This paper demonstrates that there is an exponentially stable unique equilibrium state in a Hopfield-type neural network that is subject to quite large impulses that are not too frequent. The activation functions are assumed to be globally Lipschitz continuous and unbounded. The analysis exploits an homeomorphic mapping and an appropriate Lyapunov function, and also either a geometric–arithmetic mean inequality or a Young inequality, to derive a family of easily verifiable sufficient conditions for convergence to the unique globally stable equilibrium state. These sufficiency conditions, in the norm ∥·∥ p where p  ⩾ 1, include those governing the network parameters and the impulse magnitude and frequency.

Exponential stability in Hopfield-type neural networks with impulses

Generalized Hopfield networks for associative memories with multi-valued stable states

The analog-to-digital converter (ADC) is a principal component in every data acquisition system. Unfortunately, modern ADCs tradeoff speed, power, and accuracy. In this paper, novel neuroinspired approaches are used to design a smart ADC that could be trained in real time for general purpose applications and break through conventional ADC limitations. Motivated by artificial intelligent learning algorithms and neural network architectures, the proposed ADC integrates emerging memristor technology with CMOS. We design a trainable four-bit ADC with a memristive neural network that implements the online gradient descent algorithm. This supervised machine learning algorithm fits multiple application specifications such as full-scale voltage ranges and sampling frequencies. Theoretical analysis, as well as simulation results, demonstrate highly powerful collective properties, including reconfiguration, mismatch self-calibration, adaptation to dynamic voltage and frequency scaling, noise tolerance, and power consumption optimization. The proposed ADC achieves 8.25 fJ/conv FOM, 3.7 ENOB, 0.4 LSB INL, and 0.5 LSB DNL. These promising properties make it a leading contender for general purpose and emerging data driven applications.

Breaking Through the Speed-Power-Accuracy Tradeoff in ADCs Using a Memristive Neuromorphic Architecture

In this paper we discuss the design of a cellular neural network (CNN) to solve a class of optimization problems of importance for communication networks The CNN optimization capabilities are exploited to implement an efficient cell scheduling algorithm in a fast packet switching fabric The neural-based switching fabric maximizes the cell throughput and, at the same time, it is able to meet a variety of quality of service (QoS) requirements by optimizing a suitable function of the switching delay and priority of the cells We also show that the CNN approach has advantages with respect to that based on Hopfield neural networks (HNNs) to solve the considered class of optimization problems In particular, we exploit existing techniques to design CNNs with a prescribed set of stable binary equilibrium points as a basic tool to suppress spurious responses and, hence to optimize the neural switching fabric performance

Cellular neural network approach to a class of communication problems

In this paper, a novel constructive-optimizer neural network (CONN) is proposed for the traveling salesman problem (TSP). CONN uses a feedback structure similar to Hopfield-type neural networks and a competitive training algorithm similar to the Kohonen-type self-organizing maps (K-SOMs). Consequently, CONN is composed of a constructive part, which grows the tour and an optimizer part to optimize it. In the training algorithm, an initial tour is created first and introduced to CONN. Then, it is trained in the constructive phase for adding a number of cities to the tour. Next, the training algorithm switches to the optimizer phase for optimizing the current tour by displacing the tour cities. After convergence in this phase, the training algorithm switches to the constructive phase anew and is continued until all cities are added to the tour. Furthermore, we investigate a relationship between the number of TSP cities and the number of cities to be added in each constructive phase. CONN was tested on nine sets of benchmark TSPs from TSPLIB to demonstrate its performance and efficiency. It performed better than several typical neural networks (NNs), including KNIES_TSP_Local, KNIES_TSP_Global, Budinich's SOM, Co-adaptive net, and multivalued Hopfield network as wall as computationally comparable variants of the simulated annealing algorithm, in terms of both CPU time and accuracy. Furthermore, CONN converged considerably faster than expanding SOM and evolved integrated SOM and generated shorter tours compared to KNIES_DECOMPOSE. Although CONN is not yet comparable in terms of accuracy with some sophisticated computationally intensive algorithms, it converges significantly faster than they do. Generally speaking, CONN provides the best compromise between CPU time and accuracy among currently reported NNs for TSP.

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A Novel Constructive-Optimizer Neural Network for the Traveling Salesman Problem

Due to the rugged energy function of the original Hopfield networks, the output is usually one local minimum in the energy function. An analysis on the locations of local minima in Hopfield networks is presented, and a modified network architecture to eliminate such local minima is described. In particular, another amplifier is introduced at the processor nodes to give correction terms. This modified Hopfield network has been successfully applied to the construction of analog-to-digital converters with optimal solutions. Experimental results on the voltage transfer characteristics of data converters are presented. >

B.W. Lee

Papers

Modified Hopfield neural networks for retrieving the optimal solution