Passivity Analysis of Dynamic Neural Networks with Different Time-Scales

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.

This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.

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.

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.

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.

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.

In this paper a Dynamic Neural Network has been designed to effectively estimate the states of a nonlinear single input plant. The Unscented Kalman Filter algorithm has been used to train the weights of the Dynamic Neural Network. No a priori bounds of the weights and errors are required. The non linear plant and the Dynamic Neural Network model have been simulated by the same input to illustrate the validity of the theoretical results.

Biological modeling the undulatory locomotion of C. elegans using dynamic neural network approach

Dynamic neural networks can greatly reduce computation redundancy without compromising accuracy by adapting their structures based on the input. In this paper, we explore the robustness of dynamic neural networks against energy-oriented attacks targeted at reducing their efficiency. Specifically, we attack dynamic models with our novel algorithm GradMDM. GradMDM is a technique that adjusts the direction and the magnitude of the gradients to effectively find a small perturbation for each input, that will activate more computational units of dynamic models during inference. We evaluate GradMDM on multiple datasets and dynamic models, where it outperforms previous energy-oriented attack techniques, significantly increasing computation complexity while reducing the perceptibility of the perturbations https://github.com/lingengfoo/GradMDM.

The article is devoted to the problem of optimization of search request ranking algorithms in the digital information retrieval system. The algorithm of functioning of the neural network ranking unit based on Hopfield neural network is built. The ability to generate a ranked list of pages found as a result of the request in the digital information retrieval system can be provided by solving two problems of integer optimization: the problem of assignment of combinatorial sets of criteria for assessing the relevance of web page search and the problem of sorting of numbers—relevance values. The architecture of the neural network model based on the dynamic Hopfield neural network with binary output function designed for combinatorial optimization of the final list of documents found in the digital information retrieval system was synthesized. Promising variants of neural network models with binary output function of neurons for synthesis of the optimal evaluation plan with a combinatorial set of criteria by solving the problem of assignment were built. It has been proven that the built models differ in the rules for determining the coefficients of synaptic connections and external shifts; each of the created rules can be used independently or in different combinations with one another. In the course of analytical research, it was found that the optimization formulation of the problem of sorting of relevance values of search pages is identical to the problem of assignment of combinatorial groups of evaluation criteria provided that the elements of the performance matrix of the latter are defined as linear combinations of relevance values.

This paper presents an online modeling and control strategy for a class of linearizable nonlinear systems with unknown parameters and nonlinearities. A dynamic neural network (DNN) is utilized for modeling of nonlinear systems in their equivalent feedback linearized form. Lyapunov techniques are used to derive the adaptation rules for training the DNN's weight matrices. An adaptive state feedback stabilizing control is developed based on the equivalent DNN model of the systems. An observer is also designed to estimate the states of the DNN model of the system. Subsequently, an adaptive output feedback stabilizing control law is derived for unknown nonlinear systems, using their equivalent DNN model, with guaranteed closed-loop stability. Simulation results show the effectiveness of the proposed technique.

To identify online a quite general class of nonlinear systems, this paper proposes a new stable learning law of the dynamic multilayer neural networks (DMNN). A Lyapunov-like analysis is used to derive this stable learning procedure for the hidden layer as well as for the output layer. An algebraic Riccati equation is considered to construct a bound for the identification error. The suggested learning algorithm is similar to the well-known backpropagation rule of the static multilayer perceptrons but with an additional term which assure the property of global asymptotic stability for the identification error. Two numerical examples illustrate the effectiveness of the suggested new learning laws.

In this paper the design of a dynamic neural network (DNN) for modeling and control of a class of minimum-phase controllable nonlinear systems is considered. The dynamic neural network acts as a generic model of the system, which is then used in the derivation of the control signal. The training of the network is based oil a novel scheme that arranges the outputs of the hidden layer of the DNN into a set of orthogonal basis functions. This allows for the derivation of a stable rule for the training of the DNN's weights and does not require random initialization of the weights.

We present a new method of analyzing the dynamics of self-organizing neural networks 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.