An Overview of the Stability Analysis of Recurrent Neural Networks With Multiple Equilibria

Coexistence of Cyclic Sequential Pattern Recognition and Associative Memory in Neural Networks by Attractor Mechanisms

Neural networks are developed to model the behavior of the brain. One crucial question in this field pertains to when and how a neural network can memorize a given set of patterns. There are two mechanisms to store information: associative memory and sequential pattern recognition. In the case of associative memory, the neural network operates with dynamical attractors that are point attractors, each corresponding to one of the patterns to be stored within the network. In contrast, sequential pattern recognition involves the network memorizing a set of patterns and subsequently retrieving them in a specific order over time. From a dynamical perspective, this corresponds to the presence of a continuous attractor or a cyclic attractor composed of the sequence of patterns stored within the network in a given order. Evidence suggests that the brain is capable of simultaneously performing both associative memory and sequential pattern recognition. Therefore, these types of attractors coexist within the neural network, signifying that some patterns are stored as point attractors, while others are stored as continuous or cyclic attractors. This article investigates the coexistence of cyclic attractors and continuous or point attractors in certain nonlinear neural networks, enabling the simultaneous emergence of various memory mechanisms. By selectively grouping neurons, conditions are established for the existence of cyclic attractors, continuous attractors, and point attractors, respectively. Furthermore, each attractor is explicitly represented, and a competitive dynamic emerges among these coexisting attractors, primarily regulated by adjustments to external inputs.

Multiple Mittag-Leffler Stability of Almost Periodic Solutions for Fractional-Order Delayed Neural Networks: Distributed Optimization Approach

This article proposes new theoretical results on the multiple Mittag-Leffler stability of almost periodic solutions (APOs) for fractional-order delayed neural networks (FDNNs) with nonlinear and nonmonotonic activation functions. Profited from the superior geometrical construction of activation function, the considered FDNNs have multiple APOs with local Mittag-Leffler stability under given algebraic inequality conditions. To solve the algebraic inequality conditions, especially in high-dimensional cases, a distributed optimization (DOP) model and a corresponding neurodynamic solving approach are employed. The conclusions in this article generalize the multiple stability of integer- or fractional-order NNs. Besides, the consideration of the DOP approach can ameliorate the excessive consumption of computational resources when utilizing the LMI toolbox to deal with high-dimensional complex NNs. Finally, a simulation example is presented to confirm the accuracy of the theoretical conclusions obtained, and an experimental example of associative memories is shown.

Stability Analysis of Recurrent Neural Networks With Time-Varying Delay Based on a Flexible Negative-Determination Quadratic Function Method

This brief investigates the stability problem of recurrent neural networks (RNNs) with time-varying delay. First, by introducing some flexibility factors, a flexible negative-determination quadratic function method is proposed, which contains some existing methods and has less conservatism. Second, some integral inequalities and the flexible negative-determination quadratic function method are used to give an accurate upper bound of the Lyapunov-Krasovskii functional (LKF) derivative. As a result, a less conservative stability criterion of delayed RNNs is derived, whose effectiveness and superiority are finally illustrated through two numerical examples.

On convergence properties of the brain-state-in-a-convex-domain

Convergence in the presence of multiple equilibrium points is one of the most fundamental dynamical properties of a neural network (NN). Goal of the paper is to investigate convergence for the classic Brain-State-in-a-Box (BSB) NN model and some of its relevant generalizations named Brain-State-in-a-Convex-Body (BSCB). In particular, BSCB is a class of discrete-time NNs obtained by projecting a linear system onto a convex body of Rn. The main result in the paper is that the BSCB is convergent when the matrix of the linear system is symmetric and positive semidefinite or, otherwise, it is symmetric and the step size does not exceed a given bound depending only on the minimum eigenvalue of the matrix. This result generalizes previous results in the literature for BSB and BSCB and it gives a solid foundation for the use of BSCB as a content addressable memory (CAM). The result is proved via Lyapunov method and LaSalle's Invariance Principle for discrete-time systems and by using some fundamental inequalities enjoyed by the projection operator onto convex sets as Bourbaki-Cheney-Goldstein inequality.

Stability Analysis of Recurrent Neural Networks With Time-Varying Delay by Flexible Terminal Interpolation Method

This brief studies the stability problem of recurrent neural networks with time-varying delay. Based on one tunable parameter α , a flexible terminal interpolation method is proposed to change the interval with fixed terminals as 2k+1-3 ones with flexible terminals. Associated with the flexible subintervals, a novel Lyapunov-Krasovskii functional with more delay information is constructed. In order to estimate the Lyapunov-Krasovskii functional, a quadratic reciprocally convex inequality is proposed, which covers some existing ones as its special cases. Based on these ingredients, a new stability criterion is derived in the form of linear matrix inequalities. A comprehensive comparison of results is given to illustrate the newly proposed stability criterion.

A PDCA Model for Disinfection Supply Rooms in the Context of Artificial Intelligence to Reduce the Incidence of Adverse Events and Improve the Disinfection Compliance Rate

As an important section for controlling hospital infection, the main responsibility of the sterilization supply room is to clean, disinfect, sterilize, store, and distribute all medical devices that need to be reused in the hospital, and the quality of its work is closely related to the normal work of the hospital. Disinfection and supply department is the premise and foundation of the hospital department, mainly responsible for the recovery, cleaning, disinfection, sterilization, storage, and distribution of medical devices. The cleaning and disinfection work is characterized by strong technicality and high requirements, and the work effect is directly related to the safety of patients' lives and the occurrence of hospital infections. Therefore, there is an urgent need for a scientific and efficient management mode to be applied to the work of the supply room. The traditional management mode has some drawbacks, which affects the actual work of the hospital. Disinfection and supply rooms are an important part of hospital infection control and an important department to ensure the quality of health care. An effective management mode can not only improve the efficiency but also the overall quality of work, and PDCA (plan-do-check action cycle) as an advanced management mode can effectively improve the quality of management. This study investigates the effect of PDCA cycle management based on artificial intelligence algorithms in the nursing management of sterile supply rooms, and the experimental results show that the algorithm model can effectively reduce the incidence of adverse events and improve the rate of sterilization standards, which has certain practical significance.

Deep learning for prediction of depressive symptoms in a large textual dataset

Depression is a common illness worldwide with potentially severe implications. Early identification of depressive symptoms is a crucial first step towards assessment, intervention, and relapse prevention. With an increase in data sets with relevance for depression, and the advancement of machine learning, there is a potential to develop intelligent systems to detect symptoms of depression in written material. This work proposes an efficient approach using Long Short-Term Memory (LSTM)-based Recurrent Neural Network (RNN) to identify texts describing self-perceived symptoms of depression. The approach is applied on a large dataset from a public online information channel for young people in Norway. The dataset consists of youth’s own text-based questions on this information channel. Features are then provided from a one-hot process on robust features extracted from the reflection of possible symptoms of depression pre-defined by medical and psychological experts. The features are better than conventional approaches, which are mostly based on the word frequencies (i.e., some topmost frequent words are chosen as features from the whole text dataset and applied to model the underlying events in any text message) rather than symptoms. Then, a deep learning approach is applied (i.e., RNN) to train the time-sequential features discriminating texts describing depression symptoms from posts with no such descriptions (non-depression posts). Finally, the trained RNN is used to automatically predict depression posts. The system is compared against conventional approaches where it achieved superior performance than others. The linear discriminant space clearly reveals the robustness of the features by generating better clustering than other traditional features. Besides, since the features are based on the possible symptoms of depression, the system may generate meaningful explanations of the decision from machine learning models using an explainable Artificial Intelligence (XAI) algorithm called Local Interpretable Model-Agnostic Explanations (LIME). The proposed depression symptom feature-based approach shows superior performance compared to the traditional general word frequency-based approaches where frequency of the features gets more importance than the specific symptoms of depression. Although the proposed approach is applied on a Norwegian dataset, a similar robust approach can be applied on other depression datasets developed in other languages with proper annotations and symptom-based feature extraction. Thus, the depression prediction approach can be adopted to contribute to develop better mental health care technologies such as intelligent chatbots.