Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

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 descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.

Computing Power Network:The Architecture of Convergence of Computing and Networking towards 6G Requirement

In 6G era,service forms in which computing power acts as the core will be ubiquitous in the network.At the same time,the collaboration among edge computing,cloud computing and network is needed to support edge computing service with strong demand for computing power,so as to realize the optimization of resource utilization.Based on this,the article discusses the research background,key techniques and main application scenarios of computing power network.Through the demonstration,it can be concluded that the technical solution of computing power network can effectively meet the multi-level deployment and flexible scheduling needs of the future 6G business for computing,storage and network,and adapt to the integration needs of computing power and network in various scenarios,such as user oriented,government enterprise oriented,computing power open and so on.

Projection type neural network and its convergence analysis

Projection type neural network for optimization problems has advantages over other networks for fewer parameters , low searching space dimension and simple structure. In this paper, by properly constructing a Lyapunov energy function, we have proven the global convergence of this network when being used to optimize a continuously differentiable convex function defined on a closed convex set. The result settles the extensive applicability of the network. Several numerical examples are given to verify the efficiency of the network.

New Synchronization Algorithm and Analysis of Its Convergence Rate for Clock Oscillators in Dynamical Network with Time-Delays

New synchronization algorithm and analysis of its convergence rate for clock oscillators in dynamical network with time-delays are presented.A network of nodes equipped with hardware clock oscillators with bounded drift is considered.Firstly,a dynamic synchronization algorithm based on consensus control strategy,namely fast averaging synchronization algorithm （FASA）,is presented to find the solutions to the synchronization problem.By FASA,each node computes the logical clock value based on its value of hardware clock and message exchange.The goal is to synchronize all the nodes＇ logical clocks as closely as possible.Secondly,the convergence rate of FASA is analyzed that proves it is related to the bound by a nondecreasing function of the uncertainty in message delay and network parameters.Then,FASA＇s convergence rate is proven by means of the robust optimal design.Meanwhile,several practical applications for FASA,especially the application to inverse global positioning system （IGPS） base station network are discussed.Finally,numerical simulation results demonstrate the correctness and efficiency of the proposed FASA.Compared FASA with traditional clock synchronization algorithms （CSAs）,the convergence rate of the proposed algorithm converges faster than that of the CSAs evidently.

Global exponential stability for delayed cellular neural networks and estimate of exponential convergence rate

Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.

A Study on the Convergence of Gradient Method with Momentum for Sigma-Pi-Sigma Neural Networks

In this paper, a gradient method with momentum for sigma-pi-sigma neural networks (SPSNN) is considered in order to accelerate the convergence of the learning procedure for the network weights. The momentum coefficient is chosen in an adaptive manner, and the corresponding weak convergence and strong convergence results are proved.

Multi-Radio Cooperation Technology and Heterogeneous Network Convergence

The heterogeneous network convergence is the trend of future network development. However, many bottlenecks exist in the converged system such as high time delay, high energy consumption, and low data rate. Multi-Radio Cooperation (MRC) technology is specially designed to overcome these bottlenecks and to satisfy the requirements of heterogeneous network convergence. MRC can improve network capacity, reduce the energy consumption of radio devices, and decrease handover latency between heterogeneous networks by the cooperation of multiple radios, and by efficient management and feasible allocation of multi-radio resources. MRC makes real seamless heterogeneous network convergence possible.

CONVERGENCE OF ONLINE GRADIENT METHOD WITH A PENALTY TERM FOR FEEDFORWARD NEURAL NETWORKS WITH STOCHASTIC INPUTS

Online gradient algorithm has been widely used as a learning algorithm for feedforward neural network training. In this paper, we prove a weak convergence theorem of an online gradient algorithm with a penalty term, assuming that the training examples are input in a stochastic way. The monotonicity of the error function in the iteration and the boundedness of the weight are both guaranteed. We also present a numerical experiment to support our results.

A Summary of the Large-Scale Access Convergence Network Structure

Under the requirement of everything over IP, network service shows the following characteristics:(1) network service increases its richness;(2) broadband streaming media becomes the mainstream. To achieve unified multi-service bearing in the IP network, the largescale access convergence network architecture is proposed. This flat access convergence structure with ultra-small hops, which shortens the service transmission path, reduces the complexity of the edge of the network, and achieves IP strong waist model with the integration of computation, storage and transmission. The key technologies are also introduced in this paper, including endto-end performance guarantee for real time interactive services, fog storing mechanism, and built-in safety transmission with integration of aggregation and control.

Convergence of gradient method for Elman networks

The gradient method for training Elman networks with a finite training sample set is considered. Monotonicity of the error function in the iteration is shown. Weak and strong convergence results are proved, indicating that the gradient of the error function goes to zero and the weight sequence goes to a fixed point, respectively. A numerical example is given to support the theoretical findings.

The Games in Network Convergence and Their Impact on China

In January 2010,the State Council of China decided to speed up the convergence of the telecommunications network,cable network and Internet network.That means the government-led practical exploration of the networks convergence.The convergence is related to the entities in the fields of telecommunications,broadcasting and the Internet industry.The authors apply the static game theory to analyze the games among the players in the fields of telecommunications and broadcasting,and point out that the games would strengthen the network infrastructures,promote the development of related industries,and profoundly influence and change the ways of thinking and social management in China.At last,the paper puts forward some policy recommendations.

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

This paper studies the asymptotic behavior of solutions for nonlinear RLCnetwoiks which have the following form The function p i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditiolts. Under the assumption that every element value involving voltage source is asymptotically constallt, we establish four creteria for all solutiolls of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited uonliltear circuits.This results generalize those of Brayton and Moser[1,2].

Convergence Analysis and Its Application in the Fixed Point Formulation of Medium Access in Wireless Network

In the Internet of things, it is of critical importance to fully utilize the potential capacity of the network with efficient medium access control （MAC） mechanisms. In this paper, we study the convergence property of the fixed point formulation of distributed coordination function （DCF）, which is widely used for medium access control in wireless networks. We first Kind that the fixed point could be repelling, which means that it is impossible for an MAC system to converge at its fixed point. Next, we show the existence of periodic points to prove that the fixed point function will oscillate between two periodic points when the fixed point is repelling. We also find that the average of the two periodic points is a close approximation of the fixed point. Based on the findings, we propose an algorithm to compute the fixed point efficiently. Simulation results verify the accuracy and efficiency of our algorithm compared with the previous fixed point computing method.

Network Convergence and Service Convergence

Convergence is the main trend for future network development. The multi-service bearer network,built upon the Internet Protocol/Multi-protocol Label Switching (IP/MPLS) technology,is a converged network with Quality of Service (QoS) guarantee for business and enterprise customers. The integrated and unified service provisioning platform (including both service execution and development enviroments) can provide integrated audio,video and data services over multiple access networks. However,achieving network convergence and service convergence are long-term goals,which can only be realized step by step after comprehensive consideration of many factors like market demands,technologies,services and costs.

Service Convergence in Next Generation Network

The convergence of communication services becomes a focus in the industry along with the requirement for full-service operation and technical development. Service convergence includes two aspects: The convergence of the fixed and mobile networks; and the convergence of traditional communications and Internet services. This requires balancing the conflicts between the openness and operationability of terminal capability and network convergence. Unified authentication and authorization are the basis for service convergence in terms of operationability. Modular network and open terminal are technical solutions for the service convergence.

Trends and Prospects of Network Convergence

The concept of the separation of service,control,bearer and access in the Next Generation Network (NGN) provides a unified architecture for the network convergence in the future. Network convergence involves service,core network,access network,terminal,and operation and maintenance convergence. In the future,the converged network’s trend is to use IP Multimedia Subsystem (IMS) at the core control layer; Internet Protocol/Multiple Protocol Label Switching (IP/MPLS) technology at the core bearer layer; unified and open service provisioning architecture at the service layer; as well as support fixed,mobile,narrowband and broadband access technologies and so on at the access layer. Terminals will evolve to be multi-modular and intelligent,and would finally enable users to access full services anytime and anywhere using one number,one terminal,one account and one core network.

Mesh-Based Network Convergence and Cooperation

More and more distinctive heterogeneous features are exhibited in wireless networks in multitude of networks, technologies, terminals, operation and management, and more. Effective convergence and cooperation of heterogeneous networks can be achieved through Mesh technology. The IP-based convergence integrates common features of heterogeneous networks, while the cooperation coordinates personalities of the networks. By using the convergence and cooperation, a standardized integration of separated and localized predominant capabilities and resources of heterogeneous networks can be fulfilled to enable the evolution into an ubiquitous and omnipotent intelligent network.

The Convergence of WLAN and CDMA 2000 1x Networks

The technical solutions to the convergence of WLAN and CDMA 2000 1x are presented and compared.Problems brought on by network convergence are analyzed,and solutions to problems such as the coexistence of packet data service nodes(PDSNs),user i- dentification,roaming,and handoff are discussed in detail.

Study on QoS and Communications Capacity in Heterogeneous Network Convergence

To provide any subscriber from anywhere at anytime with services that have both secured Quality of Service(QoS) and simultaneous expansion of network coverage and communications capacity is a key problem that has to be considered and solved in heterogeneous network convergence.Key technologies for a secured QoS and communications capacity analysis under heterogeneous environment are important subjects for research.Key technologies for a secured QoS are mainly on radio resource management algorithms covering Call Admission Control(CAC) algorithm,vertical handover algorithm,heterogeneous resource allocation algorithm and network selection algorithm.The applications of a novel multi-hop in heterogeneous convergence system serve the purposes of network coverage expansion,transmission power reduction,system communication capacity and throughput increase.