Energy Relaxation for Hopfield Network With the New Learning Rule

Abstract

Abstract.In this paper, the time for energy relaxation for LittleHopfield neural network using the new activation rule is shown to be better than the relaxation time using Hebbian learning. However, this should be so given the characteristics of the activation function and show through computer simulations that this is indeed so. In this paper, it has been proven that the new learning rule has a higher capacity than Hebb rule by computer simulations. section 3; logic programming on a neural network focused on the Hopfield model is described. In section 4, Hebb and the new learning rule are been discussed. This is foIIowed by section 5, where fitness landscapes are discussed. In section 6, theory implementation of the both learning rules are been discussed. Meanwhile, section 7 contains discussion regarding the results obtained from computer simulations. Finally concluding remarks regarding this work occupy the last section.

Enhanced Hopfield Network for Pattern Satisfiability Optimization

“…The Hyperbolic tangent activation function is written as follows: function is the broader output space than the linear activation function. The output range is -1 to 1, similar to the conventional sig moid function [6,10]. The scaled output or bounded properties will assist the network to produce good outputs.…”

“…The demarcation fo r unit I's activation, i a are given as follows: h [6,27]. The connection model can be generalized to include higher order connection.…”

“…Boolean Sat isfiability (SAT) can be demarcated as the decision problem since the solution will yield either -yes‖ or -no‖ response, by implement ing the Boolean formula [12,6]. Hence, SAT involves definitive task of searching truth assignments that satisfies a Boolean formu la [7].…”

“…Hence, recurrent neural network are essentially dynamical systems that feedback signals to themselves [6]. Then, the Hopfield neural network is a simple recurrent network which can work as an efficient associative memory, and it can store certain memo ries in a manner rather analogous to the brain [3,11].…”

Hopfield neural network in agent based modeling

“…Compared to neural network which is a black box model, logic program is easier to understand, easier to verify and also easier to change. 6 The assimilation between both paradigm (Logic programming and Hopfield network) was presented by Wan Abdullah and revolve around propositional Horn clauses. 7,8 Gadi Pinkas and Wan Abdullah, 7,9 proposed a bi-directional mapping between logic and energy function in a symmetric neural network.…”