数值优化改进的BP网络的模式分类对比

研究了共轭梯度算法、拟牛顿算法、LM算法三类常用的数值优化改进算法,基于这三类数值优化算法分别对BP神经网络进行改进,并构建了相应的BP神经网络分类模型,将构建的分类模型应用于二维向量模式的分类,并进行了泛化能力测试,将不同BP网络分类模型的分类结果进行对比. 仿真结果表明,对于中小规模的网络而言,LM数值优化算法改进的BP网络的分类结果最为精确,收敛速度最快,分类性能最优;共轭梯度数值优化算法改进的BP网络的分类结果误差最大,收敛速度最慢,分类性能最差;拟牛顿数值优化算法改进的BP网络的分类结果误差值、收敛速度及分类性能介于上述两种算法之间.     

Truncated-Newton training algorithm for neurocomputational viscoplastic model

We present an estimate approach to compute the viscoplastic behavior of a polymer matrix composite under different thermomechanical environments. This investigation incorporates computational neural network as the tool for determining the creep behavior of the composite. We propose a new second-order learning algorithm for training the multilayer networks. Training in the neural network is generally specified as the minimization of an appropriate error function with respect to parameters of the network (weights and learning rates) corresponding to excitory and inhibitory connections. We propose here a technique for error minimization based on the use of the truncated Newton (TN) large-scale unconstrained minimization technique with quadratic convergence rate. This technique offers a more sophisticated use of the gradient information compared to simple steepest descent or conjugate gradient methods. In this work we briefly specify the necessary details for implementing the TN method for training the neural networks that predicts the viscoplastic behavior of the polymeric composite. We provide comparative experimental results and explicit model results to verify the effectiveness of the neural networks-based model. These results verify the superiority of the present approach compared to the explicit modeling scheme. Moreover, the present study demonstrates for the first time the feasibility of introducing the TN method, with quadratic convergence rate, to the field of neural networks.     

Deterministic convergence of an online gradient method for BP neural networks

Online gradient methods are widely used for training feedforward neural networks. We prove in this paper a convergence theorem for an online gradient method with variable step size for backward propagation (BP) neural networks with a hidden layer. Unlike most of the convergence results that are of probabilistic and nonmonotone nature, the convergence result that we establish here has a deterministic and monotone nature.     

Convergence of gradient method for a fully recurrent neural network

Recurrent neural networks have been successfully used for analysis and prediction of temporal sequences. This paper is concerned with the convergence of a gradient-descent learning algorithm for training a fully recurrent neural network. In literature, stochastic process theory has been used to establish some convergence results of probability nature for the on-line gradient training algorithm, based on the assumption that a very large number of (or infinitely many in theory) training samples of the temporal sequences are available. In this paper, we consider the case that only a limited number of training samples of the temporal sequences are available such that the stochastic treatment of the problem is no longer appropriate. Instead, we use an off-line gradient training algorithm for the fully recurrent neural network, and we accordingly prove some convergence results of deterministic nature. The monotonicity of the error function in the iteration is also guaranteed. A numerical example is given to support the theoretical findings.     

A New Conjugate Gradient Method with Smoothing $$L_{1/2} $$ Regularization Based on a Modified Secant Equation for Training Neural Networks

Proposed in this paper is a new conjugate gradient method with smoothing \(L_{1/2} \) regularization based on a modified secant equation for training neural networks, where a descent search direction is generated by selecting an adaptive learning rate based on the strong Wolfe conditions. Two adaptive parameters are introduced such that the new training method possesses both quasi-Newton property and sufficient descent property. As shown in the numerical experiments for five benchmark classification problems from UCI repository, compared with the other conjugate gradient training algorithms, the new training algorithm has roughly the same or even better learning capacity, but significantly better generalization capacity and network sparsity. Under mild assumptions, a global convergence result of the proposed training method is also proved.     

A conjugate gradient learning algorithm for recurrent neural networks

The real-time recurrent learning (RTRL) algorithm, which is originally proposed for training recurrent neural networks, requires a large number of iterations for convergence because a small learning rate should be used. While an obvious solution to this problem is to use a large learning rate, this could result in undesirable convergence characteristics. This paper attempts to improve the convergence capability and convergence characteristics of the RTRL algorithm by incorporating conjugate gradient computation into its learning procedure. The resulting algorithm, referred to as the conjugate gradient recurrent learning (CGRL) algorithm, is applied to train fully connected recurrent neural networks to simulate a second-order low-pass filter and to predict the chaotic intensity pulsations of NH₃ laser. Results show that the CGRL algorithm exhibits substantial improvement in convergence (in terms of the reduction in mean squared error per epoch) as compared to the RTRL and batch mode RTRL algorithms.     

Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization

The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given.     

基于外时延反馈人工神经网络的短期负荷预测系统

针对当前人工神经网络学习算法存在的问题,使用变步伐最速下降法和共轭梯度法的混合算法来进行神经网络的训练,并建立了负荷预测的人工神经网络模型。介绍了基于Delphi下的短期电力负荷预测系统。该系统由负荷预测数据查询模块、预测方法模块、结果查询模块和图表输出模块四部分组成。事实说明,混合算法在全局收敛性和收敛速度上要好于传统的算法,所基于此的短期负荷预测系统能达到令人满意的精度。     

Comparison of new activation functions in neural network for forecasting financial time series

In artificial neural networks (ANNs), the activation function most used in practice are the logistic sigmoid function and the hyperbolic tangent function. The activation functions used in ANNs have been said to play an important role in the convergence of the learning algorithms. In this paper, we evaluate the use of different activation functions and suggest the use of three new simple functions, complementary log-log, probit and log-log, as activation functions in order to improve the performance of neural networks. Financial time series were used to evaluate the performance of ANNs models using these new activation functions and to compare their performance with some activation functions existing in the literature. This evaluation is performed through two learning algorithms: conjugate gradient backpropagation with Fletcher–Reeves updates and Levenberg–Marquardt.     

采用资格迹的神经网络学习控制算法

强化学习是解决自适应问题的重要方法,被广泛地应用于连续状态下的学习控制,然而存在效率不高和收敛速度较慢的问题.在运用反向传播(back propagation,BP)神经网络基础上,结合资格迹方法提出一种算法,实现了强化学习过程的多步更新.解决了输出层的局部梯度向隐层节点的反向传播问题,从而实现了神经网络隐层权值的快速更新,并提供一个算法描述.提出了一种改进的残差法,在神经网络的训练过程中将各层权值进行线性优化加权,既获得了梯度下降法的学习速度又获得了残差梯度法的收敛性能,将其应用于神经网络隐层的权值更新,改善了值函数的收敛性能.通过一个倒立摆平衡系统仿真实验,对算法进行了验证和分析.结果显示,经过较短时间的学习,本方法能成功地控制倒立摆,显著提高了学习效率.     

神经网络增强学习的梯度算法研究

针对具有连续状态和离散行为空间的Markov决策问题，提出了一种新的采用多层前馈神经网络进行值函数逼近的梯度下降增强学习算法，该算法采用了近似贪心且连续可微的Boltzmann分布行为选择策略，通过极小化具有非平稳行为策略的Bellman残差平方和性能指标，以实现对Markov决策过程最优值函数的逼近，对算法的收敛性和近似最优策略的性能进行了理论分析，通过Mountain-Car学习控制问题的仿真研究进一步验证了算法的学习效率和泛化性能。     

A new on-line learning model

We introduce a new supervised learning model that is a nonhomogeneous Markov process and investigate its properties. We are interested in conditions that ensure that the process converges to a "correct state," which means that the system agrees with the teacher on every "question." We prove a sufficient condition for almost sure convergence to a correct state and give several applications to the convergence theorem. In particular, we prove several convergence results for well-known learning rules in neural networks.     

A generalized learning paradigm exploiting the structure offeedforward neural networks

In this paper a general class of fast learning algorithms for feedforward neural networks is introduced and described. The approach exploits the separability of each layer into linear and nonlinear blocks and consists of two steps. The first step is the descent of the error functional in the space of the outputs of the linear blocks (descent in the neuron space), which can be performed using any preferred optimization strategy. In the second step, each linear block is optimized separately by using a least squares (LS) criterion. To demonstrate the effectiveness of the new approach, a detailed treatment of a gradient descent in the neuron space is conducted. The main properties of this approach are the higher speed of convergence with respect to methods that employ an ordinary gradient descent in the weight space backpropagation (BP), better numerical conditioning, and lower computational cost compared to techniques based on the Hessian matrix. The numerical stability is assured by the use of robust LS linear system solvers, operating directly on the input data of each layer. Experimental results obtained in three problems are described, which confirm the effectiveness of the new method.     

A general methodology for designing globally convergentoptimization neural networks

We present a general methodology for designing optimization neural networks. We prove that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets, in contrast with the gradient methods whose convergence is not guaranteed. We show that the proposed method contains both the gradient methods and nongradient methods employed in existing optimization neural networks as special cases. Based on the theoretical results of the proposed method, we study the convergence and stability of general gradient models in the case of unisolated solutions. Using the proposed method, we derive some new neural network models for a very large class of optimization problems, in which the equilibrium points correspond to exact solutions and there is no variable parameter. Finally, some numerical examples show the effectiveness of the method.     

Stability Analysis and the Stabilization of a Class of Discrete-Time Dynamic Neural Networks

This paper deals with problems of stability and the stabilization of discrete-time neural networks. Neural structures under consideration belong to the class of the so-called locally recurrent globally feedforward networks. The single processing unit possesses dynamic behavior. It is realized by introducing into the neuron structure a linear dynamic system in the form of an infinite impulse response filter. In this way, a dynamic neural network is obtained. It is well known that the crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates stability conditions for the analyzed class of neural networks. Moreover, a stabilization problem is defined and solved as a constrained optimization task. In order to tackle this problem two methods are proposed. The first one is based on a gradient projection (GP) and the second one on a minimum distance projection (MDP). It is worth noting that these methods can be easily introduced into the existing learning algorithm as an additional step, and suitable convergence conditions can be developed for them. The efficiency and usefulness of the proposed approaches are justified by using a number of experiments including numerical complexity analysis, stabilization effectiveness, and the identification of an industrial process     

基于梯度动力学的协同神经网络学习算法的改进

本文在研究协同神经网络梯度动力学过程的基础上,针对学习过程收敛速度缓慢的缺点,提出了一种改进的、基于梯度动力学的协同神经网络学习算法。该算法分析了非平衡注意参数对学习过程的影响,简化了初始伴随向量的选取;并引入最优化理论,将该问题归结为求解非线性最优化问题,用共轭梯度法代替梯度下降法,加快了学习过程的收敛。通过对汉字图像库和人脸图像库的图像识别实验表明,该算法比其他学习算法的识别率高,并能较快地收敛到极小值。     

Reformulated radial basis neural networks trained by gradientdescent

This paper presents an axiomatic approach for constructing radial basis function (RBF) neural networks. This approach results in a broad variety of admissible RBF models, including those employing Gaussian RBFs. The form of the RBFs is determined by a generator function. New RBF models can be developed according to the proposed approach by selecting generator functions other than exponential ones, which lead to Gaussian RBFs. This paper also proposes a supervised learning algorithm based on gradient descent for training reformulated RBF neural networks constructed using the proposed approach. A sensitivity analysis of the proposed algorithm relates the properties of RBFs with the convergence of gradient descent learning. Experiments involving a variety of reformulated RBF networks generated by linear and exponential generator functions indicate that gradient descent learning is simple, easily implementable, and produces RBF networks that perform considerably better than conventional RBF models trained by existing algorithms     

A parallel genetic/neural network learning algorithm for MIMDshared memory machines

A new algorithm is presented for training of multilayer feedforward neural networks by integrating a genetic algorithm with an adaptive conjugate gradient neural network learning algorithm. The parallel hybrid learning algorithm has been implemented in C on an MIMD shared memory machine (Cray Y-MP8/864 supercomputer). It has been applied to two different domains, engineering design and image recognition. The performance of the algorithm has been evaluated by applying it to three examples. The superior convergence property of the parallel hybrid neural network learning algorithm presented in this paper is demonstrated.     

基于梯度动力学的协同神经网络学习算法的改进

本文在研究协同神经网络梯度动力学过程的基础上,针对学习过程收敛速度缓慢的缺点,提出了一种改进的基于梯度动力学的协同神经网络学习算法。该算法分析了非平衡注意参数对学习过程的影响,简化了初始伴随向量的选取;并引入最优化理论,将该问题归结为求解非线性最优化问题,用共轭梯度法代替梯度下降法,加快了学习过程的收敛。通过对汉字图像库和人脸图像库的图像识别实验,表明该算法较之其他学习算法有较高的识别率,并能较快的收敛到极小值。     

Some three-term conjugate gradient methods with the inexact line search condition

The three-term conjugate gradient methods solving large-scale optimization problems are favored by many researchers because of their nice descent and convergent properties. In this paper, we extend some new conjugate gradient methods, and construct some three-term conjugate gradient methods. An remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition without any line search. Under the standard Wolfe line search, the global convergence properties of the proposed methods are proved merely by assuming that the objective function is Lipschitz continuous. Preliminary numerical results and comparisons show that the proposed methods are efficient and promising.