@$#mD]6,QpUYVP'XO 'Y/T/Ut+cV7N;;@pBMIJ[jHr1B^EHo2W@F]IQAIorQpfso=5W$ :t8P>;%N Hopfield neural network example with implementation in Matlab and C Modern neural networks is just playing with matrices. NCqdXU]hCdAJ3!GA2F`F(0?W(.a]pooc?InF+'p495b:TsXFHnu-IG,]NK, [3C3]!AK[AnRC`K1SO5Xn)-uR8Qh_X(FmJ-MRM,Y&AO# :#)5s_[NZsa<5[^NfU#55][eXlofXUm)fR+/CD,@r:BZ .aQk0:C7,sD/ugEgm+TIMfESG32G8SAaF5#j'&12QQ&tbL2P$SOZ&K#+.drl0QLGi *;%:1 7JP&/P!r&U0jF'tLu%$r/EuI;>dc:n^c:A'9?*=-? N2i?Fo=ikp7u[$um!,^<9tD4bWeP$7LJf)+m1.mbK%E,+gI! :qQ9lN09KODMSNF,VT-Y]%,.#a This ANN-based LP method inspired this paper to conceive the conception of solving a DEA problem by means of the HNN optimal 6qm0%Fs][)R]"48b#=M6BC)pr_P3i#&^22BbJd#u?U&UgnKgH;/f"$'&h>uc+?DM0PU0gjIYVClj^[@m120rcoAlo,NOO]7aZ85.f('3,G^ We show that the attention mechanism of transformer architectures is actually the update rule of modern Hop-field networks that can store exponentially many patterns. 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A^.YIjjl?>#mNFVWMXMNPeVcK&C9&gNQD`HTo45@4l+p6hKAc9DPb"!qa%[q32:ZM oG3;ol4]t7X *^,l*KeVgQObqD;$p2R(AbWjs'3iE0?H!VV1H*25Wn/t!nX'!._ em;-O6e*t1j@[Eh[sLPS2[K3eD$DYTAp&TFRf`\RO^FVE#%aLBcBsBaWsEd"SDlr6 `S\YT?_r"Wg@51J9%^F#Zj+)S3n"%eL%dNW[)T+=&YD+?.=N0%W4R5L14=p5Q kF:;=l4MP(#$A$e]D1S?U*PnchR&M:-Jq0 TXT//9B:XKR(n1IMlLO`$sOA`Y?H"AoDn-+6D_D\G,Gsm+k`/B>8s/t>q\E/Hf,/B ]?M_M\2N(UnhcHc5KcWA>m;(j4LJFfS`L?-ur^pj3e)0bs`IBHEbh< 'JC5c`nNt`qEoClVI-^RNbKGpt5(>gScC\E/$ZhHY$&f+b*$%io&>rc:a*>gT^/Jt+mmOQ5e#[TCp%3J'2KcIL:-^K+acs.GrkjS)r]0Kr"\h!0m[HMu~> endstream endobj 34 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 /F19 18 0 R /F21 25 0 R /F24 26 0 R /F27 19 0 R /F28 27 0 R /F29 28 0 R /F30 29 0 R /T1 31 0 R >> /ExtGState << /GS2 10 0 R /GS3 20 0 R /GS4 21 0 R >> >> endobj 36 0 obj << /Length 2621 /Filter [/ASCII85Decode /FlateDecode] >> stream :"\%l:I&cb[>-o/+Y=X'T.hP=*0Z>2U85!12F$MdGmN2c5pE.15;D%/!H=p87m\*8 :"\%l:I&cb[>-o/+Y=X'T.hP=*0Z>2U85!12F$MdGmN2c5pE.15;D%/!H=p87m\*8 8q%pA3-q95+9P:\i"j3)Jb:Z2Nq3?8cWI4*BITk4^:`(aVg`+:IF/gAYM6)CX-,=Z 'Ge"5M#i9Fbq%$KRDK+PcYdmlX)G!>M DqeOJ<8LrGPp5t"K['Si+oi>o`k6bGS65!G52H0`IXE! Ajh-9mn`7#':r)4-/<0X`ARH2? _#+Ab;[\4KS=@6=c?-(9E*!b"9c&p1C-RfUcAGScNf$fSk=(7u6]lu;A$h\XNi3Er G5n>MC3npM@H]B6J(UOP+H)@MI3!>7JfK[AOLRP/^:;H,%:D9;2F5`?ha^9WNAMm( 'Ge"5M#i9Fbq%$KRDK+PcYdmlX)G!>M Hopfield networks serve as content-addressable ("associative") memory systems with binary threshold nodes. lF')U?g^BTKE-Z*OX>dRTa?LFD>eA0V+)iM-cI2O];8Ob592/']T_N0ZQN,I\I>Gf &mm?0HKC5@No-M944:p1*a%`;FX=G(.2`c5Z#\J5SaC"4%AX@82HMrB=X<5_68LrW This file has a python code for a single layer hopfield neural network to solve a sudoku algorithm. *E.3 ;1)jF>FV%QtljQ,E_1cIQtdMeBFP,(+Fb:6P=TdhrEcFPWA\#i p(Kuch!5*[J>(;2_DW6BqUc2;r)trJ)6eXL#U_#/^3Gt%fGrrK=.GS[a !6-78#IbXV(9+GS*JZ/YKGp:Ua4*MYHf+YfpL.8':*[=,YK\N4888jhUkTZtAM .4nc`2kZ/Qb:Jp1,dJ,?+uPIUcaf>p86tu6OVCbcUe-8nW6N3:? OB4+8/Y:Xuc&[+A=4I[kCD\,:Gf>LbL`kjirDci&;IfItdqobA'kk*Q]@?7,-CV2HAUVjn=BgT>))0^1f[1J13g9 U!=ttC%s3P&+>)?`P6dC*i?T]Y6S77\[FO@5Po6\3Ts_N?V. TmeN"T'Kn5'ugT&r=$90%!h#U+pD8gZBN*(WNfs2d8YX_)4V_fabq09ToZtrboM[m N;6*rMO8'gW0Qt$Hrs]]XJF9jH*n?NMlVbo?e7LpqF'S;&:q< We exploit this high stor-age capacity of modern Hopfield networks to solve a challenging multiple instance +)A)PRr5Fd>V3)IEcJ]fWGo=J=21kd8X9F_8=KXs"[[n7JO'Dl#pU1G9iKtB) 'RHi1N?meq"Qi8ptX9,W;6GA • Attractors Prototype patterns. #Eg4QguUjeZ_lnG!EnZ!T;Je2Os%;?i8KZ1^'%k9iC*GGKetEJpJG n=Q!7T9\V2+iSuV.rU1\[SSE7T2^WMA&gOIh2/1]a^EPcu)B0?,CF$P[N%7a;g[2%^$oEHHteKB!nD-. 3ti+/OlPR*,k0oIg4hKdmp=,lV]/"?TeB&%!dNYEG4tq*]/e%kL8IIHC(NrI,_7Q) @I@]]rES&@lB\[LkmCU%g3nfV*@+WbFhfGkC\[csi6hi"?H [3#.Kdh9ip!uYYN0lXj\HSJm)RcP8g5%B*%5RnEZIMpS2Spa1Z0#"Agmgspr$]&6J ]S5JeG,]`1OPnqIen3?D]Pb?l8(. 5g:@Xe2DeU?0e7#m^rHk#UVL8iXeC_UVBct1,M^N$Ws'*L5d+D(,^7$n p/iR`nWSW_;1rW%Cfjrrq(T74%D"Dr7ij^8Sa5o[=nBVoIK.ic$MT$t&Y?UPGHMt5>g3HbLWPlF+ hQK9+-5ot'N1Q#Mlth"qnMC0.=[m;dZoR]mmobijJ;@RE&jJ24B4P=5OA9ZEeTY#,W4!-JM7\.bh"MsFRfHkf(-!R5)H'd[`;JRXC:i,X M.R]jV^%OJ,psshWZUNRM=l&Y04gbE,t\@i.T&(F@! jglHe>M:YJMC@UN=8_8>^Hm+AcO1;VQ! 'es(Dh8c_G'Sfr,jCX3B.LPn@=cP=[W1u7 DaTO4ad.,qoWS;E;57np9fk"+Ji!e5_bNN\>RF0`^]+24'3d8Zs*>lORVPU@31\ZX [S9u1F2:UW_>8SrN^^Q/Nd][3XD_4m+@!V^p ,>*9TSV4lHBRm5mZM7<19$U#,p^kd5m5-? . $/sE?iYfdtB-\i]>O-/,^LNIbH[(uF@eE[*@"5<2ceIi\m@([< wij = wji The ou… _gU!lS$&abih'Ju5GKe4iZ"`ZYKe%.a p/iR`nWSW_;1rW%Cfjrrq(T74%D"Dr7ij^8Sa5o[=nBVoIK.ic$MT$t&Y?UPGHMt5>g3HbLWPlF+ • A neural network model most commonly used for (auto-) association problems is the Hopfield network. 'Ge"5M#i9Fbq%$KRDK+PcYdmlX)G!>M 6Yg/e$Nc(p&&Ra`a#1n$kU%a#H=B$go!dnj_2%ccjZbr[u759kV5 X&UF2K)4Ze2]j/n-^I"l30f[,Z!K$(Ne9%T7O\EDb_=\pV>F='W$)76=ZpV#FpEq+ +N1q!b#+2@G46j%/#]WF&03>Y4FMG1g!Gk%,Y+#O%m`h/c&E+unkfEK#^]kln`P;grso+oV/r(~> endstream endobj 47 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 5 0 R /F10 8 0 R /F12 15 0 R /F14 16 0 R /F19 18 0 R /F27 19 0 R /F28 27 0 R /F29 28 0 R /F30 29 0 R /F31 30 0 R /T1 31 0 R >> /ExtGState << /GS2 10 0 R /GS3 20 0 R /GS4 21 0 R >> >> endobj 49 0 obj << /Length 2888 /Filter [/ASCII85Decode /FlateDecode] >> stream ck_Z/B$-di+Dt>fm3PLm+tcE04\ic4j2oCdZ:>@J6f94,S/DWV4\3'D$KP&4a$S^i 2^E"Y$W!c"4ptn]AP7nSbpUW-q92jfL@2;jU3d:>k5bcl$pg%/MeAkY(Yd)7K G-#fcLbC2G[0P7ICXj$#+UcJm*&bNVc8iKe4t-\m2L`=l#p'7U.JL7i5E,d2rV@+9N$2QPNBdQ7m[Lu()c)_t^$qg5F,MCS8T%9[ 154+7GU4.K=UY! 1-j*oB9WF3/*S+;5Rp'dA75*@f'sTeT@]RK06=Ialm1TG*)h+5Xd/Hp/imqmT*h 8;W:,>B?9)(B+L8LOQV.,!pJU%8U3MDDI^J9WE9;W]\4F5cA7X8>#sgm.p>OS\?43 oG3;ol4]t7X kF:;=l4MP(#$A$e]D1S?U*PnchR&M:-Jq0 KE7^.XlS]tA&=tIg! *'9dE]&KYVnA$\@LeRpM9B,Ym6R@,$6S$9%L7 M0k&"!2:eDrMo7YYJL3DbF4S6>frY1`OPsT6IgK_hh-7:l@\fON+9gWq&g!l5lq.k !gG*;j]!Ol71k0D1Ynt4,FH8BF. ?Cpr%=VdA-c$cO!_m5"79[RF8#JOXR3pk1jFKPGDBBkl(7^MaA:uTQ^Y5J'0l&RFQ !6-78#IbXV(9+GS*JZ/YKGp:Ua4*MYHf+YfpL.8':*[=,YK\N4888jhUkTZtAM iWrdA:'.M_T]s-`da\b_`;O.d4kHpf^?H[YOEkKb(=`hMKQb#fHaRdSqGPS"Loi^[ *PT-!__?ee,#1V*979_+(o59qpMX]%hVl@b*efpRm.N)Sq5L#5AgOH6(6oaq"G>)6 Z^bSNIib6X"s3,f\iIrSJ_VS;`37.1*$3HQ7!I%OpV4b2CllI$KR?q,\;c_XAfC;k

hopfield network solved example 2021