Presents a recurrent neural network for solving the Sylvester equation with time-varying coefficient matrices. The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation. Theoretical results of convergence and sensitivity analysis are presented to ...

A procedure that defines values of constraint weight parameters of single-layer relaxation-type recurrent neural networks for establishing stability of all solutions for an optimization problem is introduced. Application to the Traveling Salesman optimization problem, using the discrete dynamics Hopfield network as the recurrent neural network algorithm, is shown to illustrate the procedure. Si...

A stationary state replica analysis for a dual neural network model that interpolates between a fully recurrent symmetric attractor network and a strictly feed-forward layered network, studied by Coolen and Viana, is extended in this work to account for finite dilution of the recurrent Hebbian interactions between binary Ising units within each layer. Gradual dilution is found to suppress part ...

A novel variant of a familiar recurrent network learning algorithm is described. This algorithm is capable of shaping the behavior of an arbitrary recurrent network as it runs, and it is speciically designed to execute eeciently on serial machines.

We developed a method called Time-Slicing [1] for the analysis of the speech signal. It enables a neural network to recognize connected speech as it comes, without having to fit the input signal into a fixed time-format, nor label or segment it phoneme by phoneme. The neural network produces an immediate hypothesis of the recognized phoneme and its size is small enough to run even on a PC. To i...

We have the following dichotomy result. Theorem 2. The following are equivalent: (1) X is transient; (2) X is not recurrent; (3) U0(B(0 � �)) < ∞ for all � > 0. Theorem 2 has the following important dichotomous implication: Either X is transient, or X is recurrent [and not both]. The proof relies on a convenient series of equivalences. Proposition 3. The following are equivalent: (1) sup�∈R� U0...

The paper deals with a discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the considered network is a locally recurrent globally feedforward. In the paper, conditions for global stability of the neural network considered are derived using the Lyapunov’s second method.

In this work, we investigate the memory capability of recurrent neural networks (RNNs), where this capability is defined as a function that maps an element in a sequence to the current output. We first analyze the system function of a recurrent neural network (RNN) cell, and provide analytical results for three RNNs. They are the simple recurrent neural network (SRN), the long short-term memory...