近似符号计算的神经网络模型方法的研究：多项式因式分解的神经网络机理

定义了代数神经元与代数神经网络,将符号计算融入代数神经网络,讨论多项式因式分解机理,设计出一类一元,多元项式因式分解的神经网络模型,以整数域Ｚ,复数域Ｃ上多项式为例,指出其网络模型的可行性。     

一种混合高性能计算机代数环境模型

提出一种高性能计算机代数环境HHPCAS，综合现有的多种计算机代数软件，通过添加内核扩展函数、外部调用等方法，结合集群管理软件和并行环境，可以提供高性能的计算机代数计算环境。HHPCAS根据Slot/Ticket模型可以有效管理可用计算资源和作业优先等级，充分发挥多种计算机代数软件的特长，并且提供并行的消息传递机制，将大量复杂的计算平均分配到每个计算节点，解决单台机器内存受限和计算能力有限等问题。通过并行差分代换方法测试表明HHPCAS可以为符号计算和计算机自动推理提供有效的计算平台。     

一种激励函数可调的回归神经网络符号计算模型及应用

1引言 Hensel提升方法是由Hensel本人在1900年提出,最先用于求解一元多项式的p-adic展开式,后经Wang和Rothschlid推广到多元多项式的情形,并应用于整数域上的多项式因式分解[1],发展到今天,Hensel提升方法,在代数符号计算、近似代数符号计算等相关领域,有着广泛的应用.作者认为,几乎与Hensel构造方法有关的代数计算都是一些精确计算,从一般函数逼近的观点来看,它只是一种在p-adic意义下的逼近,完全不同于通常意义下一般函数的逼近,限制了Hensel提升方法的应用范围,因此,有必要进行推广.     

前向代数神经网络的函数逼近理论及学习算法

文中对ＭＰ神经元模型进行了推广,定义了多项代数神经元、多项式代数神经网络,将多项式代数融入代数神经网络,分析了前向多项式代数神经网络函数逼近能力及理论依据,设计出了一类双输入单输出的前向４层多层式代数神经网络模型,由该模型构成的网络能够逼近于给定的二元多项式到预定的精度。给出了在Ｐ－ａｄｉｃ意义下的多项式代数神经网络函数逼近整体学习算法,在学习的过程中,不存在局部极小,通过实例表明,该算法有效,最     

符号矩阵奇异值的计算机分解与广义逆计算

本文从符号计算(计算机代数)的观点,对数值矩阵计算理论中传统的奇异值分解算法及其相关的广义逆矩阵计算方法加以改进,使之适于处理符号矩阵且在计算机上实现.并指出其在矩阵理论及线性问题求解中的某些应用,还给出了一个有趣的物理实例.     

基于代数神经网络的不确定数据知识获取方法

定义了代数神经元、代数神经网络,讨论了不确定数据知识获取的数学机理,设计出一类单输入,单输出的三层前向网络来获取知识的代数神经网络模型,给出一种基于代数神经网络知识获取的方法,通过该网络的学习,能确定任意一组给定数据的目标函数的逼近式。     

具有时变时滞的递归神经网络的渐近稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间.研究了带时变时滞的递归神经网络的全局渐近稳定性.首先将要研究的模型转化为描述系统模型,然后利用Lyapunov-Krasovskii稳定性定理、线性矩阵不等式(LMI)技术、S过程和代数不等式方法,得到了确保时变时滞递归神经网络渐近稳定性的新的充分条件,并将它应用于常时滞神经网络和时滞细胞神经网络模型,分别得到了相应的全局渐近稳定性条件.理论分析和数值模拟显示,所得结果为时滞递归神经网络提供了新的稳定性判定准则.     

基于Linux下的高性能符号计算平台的实现

符号代数计算在最近十多年已得到了高度重视,各国都在开发具有自主知识产权的高性能符号代数计算平台,如美国的Mathematica、加拿大的Maple和欧盟的Possol等。这些系统已经广泛应用于大规模科学工程计算和理论研究中。但它们仍有种种不足,例如软件调用内存的限制,仅提供面向过程的而非面向对象的设计语言,特别是源代码的不公开性造成了在其上面开发的软件受制于开发平台。笔者目前开发的基于Linux下的高性能符号计算平台建立在快速的大整数运算、多项式运算和因式分解基础上,具有效率高、计算能力强、源码公开等显著优点,同时为用户提供了两种接口,一是在C++语言里提供源程序级类库,用户可以用基本类库和面向对象的程序设计语言编程;二是象大多数计算机代数系统那样提供一种编程语言,用户可以在平台上进行程序设计。这个平台也是我国目前唯一的基于Linux下的高性能符号计算平台。该文重点讨论该平台的实现原理和方法,并与Maple进行了对比测试,结果显示该平台具有更高的效率。     

基于HMM和新型前馈型神经网络的语音识别研究

为了进一步提高语音识别系统的准确率,使语音产品应用更加方便,提出了一种隐马尔可夫模型和代数神经网络相结合的语音识别方法.利用隐马尔可夫模型生成最佳语音状态序列,将最佳状态序列的输出概率作为前馈型神经网络的输入,通过代数神经网络进行分类识别.使用Matlab7.0实验平台进行仿真,实验结果表明,与传统神经网络相比,该方法在收敛速度、鲁棒性和识别率方面都有改善.     

求解 Burgers 方程的决定方程的两种方法研究

论文研究了两种求解偏微分方程的决定方程的方法,一种是运用向量场及其延拓方法,另一种是通过符号计算软件 maple 自动求解软件包。论文以 Burgers 方程为例,证明两种方法得到的结果相同。但运用 maple 自动求解软件包能够避免复杂的代数计算,提高计算的速度与准确率,适用于求解复杂的高阶非线性偏微分方程。     

Extension of grounding mechanism for abstract words: computational methods insights

The attempts to model cognitive phenomena effectively have split the research community in two paradigms: symbolic and connectionist. The extension of grounding phenomenon for abstract words is very important for social interactions of cognitive robots in real scenarios. This paper reviews the strength of symbolic and connectionist methods to address the abstract word grounding problem in cognitive robots. In particular, the presented work is focused on designing and simulating cognitive robotics model to achieve a grounding mechanism for abstract words by using the semantic network approach, as well as examining the utility of connectionist computation for the same problem. Two neuro-robotics models based on feed forward neural network and recurrent neural network are presented to see the pros and cons of connectionist approach. The simulation results and review of attributes of these methods reveal that the proposed symbolic model offers the solution to the problem of grounding abstract words with attributes like high data storage capacity with recall accuracy, structural integrity and temporal sequence handling. Whereas, connectionist computation based solutions give more natural solution to this problem with some shortcomings that include combinatorial ambiguity, low storage capacity and structural rigidity. The presented results are not only important for the advancement in communication system of cognitive robot, also provide evidence for embodied nature of abstract language.     

Handwritten Chinese character recognition by rule-embedded Neocognitron

This paper presents an attempt to integrate neural computation with a domain knowledge technique to resolve the problem of the wide variety in handwritten Chinese characters. Despite their complexity, Chinese characters can be seen as structured patterns. Therefore, we propose a symbolic representation to describe these structural formations. In particular, we consider the Fuzzy Attributed Production Rule (FAPR) as a possible symbolic representation. On the neural computational side, we study Fukushima's Neocognitron model, which has been successfully demonstrated to recognize handwritten alphanumerics. Despite its power and tolerance capabilities, the supervised training scheme used by Fukushima is impractical for a large character set such as Chinese characters. We thus propose a ruleembedded Neocognitron network which can be readily mapped with structure-knowledge of Chinese characters as represented in FAPRs. In this paper, we demonstrate how 50 Chinese characters are mapped onto the network, and that the system performance in tolerating character structure deviations is satisfactory.     

多项式函数型回归神经网络模型及应用

文中利用回归神经网络既有前馈通路又有反馈通路的特点，将网络隐层中神经元的激活函数设置为可调多项式函数序列，提出了多项式函数型回归神经网络新模型，它不但具有传统回归神经网络的特点，而且具有较强的函数逼近能力，针对递归计算问题，提出了多项式函数型回归神经网络学习算法，并将该网络模型应用于多元多项式近似因式分解，其学习算法在多元多项式近似分解中体现了较强的优越性，通过算例分析表明，该算法十分有效，收敛速度快，计算精度高，可适用于递归计算问题领域，该文所提出的多项式函数型回归神经网络模型及学习算法对于代数符号近似计算有重要的指导意义。     

Learning capacity and sample complexity on expert networks

A major development in knowledge-based neural networks is the integration of symbolic expert rule-based knowledge into neural networks, resulting in so-called rule-based neural (or connectionist) networks. An expert network here refers to a particular construct in which the uncertainty management model of symbolic expert systems is mapped into the activation function of the neural network. This paper addresses a yet-to-be-answered question: Why can expert networks generalize more effectively from a finite number of training instances than multilayered perceptrons? It formally shows that expert networks reduce generalization dimensionality and require relatively small sample sizes for correct generalization.     

Neural computation with cellular cultures

There exist two classical paradigms in computation: the symbolic representation and the connectionist approximation. In addition to these two conventional paradigms, there are other, newer, approaches that are not so well established, but belonging to the brainstorming frontier between science and engineering. These new approaches include Bioware computation that proposes using real biological systems as computing elements. In this paper biological computing paradigms are studied by the programming capabilities of cellular cultures, mostly neural cultures, grown over multielectrode arrays with bi-directional communications. The systems are able of reading the cellular network activity and act over the network by stimulating the cells in different locations and with different approaches for superimposing a desired behaviour over the cultures.     

Distributed Computation Multi-agent System

This article addresses a formal model of a distributed computation multi-agent system. This model has evolved from the experimental research on using multi-agent systems as a ground for developing fuzzy cognitive maps. The main paper contribution is a distributed computation multi-agent system definition and mathematical formalization based on automata theory. This mathematical formalization is tested by developing distributed computation multi-agent systems for fuzzy cognitive maps and artificial neural networks – two typical distributed computation systems. Fuzzy cognitive maps are distributed computation systems used for qualitative modeling and behavior simulation, while artificial neural networks are used for modeling and simulating complex systems by creating a non-linear statistical data model. An artificial neural network encapsulates in its structure data patterns that are hidden in the data used to create the network. Both of these systems are well suited for formal model testing. We have used evolutionary incremental development as an agent design method which has shown to be a good approach to develop multi-agent systems according to the formal model of a distributed computation multi-agent system.     

Hierarchical intelligent control for robotic motion

This paper presents a new scheme for intelligent control of robotic manipulators. This scheme is a hierarchically integrated approach to neuromorphic and symbolic control of robotic manipulators. This includes an applied neural network for servo control and knowledge-based approximation. The neural network in the servo control level is based on a numerical manipulation, while the knowledge based part is symbolic manipulation. The knowledge base part develops control strategies symbolically for the servo level. The neural network compensates for vagueness in the control strategies, nonlinearities of the system and uncertainties in its environment using neuromorphic control.     

Knowledge discovery by inductive neural networks

A new neural network model for inducing symbolic knowledge from empirical data is presented. This model capitalizes on the fact that the certainty factor-based activation function can improve the network generalization performance from a limited amount of training data. The formal properties of the procedure for extracting symbolic knowledge from such a trained neural network are investigated. In the domain of molecular genetics, a case study demonstrated that the described learning system effectively discovered the prior domain knowledge with some degree of refinement. Also, in cross-validation experiments, the system outperformed C4.5, a commonly used rule learning system     

基于神经网络结构搜索的轻量化网络构建

轻量化网络可解决深度神经网络参数较多、计算量较高、难以部署在计算能力有限的边缘设备上等问题.针对轻量化网络中常用的分组卷积的分组结构问题,文中提出基于神经网络结构搜索的轻量化网络.将不同分组的卷积单元作为搜索空间,使用神经网络结构搜索,得到网络的分组结构和整体架构.同时为了兼顾准确率与计算量,提出循环退火搜索策略,用于解决神经网络结构搜索的多目标优化问题.在数据集上的实验表明,文中网络识别准确率较高,时间复杂度和空间复杂度较低.     

基于神经网络机器翻译模型的英文分词研究

针对英文等符号语言不能直接使用现有的神经网络机器翻译模型(NMT)的问题。在简述LSTM神经网络的基础上,采用分桶(b ucketing)的方式将样本进行batch划分,在NMT模型中加入注意力机制提高了系统的性能,并分别利用双向LSTM神经网络和贪婪算法设计了基于上下文特征提取的编码器和输出算法的解码器。最后从语句还原程度和语义识别情况两个角度对英文的一元分词和HMM分词在NMT模型上的应用结果进行了对比,研究了英文的NMT模型适配方案。