CaliforniaIrvineCAUSA Department of mathematics Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUTUSA

We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient *** also discuss a Riemann... 详细信息

关键词： Hyperbolic neural network Riemannian gradient descent Riemannian Adam(RAdam) Training convergence

Imaging a force field via an optically levitated nanoparticle array

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Chinese Physics B 2024年第9期33卷 179-184页

作者： Bihu Lv Jiandong Zhang Chuang Li Research center for Novel computing Sensing and Intelligent Processing Zhejiang LaboratoryHangzhou 311121China School of mathematics and Physics Jiangsu University of TechnologyChangzhou 213001China

Levitated optomechanical systems represent an excellent candidate platform for force and acceleration *** propose a force-sensing protocol utilizing an optically levitated nanoparticle *** our scheme,N nanoparticles are trapped in an optical cavity using holographic optical *** external laser drives the cavity,exciting N cavity modes interacting simultaneously with the N *** optomechanical interaction encodes the information of the force acting on each nanoparticle onto the intracavity photons,which can be detected directly at the output ports of the ***,our protocol enables real-time imaging of a force field.

关键词： optomechanics levitated nanoparticles force field detection

A Deep Learning Method for computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems Science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MING Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International center for mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National Science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li center for Data Science Peking University Zuse institute Berlin Department of mathematics and Computer Science Freie Universit?t Berlin Laboratory of mathematics and Applied mathematics(LMAM)and School of Mathematical Sciences Peking University center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

Advancing brain-inspired computing with hybrid neural networks

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National Science Review 2024年第5期11卷 56-71页

作者： Faqiang Liu Hao Zheng Songchen Ma Weihao Zhang Xue Liu Yansong Chua Luping Shi Rong Zhao center for Brain-Inspired computing Research Optical Memory National Engineering Research CenterTsinghua University-China Electronics Technology HIK Group Co.Joint Research Center for Brain-inspired ComputingIDGMc Govern Institute for Brain Research Department of Precision Instrument Tsinghua University Neuromorphic computing Laboratory China Nanhu Academy of Electronics and Information Technology

Brain-inspired computing, drawing inspiration from the fundamental structure and information-processing mechanisms of the human brain, has gained significant momentum in recent years. It has emerged as a research paradigm centered on brain–computer dual-driven and multi-network integration. One noteworthy instance of this paradigm is the hybrid neural network(HNN), which integrates computer-science-oriented artificial neural networks(ANNs) with neuroscience-oriented spiking neural networks(SNNs). HNNs exhibit distinct advantages in various intelligent tasks, including perception, cognition and learning. This paper presents a comprehensive review of HNNs with an emphasis on their origin, concepts, biological perspective, construction framework and supporting systems. Furthermore, insights and suggestions for potential research directions are provided aiming to propel the advancement of the HNN paradigm.

关键词： brain-inspired computing hybrid neural network dual-brain driven multi-network integration neuromorphic system

Resource management at the network edge for federated learning

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Digital Communications and Networks 2024年第3期10卷 765-782页

作者： Silvana Trindade Luiz F.Bittencourt Nelson L.S.da Fonseca institute of computing State University of CampinasCampinasBrazil

Federated learning has been explored as a promising solution for training machine learning models at the network edge,without sharing private user *** limited resources at the edge,new solutions must be developed to leverage the software and hardware resources as the existing solutions did not focus on resource management for network edge,specially for federated *** this paper,we describe the recent work on resource manage-ment at the edge and explore the challenges and future directions to allow the execution of federated learning at the *** such as the discovery of resources,deployment,load balancing,migration,and energy effi-ciency are discussed in the paper.

关键词： Resource management Edge computing Federated learning Machine learning

Aubry-Mather theory for contact Hamiltonian systems Ⅲ

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Science China mathematics 2024年第11期67卷 2541-2570页

作者： Panrui Ni Lin Wang Shanghai center for Mathematical Sciences Fudan University School of mathematics and Statistics Beijing Institute of Technology

By exploiting the contact Hamiltonian dynamics（T*M × R,Φ_t） around the Aubry set of contact Hamiltonian systems,we provide a relation among the Mather set,the Φ_t-recurrent set,the strongly static set,the Aubry set,the Ma?é set,and the Φ_t-non-wandering ***,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing *** show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser（KAM） solutions and the existence of transitive orbits around the Aubry set.

关键词： Aubry-Mather theory weak KAM theory contact Hamiltonian systems Hamilton-Jacobi equations

A survey on federated learning:a perspective from multi-party computation

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Frontiers of Computer Science 2024年第1期18卷 93-103页

作者： Fengxia LIU Zhiming ZHENG Yexuan SHI Yongxin TONG Yi ZHANG institute of Artificial Intelligence and Key Laboratory of mathematics Informatics Behavioral Semantics Beihang UniversityBeijing 100191China State Key Laboratory of Software Development Environment and Advanced Innovation center for Future Blockchain and Privacy computing Beihang UniversityBeijing 100191China Pengcheng Laboratory Shenzhen 518055China Zhongguancun Laboratory Beijing 100190China institute for Mathematical Sciences and Engineering Research center of Financial computing and Digital Engineering Renmin University of ChinaBeijing 100872China

Federated learning is a promising learning paradigm that allows collaborative training of models across multiple data owners without sharing their raw *** enhance privacy in federated learning,multi-party computation can be leveraged for secure communication and computation during model *** survey provides a comprehensive review on how to integrate mainstream multi-party computation techniques into diverse federated learning setups for guaranteed privacy,as well as the corresponding optimization techniques to improve model accuracy and training *** also pinpoint future directions to deploy federated learning to a wider range of applications.

关键词： sfederated learning multi-party ycomputation privacy-preserving data mining distributed learning