Stability Analysis for Higher Order Complex-Valued Hopfield Neural Network

2006 ◽  
pp. 608-615 ◽  
Author(s):  
Deepak Mishra ◽  
Arvind Tolambiya ◽  
Amit Shukla ◽  
Prem K. Kalra
Keyword(s):  
Neural Network ◽  
Stability Analysis ◽  
Hopfield Neural Network ◽  
Higher Order ◽  
Order Complex ◽  
Complex Valued

Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay

2017 ◽  
Vol 86 ◽  
pp. 42-53 ◽  
Author(s):  
G. Velmurugan ◽  
R. Rakkiyappan ◽  
V. Vembarasan ◽  
Jinde Cao ◽  
Ahmed Alsaedi
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Order Complex ◽  
Complex Valued

scholarly journals Random Satisfiability: A Higher-Order Logical Approach in Discrete Hopfield Neural Network

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Syed Anayet Karim ◽  
Nur Ezlin Zamri ◽  
Alyaa Alway ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Ahmad Izani Md Ismail ◽  
...  
Keyword(s):  
Neural Network ◽  
Hopfield Neural Network ◽  
Higher Order ◽  
Logical Approach

scholarly journals Novel Hopfield Neural Network Model with Election Algorithm for Random 3 Satisfiability

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1292
Author(s):  
Muna Mohammed Bazuhair ◽  
Siti Zulaikha Mohd Jamaludin ◽  
Nur Ezlin Zamri ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Mohd. Asyraf Mansor ◽  
...  
Keyword(s):  
Neural Network ◽  
Performance Metrics ◽  
Hopfield Neural Network ◽  
Higher Order ◽  
Research Field ◽  
Learning Phase ◽  
Logical Rule ◽  
Election Algorithm ◽  
Logical Rules ◽  
Retrieval Phase

One of the influential models in the artificial neural network (ANN) research field for addressing the issue of knowledge in the non-systematic logical rule is Random k Satisfiability. In this context, knowledge structure representation is also the potential application of Random k Satisfiability. Despite many attempts to represent logical rules in a non-systematic structure, previous studies have failed to consider higher-order logical rules. As the amount of information in the logical rule increases, the proposed network is unable to proceed to the retrieval phase, where the behavior of the Random Satisfiability can be observed. This study approaches these issues by proposing higher-order Random k Satisfiability for k ≤ 3 in the Hopfield Neural Network (HNN). In this regard, introducing the 3 Satisfiability logical rule to the existing network increases the synaptic weight dimensions in Lyapunov’s energy function and local field. In this study, we proposed an Election Algorithm (EA) to optimize the learning phase of HNN to compensate for the high computational complexity during the learning phase. This research extensively evaluates the proposed model using various performance metrics. The main findings of this research indicated the compatibility and performance of Random 3 Satisfiability logical representation during the learning and retrieval phase via EA with HNN in terms of error evaluations, energy analysis, similarity indices, and variability measures. The results also emphasized that the proposed Random 3 Satisfiability representation incorporates with EA in HNN is capable to optimize the learning and retrieval phase as compared to the conventional model, which deployed Exhaustive Search (ES).

Finite-time stability analysis of discrete-time fuzzy Hopfield neural network

2015 ◽  
Vol 159 ◽  
pp. 263-267 ◽  
Author(s):  
Jianjun Bai ◽  
Renquan Lu ◽  
Anke Xue ◽  
Qingshan She ◽  
Zhonghua Shi
Keyword(s):  
Neural Network ◽  
Stability Analysis ◽  
Discrete Time ◽  
Finite Time ◽  
Hopfield Neural Network ◽  
Time Stability ◽  
Finite Time Stability

Storage Capacity of Quaternion-Valued Hopfield Neural Networks with Dual Connections

2021 ◽  
pp. 1-15
Author(s):  
Masaki Kobayashi
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Stochastic Analysis ◽  
Storage Capacity ◽  
Hopfield Neural Network ◽  
Activation Function ◽  
Hopfield Neural Networks ◽  
Noise Tolerance ◽  
Complex Valued ◽  
Projection Rule

Abstract A complex-valued Hopfield neural network (CHNN) is a multistate Hopfield model. A quaternion-valued Hopfield neural network (QHNN) with a twin-multistate activation function was proposed to reduce the number of weight parameters of CHNN. Dual connections (DCs) are introduced to the QHNNs to improve the noise tolerance. The DCs take advantage of the noncommutativity of quaternions and consist of two weights between neurons. A QHNN with DCs provides much better noise tolerance than a CHNN. Although a CHNN and a QHNN with DCs have the samenumber of weight parameters, the storage capacity of projection rule for QHNNs with DCs is half of that for CHNNs and equals that of conventional QHNNs. The small storage capacity of QHNNs with DCs is caused by projection rule, not the architecture. In this work, the ebbian rule is introduced and proved by stochastic analysis that the storage capacity of a QHNN with DCs is 0.8 times as many as that of a CHNN.

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