hop field
DESCRIPTION
neural networkTRANSCRIPT
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