Stability analysis of a self-organizing neural network with feedforward and feedback dynamics

We present a new method of analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We are able to show the conditions under which the solutions of such a system are bounded being less restrictive than with the K-monotone theory, singular perturbation theory, or those based on supervised synaptic learning. We prove the existence and the uniqueness of the equilibrium. A strict Lyapunov function for the flow of a competitive neural system with different time scales is given and based on it we are able to prove the global exponential stability of the equilibrium point.

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of the designed network be stable. In this paper, the passivity-based approach is used to derive stability conditions for dynamic neural networks with different time-scales. Several stability properties, such as passivity, asymptotic stability, input-to-state stability and bounded input bounded output stability, are guaranteed in certain senses. Numerical examples are also given to demonstrate the effectiveness of the theoretical results.

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of the designed networks are stable. In this paper, the passivity-based approach is used to derive stability conditions for dynamic neural networks with different time-scales. Several stability properties, such as passivity, asymptotic stability, input-to-state stability and bounded input bounded output stability, are guaranteed in certain senses. A numerical example is also given to demonstrate the effectiveness of the theoretical results.

This paper is concerned with stability analysis for a class of dynamical neural networks with distributed delays. The M-matrix theory and new analysis technique are used to obtain new sufficient conditions for the existence, uniqueness and global stability of the equilibrium point of dynamical neural networks with distributed delays. The importance of the new stability criteria in the design and application of dynamical neural networks with distributed delays is due to the fact that they can handle the case when the non-delayed terms can not dominate the delayed terms. The effectiveness of the obtained theoretical results are illustrated by numerical examples.

A stable discrete time tracking control approach based on dynamic inversion using dynamic neural networks (DNNs) is developed in the paper for robotic manipulators with unknown dynamics nonlinearities. Two novel design technologies-dynamic inversion constructed by DNNs and the NN variable structure control-are used for adaptive tracking controller design. The robot control law is composed of the dynamic inversion of the DNN system, adaptive compensation and the NN variable structure control (VSC) components. The developed control scheme guarantees the global stability and tracking error convergence of the NN control system. Finally, the control performance of the proposed control approach is illustrated through the comparison studies with robot tracking control approach using static NNs.

Recurrent neural networks unlike feed-forward networks are able to process inputs with time context. The key role in this process is played by the dynamics of the network, which transforms input data to the recurrent layer states. Several authors have described and analyzed dynamics of small sized recurrent neural networks with two or three hidden units. In our work we introduce techniques that allow to visualize and analyze the dynamics of large recurrent neural networks with dozens units, reveal both stable and unstable points (attractors and saddle points), which are important to understand the principles of successful task processing. As a practical example of this approach, dynamics of the simple recurrent network trained by two different training algorithms on context-free language anbnwas studied.

Global stability analysis of competitive neural networks with mixed time-varying delays and discontinuous neuron activations

We present new methods of analyzing the dynamics of a competitive neural system with different time scales: the K-monotone system theory developed by Kamke (1932) as a global analysis techniques, and the theory of singular perturbation as a local analysis method.

Thyroid nodules with a predominant follicular structure are often diagnosed as indeterminate at fine-needle aspiration biopsy (FNAB). We studied 453 patients with a thyroid nodule diagnosed as indeterminate at FNAB by using a feed-forward artificial neural network (ANN) analysis to integrate cytologic and clinical data, with the goal of subgrouping patients into a high-risk and in a low-risk category. Three hundred seventy-one patients were used to train the network and 82 patients were used to validate the model. The cytologic smears were blindly reviewed and classified in a high-risk and a low-risk subgroup on the basis of standard criteria. Neural network analysis subdivided the 371 lesions of the first series into a high-risk group (cancer rate of approximately 33% at histology) and a low-risk group (cancer rate of 3%). Only cytologic parameters contributed to this classification. Analysis of the receiver operating characteristic (ROC) curves demonstrated that the ANN model discriminated with higher sensitivity and specificity between benign and malignant nodules compared to standard cytologic criteria (p < 0.001). This value did not show degradation when ANN predictions were applied to the validation series of 82 nodules. In conclusion, neural network analysis of cytologic data may be a useful tool to refine the risk of cancer in patients with lesions diagnosed as indeterminate by FNAB.

With the ubiquity of complex networks in domains as diverse as social network analysis, recommender systems and epidemiology, improvements in link predictions have a potential for far-reaching impact. In machine learning, a well-known approach to improve classification performance is to combine several methods in an ensemble. It is also well established that, diversity or complementarity of the classifiers to be combined, is a prerequisite for a potential performance improvement of the formed ensemble. In this work, we combine link prediction heuristics (e.g. Common Neighbour, Adamic-Adar etc.), with static graph neural networks, discrete dynamic graph neural networks, and continuous dynamic graph neural networks. We analyze the importance of each of the methods and how complementary they are with respect to each other. We also use greedy searches to select better subsets of methods to combine and train the ensemble in a roll-forward manner to make it adapt to changes in the dynamic network over time. In the conducted experiments on a number of challenging link prediction tasks, the ensemble from the greedy search and the roll-forward ensemble shows on average a 55% and 61% improvement respectively, over the best single method.

The dynamical behaviour of neural networks consisting of excitatory and inhibitory neuron population, influence of noise on their function and dynamics, and stochastic modelling of memory search are considered. The memory search based on the input-output interrelations in a network, is determined by the transitions between different stable states of a system. The transition probabilities between the neural network attractors are calculated using the algorithm based on the path integral method. In this work we study the processes of self-organization in neural networks which appear both in spatially homogeneous and heterogeneous structures of synaptic connections between neurons. Such self-organization arises due to the spatial and temporal character of nonlinear interaction between elements. The proposed scheme of network structural organization can provide generation of stable rhythmic activity.

Synaptic dynamics: Linear model and adaptation algorithm

One of the difficulties encountered in the application of reinforcement learning methods to real-world problem is the generalization of large-scale or continuous state space. In order to solve the curse of dimensionality problem caused by discretizing continuous state space, a kind of Q-learning method for continuous state space based on a dynamic Elman neural network was proposed in this paper. The inputs and the output of Elman network are the system state-action pair and the corresponding Q-value. That is, Elman network is used to estimate the Q-value of state-action pair on-line. Eligibility trace for connecting weights is introduced by borrowing ideas from the eligibility trace mechanism of state in temporal difference algorithm to improve the learning speed of neural network. Computer simulations on mountain car control illustrate the performance and applicability of the proposed Q-learning scheme.

This paper presents a novel Dynamic Self-Organised Multilayer Neural Network that can be used for prediction of noisy time series data. The proposed technique is based on the Immune Algorithm for financial time series prediction; combining the properties of both recurrent and self-organised neural networks. The network is derived to ensure that a unique equilibrium state can be achieved to overcome the known stability and convergence problems. Extensive simulations for multi-step prediction in stationary and non-stationary time series were performed. The resulting projection made by the proposed network shows substantial profits on financial historical signals when compared to other neural network approaches. These simulations have suggested that dynamic immunology-based self-organised neural networks have a better ability to capture the chaotic movement in financial signals.

Several mathematical approaches to studying analytically the dynamics of neural networks rely on mean-field approximations, which are rigorously applicable only to networks of infinite size. However, all existing real biological networks have finite size, and many of them, such as microscopic circuits in invertebrates, are composed only of a few tens of neurons. Thus, it is important to be able to extend to small-size networks our ability to study analytically neural dynamics. Analytical solutions of the dynamics of small-size neural networks have remained elusive for many decades, because the powerful methods of statistical analysis, such as the central limit theorem and the law of large numbers, do not apply to small networks. In this article, we critically review recent progress on the study of the dynamics of small networks composed of binary neurons. In particular, we review the mathematical techniques we developed for studying the bifurcations of the network dynamics, the dualism between neural activity and membrane potentials, cross-neuron correlations, and pattern storage in stochastic networks. Then, we compare our results with existing mathematical techniques for studying networks composed of a finite number of neurons. Finally, we highlight key challenges that remain open, future directions for further progress, and possible implications of our results for neuroscience.