A fast recursive neuronal learning algorithm applied to intelligent control

A fast and robust algorithm for training feedforward neural networks (FNNs) by using a variable forgetting factor and U-D factorization-based recursive prediction error (RPE) method is proposed. In comparison with the backpropagation (BP) and RPE based learning algorithms, the proposed algorithm, called UD-RPE, can provide much more accurate learning results in fewer iterations with fewer hidden nodes and improve convergence rate and numerical stability (robustness). In addition, it is less sensitive to start-up parameters, such as initial weights and initial covariance matrix, and the randomness in the observed data. It also has good generalization ability and needs less learning time. Simulation results of nonlinear dynamic system modeling and identification show that the algorithm proposed here is an effective and efficient learning algorithm for FNNs.

Bayesian spiking neurons (BSNs) provide a probablisitic and intuitive interpretation of how spiking neurons could work and have been shown to be equivalent to leaky integrate-and-fire neurons under certain conditions [1]. The study of BSNs has been restricted mainly to small networks because online learning, which currently involves a maximum-likelihood-expectation-maximisation (ML-EM) approach [2,3], is quite slow. Here a new approach to estimating the parameters of Bayesian spiking neurons, referred to as fast learning (FL), is presented and compared to online ML-EM learning. Learning in a BSN is local to the neuron and involves estimation of the transition rate and observation rate parameters of an underlying implicit hidden Markov model (HMM), the hidden state of which the BSN output encodes [1]. Rather than estimating the parameters by maximizing the log-likelihood of the hidden states and the synaptic observations given the parameters as is done in ML-EM [2,3], the FL algorithm directly calculates statistics upon which the parameters depend. This is achieved by taking advantage of the relationship between the log-odds ratio of the hidden state computed by the BSN and the probability that the hidden state is ‘on’ given the past synaptic observations, . Online learning in a two BSN neuron hierarchy is explored, where the first neuron receives N=20 synapses driven by Poisson processes and the second neuron receives input from only the first neuron. Simulations were performed for a fixed set of transition rates and observation rates for 10 different perturbations of the initial transition and observation rate estimates: ±0-20%, ±20-40%,..., ±180-200%. Initial rates were not allowed to go below 10-6. Each perturbation condition was simulated 100 times by randomly selecting the initial parameter values. Although the FL algorithm is not as exact as the ML-EM at estimating the true parameter values for small perturbations of the initial rate estimates relative to the true rates, the FL algorithm is able to reliably estimate the parameters for initial perturbations of up to 200%, whereas the ML-EM algorithm estimates begin to deviate after perturbations of about 40-60%. Moreover, the simplicity of the FL algorithm means that it runs on the order of 25 times faster than the ML-EM implementation considered. These results hold true for both the first and second neurons in the two BSN neuron hierarchy. For the first neuron in the hierarchy, the RMS difference in the time series of the probability calculated for the estimated and the true parameter values, follows a similar pattern to the parameter estimates when the FL and ML-EM algorithms are compared, with average RMS errors of 0.2% obtained for the FL algorithm across the range of perturbations studied. Although we do not have a formal proof of convergence of the FL algorithm, we conclude that the FL algorithm can stably estimate the parameters over a large range of initial perturbations and it can do this very quickly. Thus the FL algorithm makes online learning in networks of BSNs much more tractable.

The Sixth International Symposium on Neural Networks (ISNN 2009)

In this work, a Recursive Levenberg-Marquardt learning algorithm in the complex domain is developed and applied in the training of two adaptive control schemes composed by Complex-Valued Recurrent Neural Networks. Furthermore, we apply the identification and both control schemes for a particular case of nonlinear, oscillatory mechanical plant to validate the performance of the adaptive neural controller and the learning algorithm. The comparative simulation results show the better performance of the newly proposed Complex-Valued Recursive Levenberg-Marquardt learning algorithm over the gradient-based recursive Back-propagation one.

The paper proposes a fast online learning method for neural network structures by using genetic algorithm (GA) and dynamic back propagation algorithm (BP) jointly. GA is used in the coarse tuning process which adjusts interconnection weights of the neural network. The dynamic back propagation algorithm is subsequently applied to achieve fine adjusting of the network weights. The fitness function, based on the squared error between the teaching signal and the network output value, is redefined at every time step and the proposed GA based algorithm solves a nonstationary function optimization task. At every time step the solution with the best fitness function is used for current representation of the neural network weights and biases. It is shown through the simulations and real time temperature control of drying oven that this learning algorithm has faster convergence ability and better performance on reducing mapping error in the online learning neural network structures. This leads to an improvement of the transient response of neuro adaptive systems. The proposed method has the potential to be applied to many practical areas such as system modeling and control, signal processing and pattern recognition.

A fast learning algorithm is proposed for training of multilayer feedforward neural networks, based on a combination of optimal linear Kalman filtering theory and error propagation. In this algorithm, all the information available from the start of the training process to the current training sample is exploited in the update procedure for the weight vector of each neuron in the network in an efficient parallel recursive method. This innovation is a massively parallel implementation and has better convergence properties than the conventional backpropagation learning technique. Its performance is illustrated on some examples, such as a XOR logical operation and a nonlinear mapping of two continuous signals. >

In this paper, a novel neural-fuzzy controller based on fuzzy differential competitive learning is proposed. Since one of the most important parts is the generation of the fuzzy rules in the design of the fuzzy control system, a fast learning algorithm, fuzzy differential competitive learning (FDCL), for the generation of the rules is applied in the fuzzy control system. The FDCL algorithm adopts a principle of learn according to how well it wins. Unlike the previous competitive learning algorithm such as crisp competitive learning algorithms where only one neuron will win and learn at each competition step every neuron in the neural network based on FDCL algorithm will along with its different distance to the input pattern and learns the pattern accordingly. Compared with the ordinary competitive learning algorithm the proposed FDCL algorithm has the various distinguishing features. The FDCL algorithm is implanted in the neural network based fuzzy system and the network adopted is fuzzy associative memory system (FAMS) which simulates the knowledge representation and inference process by using fuzzy notation and by association in neural networks. In FAMS the fuzzy rules will be generated by clustering the input-output training data through the FDCL paradigm. By using the FDCL algorithm the neural network can highly refine knowledge and represent the expert experience.

Since the introduction of artificial neurons by McCulloch and Pitts in the early 1940's, many attempts aiming at fast learning algorithms with satisfactory performance have been made. Although neural networks have been successfully applied in many different areas, they still suffer from several problems, such as convergence problems and long training time. Almost all existing neural network learning algorithms are based on gradient descent technique, which needs iterative computations and long training time.

Fast Learning Algorithms

The feedforward layered neural networks have been applied to the various classification problem and control. The generalization capability of neural networks is one of the most important properties to be acquired such that it depends on the numbers of units or weights. In this paper, we propose a fast and effective structural learning algorithm to construct a suitable structure for neural networks and apply to the pattern recognition problem for handwritten numerical characters. At every learning step evaluations for unknown data are computed , and decide the stopping time of learning (test set validation). Furthermore we consider the validity to select an optimal neural network model by information criteria.

Neural network based variable structure control is proposed for the design of nonlinear discrete systems. Sliding mode control is used to provide good stability and robustness performance for nonlinear systems. An affine nonlinear neural predictor is introduced to predict the outputs of the nonlinear process and to make the variable structure control algorithm simple and easy to implement. When the predictor model is inaccurate, variable structure control with sliding modes is used to improve the stability of the system. A recursive weight learning algorithm for the neural networks based affine nonlinear predictor is also developed and the convergence of both the weights and the estimation error is analysed.

Bayesian spiking neurons (BSNs) provide a probabilistic interpretation of how neurons perform inference and learning. Online learning in BSNs typically involves parameter estimation based on maximum-likelihood expectation-maximization (ML-EM) which is computationally slow and limits the potential of studying networks of BSNs. An online learning algorithm, fast learning (FL), is presented that is more computationally efficient than the benchmark ML-EM for a fixed number of time steps as the number of inputs to a BSN increases (e.g., 16.5times faster run times for 20 inputs). Although ML-EM appears to converge 2.0 to 3.6times faster than FL, the computational cost of ML-EM means that ML-EM takes longer to simulate to convergence than FL. FL also provides reasonable convergence performance that is robust to initialization of parameter estimates that are far from the true parameter values. However, parameter estimation depends on the range of true parameter values. Nevertheless, for a physiologically meaningful range of parameter values, FL gives very good average estimation accuracy, despite its approximate nature. The FL algorithm therefore provides an efficient tool, complementary to ML-EM, for exploring BSN networks in more detail in order to better understand their biological relevance. Moreover, the simplicity of the FL algorithm means it can be easily implemented in neuromorphic VLSI such that one can take advantage of the energy-efficient spike coding of BSNs.

A fast learning algorithm for parsimonious fuzzy neural systems

An agent must learn and adapt quickly when playing against other agents. This process is challenging in particular when playing in stochastic environments against other learning agents. In this paper, we introduce a fast and adaptive learning algorithm for repeated stochastic games (FAL-SG). FAL-SG utilizes lossy game abstraction to reduce the state space of the game and facilitate learning and adapting rapidly. We analyze FAL-SG's performance by proving bounds on the abstraction loss and prediction mistakes and show that FAL-SG satisfies three criteria prescribed for multiagent learning algorithms. We successfully establish the robustness and scalability of FAL-SG with extensive theoretical and experimental results.

Online adaptation is a key requirement for image processing applications when used in dynamic environments. In contrast to batch learning, where retraining is required each time a new observation occurs, sequential learning algorithms offer the ability to iteratively adapt the existing classifier. In this paper, we present a neural network architecture and a fast online learning algorithm that allow to use the class of resource allocation networks for such adaptive image processing applications. The network is based on receptive fields that are processed by RBF sub-nets. The learning algorithm builds such networks online by adding new units to the sub-nets each time novel input data is observed. For this, we define a global and a local novelty criterion. Experimental results show that the proposed network outperforms existing RAN algorithms when used for face detection and recognition and is competitive with existing classifiers.