Recurrent neural nets as dynamical Boolean systems with application to associative memory

Abstract

Discrete-time/discrete-state recurrent neural networks are analyzed from a dynamical Boolean systems point of view in order to devise new analytic and design methods for the class of both single and multilayer recurrent artificial neural networks. With the proposed dynamical Boolean systems analysis, we are able to formulate necessary and sufficient conditions for network stability which are more general than the well-known but restrictive conditions for the class of single layer networks: (1) symmetric weight matrix with (2) positive diagonal and (3) asynchronous update. In terms of design, we use a dynamical Boolean systems analysis to construct a high performance associative memory. With this Boolean memory, we can guarantee that all fundamental memories are stored, and also guarantee the size of the basin of attraction for each fundamental memory.

An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks

“…The dynamics of rather simple Boolean recurrent neural networks can implement an associative memory with bioinspired features [71], [72]. In the Hopfield framework, stable equilibria of the network that do not represent any valid configuration of the optimisation problem are referred to as spurious attractors .…”

Non-fragile finite-timel2−l∞state estimation for discrete-time Markov jump neural networks with unreliable communication links

“…Now, we will present a solution to ensure the non-fragile finite-time l 2 − l ∞ state estimator design problem for the augmented estimation error system (˜ ) based on Theorem 2. MSFTB with respect to (a 1 , a 2 , N, R, W) and satisfies a prescribed (11) i˜ (12) i˜ (13) i˜ (14) i * ˜ (22) i˜ (23) i˜ (24) …”

“…By the Schur complement, it follows from (38) that i = ⎡ ⎣ (11) i (12) i¯ (13) i * (22) i¯ (23) i * * ¯ (33)…”

“…The last several decades have witnessed a variety of applications for neural networks (NNs) in practical fields, such as associative memory [22,28], target tracking [5], image processing [27], pattern recognition [8,12] and so on. There are two aspects of studying such applications of NNs that attract researchers' attention: One is the information latching problem in NNs, which can lead to the occurrence of the jumping or switching between different neural network modes [10,16,30]; The other is the partly accessible, even or fully unavailable states of NNs.…”

Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay

“…Neural networks (NNs) have received considerable attention for their potential applications in many areas, such as image processing, pattern recognition, associative memories, solving certain optimization problems, and so on [1,2,3]. Since the switching speed of information processing and the inherent neuron communication is finite, time delays are always unavoidably existent in neural networks, and their existence may lead to instability or significantly deteriorated performances.…”