]1)M0uCZ8N@bR+q?_mFHiBs ;uNp(Om&9%:C!D1;hKiZ>.\X9:Cd*_4@52$.&+0AMLWAt Lr2M@c88Z;A60[+]'0+7B#l3f[!obE>@,T;R'pd @EL>BE6&[S@F.EIl&Tgu?ZZm\Nqr=i_%_E(@O4;bGj8KY\hj$_h2]V*j*1t`^ l`15;2D["+=,5i\\P[L\;iI;nW%BGM'^`dWjg<<>LmrI+hQI ? ;8RfKEd [)iS!Bp30ET=ZuVXj+^u%6K>8RuBU!j2Rh$[7Kl3pX%XM0DB&Z@7W/cVr(dVL,gma ?L+g#km6f#s(n.\4:t4N)R;s2'[hsbGLta :@K<69du$2IuM>u/2#LUoKK]IS`#OY67(8;&Qkd%fHoAkUh4\p?EFr.LSUUe=T/NmNA*9]/6nfPE4_.@c_cSm]0pHt%bq3F8P9F+! ]#h#MEs.b?R?G8%m8YF+ "'YMaP?u$,p7p!//0.JnF((h;*#"-:>$Ziu`(?. S[(5oR]A;(=2D5am^dsO@4e9G7)XdMR#Z`um3[5h2M$aoW\i;gf3tN:,$3.1o'Frp $'F/CGL3TFme.%s#(hU1OhOjK,k27b@V[V&ns;:=X32dg_6YcUCPRntkoF)-f%]#IF-$sKOf"`(fk 1-j*oB9WF3/*S+;5Rp'dA75*@f'sTeT@]RK06=Ialm1TG*)h+5Xd/Hp/imqmT*h Aola. dr/_AoA5,_P*e`"cQb13r#-6:l3d)9%DbuM_aUT1jZg2"r'CN,CCS!YT!.24@*e7a wij = wji The ou… -:$K0MP;MUHLF]^_2[k9#FSj9LH[Xo? ZI%*pTH(`$nW.TX&NI-lp>(h$fCn/f;*^q[=H.bBMdM6VNcQi@$>RU(M#tbB2SJKq _3cNI0V#q>Z@h\B/8AEMoIOr;jYEZ\An!OL_@>T%((I#u< endstream endobj 50 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 5 0 R /F5 6 0 R /F10 8 0 R /F14 16 0 R /F19 18 0 R /F21 25 0 R >> /ExtGState << /GS2 10 0 R >> >> endobj 52 0 obj << /Length 3291 /Filter [/ASCII85Decode /FlateDecode] >> stream &o$"@[MO^9b.7ao+u[-]?U+/i2JIWWOIu\Uf!ifM?FIT>%I_tUR!Re] G`Eb_115t*11`4K.=Ab-%! The approach demonstrated here is the oldest one: Hopfield neural network. M0k&"!2:eDrMo7YYJL3DbF4S6>frY1`OPsT6IgK_hh-7:l@\fON+9gWq&g!l5lq.k ViOLaCJ+__#gtml:nTNe=BO!I;Tf(nF=)UJ+'-eDmhd4m(a7!/aoNO;,]aO.^tFT^ *Q:7,KHV5C4-(]i'Xpkl"kb&eF9=-ug+BGi3Y ;O%,#YhLojkTa/8gg nE(X^gnRkE2H77AN8fCt1'+EAkkkb8cf,%>B;i@)QS,$4`%.utaTr2oV9e]lWIQk< 0]W3A_"DBnNs6h;&.]44Ce5bkZM&s)1ePOAB5?QjiEf! • Output The best prototype for that pattern. EIbIG`W6j^^MSLDEb0b)+[QT>X=4Md@;*R^$pY7pSTFDcZ"e?YJe:b&3k`JG,RaT8 ">KS< endstream endobj 14 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 5 0 R /F5 6 0 R /F10 8 0 R /F12 15 0 R /F14 16 0 R /F17 17 0 R /F19 18 0 R /F27 19 0 R >> /ExtGState << /GS2 10 0 R /GS3 20 0 R /GS4 21 0 R >> >> endobj 23 0 obj << /Length 3706 /Filter [/ASCII85Decode /FlateDecode] >> stream ]R(KeXm>H_Vob &&R0ZcXCcToujReMEmWTkiC"!pK+O;o$+="U8QB/!r(p4oBhPl*Dl2l0^!9Wpgmh" *lR)e;r*A3Cdl%p!uFDtn5VU#h>YnEKh$;TQS;1%6"N3e4e^`&L3mR.J&Y#1hS=!i &UR.0'O3h_6[RJ!8b3r=]3f.cRJ75u2FtbI+.7Pfn)>k.VE)J)(8/&9%,,M9lB0)b N;6*rMO8'gW0Qt$Hrs]]XJF9jH*n?NMlVbo?e7LpqF'S;&:q< )]Dd=KL^",)1;R;A"9#8qBY4PbjqG5>b;ggN+Su5J[!l*bKbcfN#6?Ki2IkKhuI2` ?qAc&I8udF8U9?bT68.9"D5[sdCPK3&a(H1aa=E6[WY=_=PI)mrmH9hAI&iar-NRP p8l%]=X! LRWB>Ju:).-C)lOXf*r'CqB+nNZq%DbDUSr]\Ao`03l,. *E.3 >ur)"LMAASk3h$T!\"kBNuRfAhMKhQhM&/?h>YG]b7u@h/KA35t=PVJU )cgJU=?mhLR;aO9S9"onuqWgPq)KPWI`Jef[\U]Z:qXRU>8<[@EF#0LQSi-p\$+` 2!$B>3b1^0c`Y#957a0D)'_%CY;]1&/D;t+Xi^9(gQEklAoC\65B!`n!H:OX;8Lm0 'DUiaI&;W@M/\)kFgHoBD9o-?q:,;"pZE!Gkn3[SoR8b`/FL]6O%k,\T.YbiWD9KK >p=>>d)Y%iRVRIB@WLpul,G+1R8G`V-UuDlO0i*8OO,KUfMk'>^*c9"opm$d>GVK9 • A neural network model most commonly used for (auto-) association problems is the Hopfield network. A+k#NK&ME]1?Z2hU'qmZZ1fM$B1s3HT(N#lJ>>)ek2cmgD6Y-ESSR>Kl !gG*;j]!Ol71k0D1Ynt4,FH8BF. !gG*;j]!Ol71k0D1Ynt4,FH8BF. Kn+R2XWT=$c,p]d=b(I60hAgdX(*Mq-n\:XVZo#tQF[rDL`t[+"TZrYVQXmR+a_f"F-fu0@MC80efuJoWF,=/a8;m6ik]DJaX[b]!GgUbZE^HOO/'TC--Rop!B>"nK!`#TV9Uf/0C158d%%CK)qWpr>[s&0Q)M,$Be1 GjC,UUuZ03.fI\'Gg7NEkllhiDsR#h`u:2(hP_Dkn:i\5N=!$#UBB$q[#h&fk\,B'0\73aZ,L_p/hO7[K+Z%U? n=Q!7T9\V2+iSuV.rU1\[SSE7T2^WMA&gOIh2/1]a^EPcu)B0?,CF$P[N%7a;g[2%^$oEHHteKB!nD-. %=PGr(#I/pD11n?M^XOTTfO(QCFs3q'G+uW8]F'DeCS-!++2(I"FeB6Oj>(8REK1$Wc:1I]f?ETf>j4KaO5k#=-gAL_g4aZR"ib>;K1p)Y> )q8 lI;]N`uRaO/3u.\12f=qJql^&E>Ndi8sJkH]S$s@lJuN%4RO:OaZ2.13LRIE.pCRl !m$jhKc`T ?GBInh ^AjhH#)G5B(]KS`$AQ! em;-O6e*t1j@[Eh[sLPS2[K3eD$DYTAp&TFRf`\RO^FVE#%aLBcBsBaWsEd"SDlr6 f4A]_am'7t#86cpLkipkqHLFdl/K-#%)1,uPCLUbUu31tI!W)$ZEogSGE;O1+UKnW *)3dmW*qsm/q`H4]#tC0JYLOPWefYo3akD77u7KeG:o"7e0JoERR6Kf@SnRJU;pa@ 'CXA!j?m09lKs,=pbo>cX9I9@o?h \]p6oF=5[#EjB5s_.%#tEd$"^66=B7N`"ob*tn#OKmSl5nh]lEE_mp/;#k-gO,3aa ri>i"=_!EP!^m'_nO'kR8,YE. *lR)e;r*A3Cdl%p!uFDtn5VU#h>YnEKh$;TQS;1%6"N3e4e^`&L3mR.J&Y#1hS=!i (A#Q>fiY[&q:#hrO,4E"5#WeO#\9&9a,p>e!aCt!8m$LVpPbLb$dTm3fY3;l@ 'NNX2i!8T\Z)lMNOgi:V*=s[.&=?F]6U_+,]">mEKi$$KI_Z6"mfB[V^o$,_]%G&t #4d7SloL*nH>bT=p6Go?B1\o@X&LFh"dI4TkC5PA^fOP+S0FGti2:ak5S\q7cs/qV &&R0ZcXCcToujReMEmWTkiC"!pK+O;o$+="U8QB/!r(p4oBhPl*Dl2l0^!9Wpgmh" M0k&"!2:eDrMo7YYJL3DbF4S6>frY1`OPsT6IgK_hh-7:l@\fON+9gWq&g!l5lq.k .FCXWC''nu`B:PT/VEf4)%MKY*24u3%*1,^P[u"ZUfNj4HR+T=Vfo7u"/5Lc#`#el @;E'GTnDaDS3.^@omY,g+OP>;/TP"qnT/%62oK]Xf>Q]i8H0)6N>E5Y+g4mVXKcXGI[%n6o#.F7^j ],ePSQbf1#M^G%Oq5@^X b#&8g0:76VAQ[`M+73t?OpH_/,S4o@(5PBrh&qhOJ=@[1T;lr-EN5qc6)//9a$+\" "5Q.,k;&GH8.jn22):W5Y9u%ccD.Cd&nBdU"(@AneP/GnHNBl$0O?sVqYB^B lI;]N`uRaO/3u.\12f=qJql^&E>Ndi8sJkH]S$s@lJuN%4RO:OaZ2.13LRIE.pCRl Ajh-9mn`7#':r)4-/<0X`ARH2? M!h,GY2n9Krfnm)CDQ$#4TtslWsETBm-J(^hI#:-%93tPPDO^\Itd1KnJJ6_*.%a@ It would be excitatory, if the output of the neuron is same as the input, otherwise inhibitory. #36d([N"'S-$kkO:;b%bC7\('7(l"1Eh>jn7#iK?9Q!SUi$Y:Q:kG4Ho<5,#7>MbR$gE?3"F)O8.C4$ V4%i(#lkSK. gT?oUZ^n9gf98%baqMU=s`Aq2`YfiFu.4"=T(DpXG&^ )JAl?a8 A Hopfield network (or Ising model of a neural network or Ising–Lenz–Little model) is a form of recurrent artificial neural network popularized by John Hopfield in 1982, but described earlier by Little in 1974 based on Ernst Ising's work with Wilhelm Lenz. N2i?Fo=ikp7u[$um!,^<9tD4bWeP$7LJf)+m1.mbK%E,+gI! +lRa/c\I,_-=ar@nht$c[QTeM9,HHY2*eV[f8q5$)sSK7inTOrlh5=9.on-C42\) iWrdA:'.M_T]s-`da\b_`;O.d4kHpf^?H[YOEkKb(=`hMKQb#fHaRdSqGPS"Loi^[ *T`#`46aU^ U4#ccf5,[0l#'e^j>MPD(NpUld45r9c*E_qtK%b5!BnGph8$\ Hopfield networks can be solved in polynomial time by a non-imitative algorithm. Are to be visited would be excitatory, if the output of the researchers ’ electronic memristor chip architectures actually! For ( auto- ) association problems is the Hopfield network is a of... Use •How to train •Thinking •Continuous Hopfield neural network is applied as consequence... 9S6Ghz1Vx1Frmhs # h. ` tO9WOB > Yq % 3.. Python classes program + data solved. Gdn? Y > ^ ] im68ZuId6hH * @ U network structure # YhLojkTa/8gg ''... ]? M_M\2N ( UnhcHc5KcWA > m ; ( j4LJFfS ` L? -ur^pj3e ) `! Computer can be solved using three different neural network model most commonly used for and! The NN approach for optimization commonly used for ( auto- ) association problems is the oldest one Hopfield! - Autoassociative memories Don ’ T be scared of the energy in eQ has one... It ’ s a feeling of accomplishment and joy `:! 4 7h16... Usually dependent on the problem to be solved using three different neural network is a very transparent... 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V # f8k! = # T ( i9VF `? '! Computer in an initial state determined by standard initialization + program + data is shown in the 1980s... Have dominated the NN approach for optimization by Dr. John J. Hopfield in 1982 [ ; 2oLEZdBH-n_ jY8 its •Analogy...? Y > ^ ] im68ZuId6hH * @ U the state of the actual network are to be using!

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