On the capacity of multilayer neural networks trained with backpropagation

The capacity of a layered neural network for learning hetero-associations is studied numerically as a function of the number M of hidden neurons. We find that there is a sharp change in the learning ability of the network as the number of hetero-associations increases. This fact allows us to define a maximum capacity C for a given architecture. It is found that C grows logarithmically with M.     

A modified error backpropagation algorithm for complex-value neural networks

The complex-valued backpropagation algorithm has been widely used in fields of dealing with telecommunications, speech recognition and image processing with Fourier transformation. However, the local minima problem usually occurs in the process of learning. To solve this problem and to speed up the learning process, we propose a modified error function by adding a term to the conventional error function, which is corresponding to the hidden layer error. The simulation results show that the proposed algorithm is capable of preventing the learning from sticking into the local minima and of speeding up the learning.     

儿童青少年肺通气功能预测的后向传播神经网络方法

本文旨在研究儿童青少年肺通气功能预测的后向传播神经网络(backpropagation neural network,BPNN)方法,以期得到更准确的肺通气功能预计值。样本数据包括内蒙古自治区10~18岁汉族健康儿童青少年999人(男性500人,女性499人),测量身高和体重,使用肺功能仪检测肺通气功能。利用BPNN和多元逐步回归,对用力肺活量(forced vital capacity,FVC)、用力呼气一秒量(forced expiratory volume in one second,FEV1)、最大呼气流量(peak expiratory flow,PEF)、用力呼出25%肺活量时呼气流量(forced expiratory flow at25%of forced vital capacity,FEF25%)、用力呼出50%肺活量时呼气流量(forced expiratoryflow at50%of forced vital capacity,FEF50%)、最大呼气中段流量(maximal mid-expiratory flow,MMEF)、用力呼出75%肺活量时呼气流量(forced expira...     

Neural networks learning with sliding mode control: the sliding mode backpropagation algorithm

Based on the classical backpropagation weight update equations, sliding mode control theory is introduced as a technique to adapt weights of a multi-layer perceptron. As will be demonstrated, the introduction of sliding mode has resulted in a much faster version of the standard backpropagation. The results show also that the proposed algorithm presents some important features of sliding mode control, which are robustness and high speed of learning. In addition to that, this paper shows also how control theory can be applied to train neural networks.     

The backpropagation algorithm in J, a fast prototyping tool for researching neural networks

This paper illustrates the use of a powerful language, called J, that is ideal for simulating neural networks. The use of J is demonstrated by its application to a gradient descent method for training a multilayer perceptron. It is also shown how the back-propagation algorithm can be easily generalized to multilayer networks without any increase in complexity and that the algorithm can be completely expressed in an array notation which is directly executable through J. J is a general purpose language, which means that its user is given a flexibility not available in neural network simulators or in software packages such as MATLAB. Yet, because of its numerous operators, J allows a very succinct code to be used, leading to a tremendous decrease in development time.     

Improved learning capacity and discrimination performance of neural networks in pattern recognition of biosignals]

Pattern recognition was an important goal in the early work on artificial neural networks. Without arousing dramatic speculation, the paper describes, how a "natural" method of dealing with the configuration of the input layer can considerably improve learning behaviour and classification rate of a modified multi-layered perception with backpropagation of the error learning rule. Using this method, recognition of complex patterns in electrophysiological signals can be performed more accurately, without rules or complicated heuristic procedures. The proposed technique is demonstrated using recognition of the J-point in the ECG as an example.     

Improved neuronal models for studying neural networks

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.     

Successive learning in hetero-associative memory using chaotic neural networks

In this paper, we propose a successive learning method in hetero-associative memories, such as Bidirectional Associative Memories and Multidirectional Associative Memories, using chaotic neural networks. It can distinguish unknown data from the stored known data and can learn the unknown data successively. The proposed model makes use of the difference in the response to the input data in order to distinguish unknown data from the stored known data. When input data is regarded as unknown data, it is memorized. Furthermore, the proposed model can estimate and learn correct data from noisy unknown data or incomplete unknown data by considering the temporal summation of the continuous data input. In addition, similarity to the physiological facts in the olfactory bulb of a rabbit found by Freeman are observed in the behavior of the proposed model. A series of computer simulations shows the effectiveness of the proposed model.     

Intelligent scheduling of FMSs with inductive learning capability using neural networks

With the growing uncertainty and complexity in the manufacturing environment, most scheduling problems have been proven to be NP-complete and this can degrade the performance of conventional operations research (OR) techniques. This article presents a system-attribute-oriented knowledge-based scheduling system (SAOSS) with inductive learning capability. With the rich heritage from artificial intelligence (AI), SAOSS takes a multialgorithm paradigm which makes it more intelligent, flexible, and suitable than others for tackling complicated, dynamic scheduling problems. SAOSS employs an efficient and effective inductive learning method, a continuous iterative dichotomister 3 (CID3) algorithm, to induce decision rules for scheduling by converting corresponding decision trees into hidden layers of a self-generated neural network. Connection weights between hidden units imply the scheduling heuristics, which are then formulated into scheduling rules. An FMS scheduling problem is also given for illustration. The scheduling results show that the system-attribute-oriented knowledge-based approach is capable of addressing dynamic scheduling problems.     

Reinforcement learning with internal expectation in the random neural networks for cascaded decisions

The reinforcement learning scheme proposed in Halici (J. Biosystems 40 (1997) 83) for the random neural network (RNN) (Neural Computation 1 (1989) 502) is based on reward and performs well for stationary environments. However, when the environment is not stationary it suffers from getting stuck to the previously learned action and extinction is not possible. To overcome the problem, the reinforcement scheme is extended in Halici (Eur. J. Oper. Res., 126(2000) 288) by introducing a new weight update rule (E-rule) which takes into consideration the internal expectation of reinforcement. Although the E-rule is proposed for the RNN, it can be used for training learning automata or other intelligent systems based on reinforcement learning. This paper looks into the behavior of the learning scheme with internal expectation for the environments where the reinforcement is obtained after a sequence of cascaded decisions. The simulation results have shown that the RNN learns well and extinction is possible even for the cases with several decision steps and with hundreds of possible decision paths.     

Evidence of hyperplanes in the genetic learning of neural networks

Genetic Algorithms have been successfully applied to the learning process of neural networks simulating artificial life. In previous research we compared mutation and crossover as genetic operators on neural networks directly encoded as real vectors (Manczer and Parisi 1990). With reference to crossover we were actually testing the building blocks hypothesis, as the effectiveness of recombination relies on the validity of such hypothesis. Even with the real genotype used, it was found that the average fitness of the population of neural networks is optimized much more quickly by crossover than it is by mutation. This indicated that the intrinsic parallelism of crossover is not reduced by the high cardinality, as seems reasonable and has indeed been suggested in GA theory (Antonisse 1989). In this paper we first summarize such findings and then propose an interpretation in terms of the spatial correlation of the fitness function with respect to the metric defined by the average steps of the genetic operators. Some numerical evidence of such interpretation is given, showing that the fitness surface appears smoother to crossover than it does to mutation. This confirms indirectly that crossover moves along privileged directions, and at the same time provides a geometric rationale for hyperplanes.     

Improved long-term temperature prediction by chaining of neural networks

When an artificial neural network (ANN) is trained to predict signals p steps ahead, the quality of the prediction typically decreases for large values of p. In this paper, we compare two methods for prediction with ANNs: the classical recursion of one-step ahead predictors and a new kind of chain structure. When applying both techniques to the prediction of the temperature at the end of a blast furnace, we conclude that the chaining approach leads to an improved prediction of the temperature and avoidance of instabilities, since the chained networks gradually take the prediction of their predecessors in the chain as an extra input. It is observed that instabilities might occur in the iterative case, which does not happen with the chaining approach. To select relevant inputs and decrease the number of weights in this approach, Automatic Relevance Determination (ARD) for multilayer perceptrons is applied.     

Clustering with neural networks

Partitioning a set ofN patterns in ad-dimensional metric space intoK clusters — in a way that those in a given cluster are more similar to each other than the rest — is a problem of interest in many fields, such as, image analysis, taxonomy, astrophysics, etc. As there are approximatelyK ^N/K! possible ways of partitioning the patterns amongK clusters, finding the best solution is beyond exhaustive search whenN is large. We show that this problem, in spite of its exponential complexity, can be formulated as an optimization problem for which very good, but not necessarily optimal, solutions can be found by using a Hopfield model of neural networks. To obtain a very good solution, the network must start from many randomly selected initial states. The network is simulated on the MPP, a 128 × 128 SIMD array machine, where we use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also in starting the network from many initial states at once thus obtaining many solutions in one run. We achieve speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of further speedups of three to six orders of magnitude.Supported by a National Research Council-NASA Research Associatship     

Synchrony based learning rule of Hopfield like chaotic neural networks with desirable structure

In this paper a new learning rule for the coupling weights tuning of Hopfield like chaotic neural networks is developed in such a way that all neurons behave in a synchronous manner, while the desirable structure of the network is preserved during the learning process. The proposed learning rule is based on sufficient synchronization criteria, on the eigenvalues of the weight matrix belonging to the neural network and the idea of Structured Inverse Eigenvalue Problem. Our developed learning rule not only synchronizes all neuron’s outputs with each other in a desirable topology, but also enables us to enhance the synchronizability of the networks by choosing the appropriate set of weight matrix eigenvalues. Specifically, this method is evaluated by performing simulations on the scale-free topology.     

Route searching based on neural networks and heuristic reinforcement learning

In this paper, an improved and much stronger RNH-QL method based on RBF network and heuristic Q-learning was put forward for route searching in a larger state space. Firstly, it solves the problem of inefficiency of reinforcement learning if a given problem’s state space is increased and there is a lack of prior information on the environment. Secondly, RBF network as weight updating rule, reward shaping can give an additional feedback to the agent in some intermediate states, which will help to guide the agent towards the goal state in a more controlled fashion. Meanwhile, with the process of Q-learning, it is accessible to the underlying dynamic knowledge, instead of the need of background knowledge of an upper level RBF network. Thirdly, it improves the learning efficiency by incorporating the greedy exploitation strategy to train the neural network, which has been testified by the experimental results.     

A real time learning algorithm for recurrent analog neural networks

A new learning algorithm is described for a general class of recurrent analog neural networks which ultimately settle down to a steady state. Recently, Pineda (Pineda 1987; Almeida 1987; Ikeda et al. 1988) has introduced a learning rule for the recurrent net in which the connection weights are adjusted so that the distance between the stable outputs of the current system and the desired outputs will be maximally decreased. In this method, many cycles are needed in order to get a target system. In each cycle, the recurrent net is run until it reaches a stable state. After that, the weight change is calculated by using a linearized recurrent net which receives the current error of the system as a bias input. In the new algorithm the weights are changed so that the total error of neuron outputs over the entire trajectory is minimized. The weights are adjusted in real time when the network is running. In this method, the trajectory to the target system can be controlled, whereas Pineda's algorithm only controls the position of the fixed point. The relation to the back propagation method (Hinton et al. 1986) is also discussed.     

Spiking neural networks with different reinforcement learning (RL) schemes in a multiagent setting

This paper investigates the effectiveness of spiking agents when trained with reinforcement learning (RL) in a challenging multiagent task. In particular, it explores learning through reward-modulated spike-timing dependent plasticity (STDP) and compares it to reinforcement of stochastic synaptic transmission in the general-sum game of the Iterated Prisoner's Dilemma (IPD). More specifically, a computational model is developed where we implement two spiking neural networks as two "selfish" agents learning simultaneously but independently, competing in the IPD game. The purpose of our system (or collective) is to maximise its accumulated reward in the presence of reward-driven competing agents within the collective. This can only be achieved when the agents engage in a behaviour of mutual cooperation during the IPD. Previously, we successfully applied reinforcement of stochastic synaptic transmission to the IPD game. The current study utilises reward-modulated STDP with eligibility trace and results show that the system managed to exhibit the desired behaviour by establishing mutual cooperation between the agents. It is noted that the cooperative outcome was attained after a relatively short learning period which enhanced the accumulation of reward by the system. As in our previous implementation, the successful application of the learning algorithm to the IPD becomes possible only after we extended it with additional global reinforcement signals in order to enhance competition at the neuronal level. Moreover it is also shown that learning is enhanced (as indicated by an increased IPD cooperative outcome) through: (i) strong memory for each agent (regulated by a high eligibility trace time constant) and (ii) firing irregularity produced by equipping the agents' LIF neurons with a partial somatic reset mechanism.     

Biologically plausible learning in neural networks: a lesson from bacterial chemotaxis

Learning processes in the brain are usually associated with plastic changes made to optimize the strength of connections between neurons. Although many details related to biophysical mechanisms of synaptic plasticity have been discovered, it is unclear how the concurrent performance of adaptive modifications in a huge number of spatial locations is organized to minimize a given objective function. Since direct experimental observation of even a relatively small subset of such changes is not feasible, computational modeling is an indispensable investigation tool for solving this problem. However, the conventional method of error back-propagation (EBP) employed for optimizing synaptic weights in artificial neural networks is not biologically plausible. This study based on computational experiments demonstrated that such optimization can be performed rather efficiently using the same general method that bacteria employ for moving closer to an attractant or away from a repellent. With regard to neural network optimization, this method consists of regulating the probability of an abrupt change in the direction of synaptic weight modification according to the temporal gradient of the objective function. Neural networks utilizing this method (regulation of modification probability, RMP) can be viewed as analogous to swimming in the multidimensional space of their parameters in the flow of biochemical agents carrying information about the optimality criterion. The efficiency of RMP is comparable to that of EBP, while RMP has several important advantages. Since the biological plausibility of RMP is beyond a reasonable doubt, the RMP concept provides a constructive framework for the experimental analysis of learning in natural neural networks.