Hopfield Neural Network

Presented by:V.Bharanigha 10MEPE06Hopfield Neural NetworkFEEDBACK/RECURRENT NETWORKOne output vector is assigned to every input vectorReturns back the output to the input- iterative processTypes: 1)Simulated annealing 2)Boltzmann machine 3)Hopfield net

TYPES OF HOPFIELD NETDiscrete hopfield net

Continuous hopfield netDISCRETE HOPFIELD NETJohn Hopfield (1982)Very simple network

Solution for optimization problems

Have n neurons networked with each otherHOPFIELD NETWORKAn interconnected networkEvery node is connected to every other nodeIf the weight is 0, the connection doesnt matterTo use the network, set the values of the nodes and let the nodes adjust their values according to the weights.All the diagonal elements of weight matrix are zero Wij=Wji Wii=0NEURONS IN HOPFIELD NETWORKThe neurons are binary unitsThey are either active (1) or passive(0)Alternatively + or The network contains N neuronsThe state of the network is described as a vector of 0s and 1s

ARCHITECTUREThe network is fully interconnectedx input and y output neuronsThe connections are bidirectional and symmetric

The setting of weights depends on the application

ARCHITECHTURE OF HOPFIELD NET(DISCRETE)

TRAINING ALGORITHMApplied for both binary and bipolar vector patternsWeight of the matrix is determined by HEBBs ruleStores the set of binary input patterns s(p) for p=1,P where s(p)={s1(p),si(p),sn(p)} Contd..,The weight matrix is given by,For binary input patterns,

For bipolar input patterns,

for ij and wii=0

for ij and wii=0APPLICATION ALGORITHMStep 1: Initialize weights to store pattern using hebbs ruleStep 2: For each input vector x, repeat steps 3 to 7Step 3; Set initial activations of the net equal to the external input vector x,yi=xi (i=1,n) Step 4:Perform steps 5 to 7 for each unit yi

Step 5:Compute the net input,

Step 6:Determine output signal,

Step 7:Broadcast the value of yi to all other unitsStep 8:test for convergenceThe value of threshold i is taken to be zeroEach unit is randomly updated at same average rateANALYSIS Storage capacity

Accuracy, for bipolar patterns for binary patterns

ENERGY CAPACITYEnergy function

Change in energy due to change in energy of neuron,

If yi is positive , E