Energy Relaxation For Hopfield Network With The New Learning Rule.

In this paper, the time for energy relaxation for Little Hopfield neural network using the new activation rule is shown to be better than the relaxation time using Hebbian learning

Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network

The restricted Maximum k-Satisfiability MAX- kSAT is an enhanced Boolean satisfiability counterpart that has attracted numerous amount of research. Genetic algorithm has been the prominent optimization heuristic algorithm to solve constraint optimization problem. The core motivation of this paper is to introduce Hopfield network incorporated with genetic algorithm in solving MAX-kSAT problem. Genetic algorithm will be integrated with Hopfield network as a single network. The proposed method will be compared with the conventional Hopfield network. The results demonstrate that Hopfield network with genetic algorithm outperforms conventional Hopfield networks. Furthermore, the outcome had provided a solid evidence of the robustness of our proposed algorithms to be used in other satisfiability problem

Robust Artificial Immune System in the Hopfield network for Maximum k-Satisfiability

Artificial Immune System (AIS) algorithm is a novel and vibrant computational paradigm, enthused by the biological immune system. Over the last few years, the artificial immune system has been sprouting to solve numerous computational and combinatorial optimization problems. In this paper, we introduce the restricted MAX-kSAT as a constraint optimization problem that can be solved by a robust computational technique. Hence, we will implement the artificial immune system algorithm incorporated with the Hopfield neural network to solve the restricted MAX-kSAT problem. The proposed paradigm will be compared with the traditional method, Brute force search algorithm integrated with Hopfield neural network. The results demonstrate that the artificial immune system integrated with Hopfield network outperforms the conventional Hopfield network in solving restricted MAX-kSAT. All in all, the result has provided a concrete evidence of the effectiveness of our proposed paradigm to be applied in other constraint optimization problem. The work presented here has many profound implications for future studies to counter the variety of satisfiability problem

Discrete hopfield neural network in restricted maximum k-satisfiability logic programming

Maximum k-Satisfiability (MAX-kSAT) consists of the most consistent interpretation that generate the maximum number of satisfied clauses. MAX-kSAT is an important logic representation in logic programming since not all combinatorial problem is satisfiable in nature. This paper presents Hopfield Neural Network based on MAX-kSAT logical rule. Learning of Hopfield Neural Network will be integrated with Wan Abdullah method and Sathasivam relaxation method to obtain the correct final state of the neurons. The computer simulation shows that MAX-kSAT can be embedded optimally in Hopfield Neural Network

What does the Landscape of a Hopfield Associative Memory Look Like?

. We apply evolutionary computations to the Hopfield's neural network model of associative memory. In the model, some of the appropriate configurations of synaptic weights give the network a function of associative memory. One of our goals is to obtain the distribution of these configurations in the synaptic weight space. In other words, our aim is to learn a geometry of a fitness landscape defined on the space. For the purpose, we use evolutionary walks to explore the fitness landscape in this paper. 1 INTRODUCTION Associative memory is a dynamical system which has a number of stable states with a domain of attraction around them (Koml'os and Paturi 1988). If the system starts at any state in the domain, it will converge to the stable state. Hopfield (1982) proposed a fully connected neural network model of associative memory in which information is stored by being distributed among neurons. The dynamical behavior of its neuron states strongly depends on synaptic strengths between ne..