Energy Relaxation for Hopfield Network with the New Learning Rule

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. 2. THE LITTLE-HOPFIELD MODEL (3) which monotone decreases with the dynamics. (1) (2) _ '" '" (3) '" (2) (I) hi .... + L.L.JUk S/k + LJU Sj +J; i k j where " ....." denotes still higher orders, and an energy function can be written as foIIows: The Hopfield model [7,8] is a standard model for associative memory. The Little dynamics is asynchronous, with each neuron updating their state deterministically. The system consists of N formal neurons, each of which is described by an Ising variable [9] Si(t),(i = l,2, ....N) . Neurons then are bipolar, SiE{-l,1 }, obeying the dynamics Si ---? sgn(hi ) , where the field, hi = ·L.J&2)Vj + J?) , i and j running over all neurons j N, J;j2) is the synaptic strength from neuron j to neuron i, and -Ji is the threshold of neuron i. Restricting the connections to be symmetric and zero-diagonal J(2) = J('?) J~..2) =0 aIIows one to write a 'IJ JI' II ' Lyapunov or energy function, The two-connection model can be generalized to include higher order connections. This modifies the "field" to be