Hopfield Network model of associative memory¶. Pattern Recognition Example 3-5 Hamming Network 3-8 Feedforward Layer 3-8 Recurrent Layer 3-9 Hopfield Network 3-12 Epilogue 3-15 Exercise 3-16 Objectives Think of this chapter as a preview of coming attractions. s!ZO3chVIn/P,fq.M7;*5Skn3f4&d/OFDBH67iB0;*H;C0ul%bR)L_%Ipa!L)m5RR pDr]jU*(DX\ca.uecQfbJJp'iio:()MH;]FkJ+(>5k3B3&6p`5[3[YGl_ [MI;Jrld:VNWHPr7&S@meP6$c]2kAqjPr=B9`s&?=jK^/L:B&NHU/m^&/p#LVDq3_jYur ;\lA)NK?e7'b[RUFH_@AQ26Nq^63(i1Y4lKtJ"8`J7.mQN_7_-+>4Rku)TqXGY/gZr@1tp5Z 5g:@Xe2DeU?0e7#m^rHk#UVL8iXeC_UVBct1,M^N$Ws'*L5d+D(,^7$n *(U9q:V36om9J2::b6R:_.auL**VlIX-HC< Z9*7jDgbYkfnM'g2AH0+-/f]EMrH:[]0:UiQPu*>4%*4:`p4hKg/iI0TDo)qJ(RO(~> endstream endobj 43 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 5 0 R /F5 6 0 R /F7 7 0 R /F10 8 0 R /F17 17 0 R /F19 18 0 R /F21 25 0 R /F24 26 0 R /F26 44 0 R >> /ExtGState << /GS2 10 0 R /GS3 20 0 R /GS4 21 0 R >> >> endobj 46 0 obj << /Length 5246 /Filter [/ASCII85Decode /FlateDecode] >> stream 8`*tAN"je1?e":Aa2jb[;Ip=K!VnlerY@*4Ghs`r>UN:i>s_58TX7cl?j6(L$ZTll lS1c,>[-_$X%1S(WC"#`F#5^[l,F'U1gJ-*W,f=pPh_uWBoqi9bps[JK:t27Q*e6rtki&/n^=5.C0qnbfnPDs6"AOZbnB6fhjn4MM]R@tk*kH1=PqitO4O,H8f6HJ2k`eFMbC(pmSU4$/Js jY8? p/iR`nWSW_;1rW%Cfjrrq(T74%D"Dr7ij^8Sa5o[=nBVoIK.ic$MT$t&Y?UPGHMt5>g3HbLWPlF+ Nh0i'JB4VNC%]c:KKr^C@qe@KTiiBON5[#5l)VFG4YHh]lT.5HsObX8mTEq0@Y:j$1cWG1D+b%ed4#dfGN's s2\89s&S.NkRZ*@P9)nF$RIMmUn2fZs-iB:l`eY.c-]b3m2.+s2(eB`UaIdcYN*dN cY/o>djCN]b0Y`n#K[G`($HMVoS2FPAqGZKZ>>Wj+4nUFhZ\\W"pF?V`ILPi[h1rP $/sE?iYfdtB-\i]>O-/,^LNIbH[(uF@eE[*@"5<2ceIi\m@([< A Hopfield network is a simple assembly of perceptrons that is able to overcome the XOR problem (Hopfield, 1982).The array of neurons is fully connected, although neurons do not have self-loops (Figure 6.3).This leads to K(K − 1) interconnections if there are K nodes, with a w ij weight on each. iZK]=Ab`dR_Ens-.%R+_uN%J(4[gPN?kTU:BZ(K? Inm^,^:@GuW,2Uc:6aJ`[U7b3aFC2FC$=5uLs0+VLNPM]/8An*b)>q)O,>Yc4fj`2Ji3j(-YtR7lM=VX#]8MRk 0BJc0_W`P%e6NMg%@%NuJd13:Ur[_h5JO&OM9m=Drqo%'hXa\3OFjNTnF[5Rd8OT] NIdj%ZtI7#VMnmU9s-rF,i3jd*c!heOfK?4M%+i^CoQL5b*gr?/QBa#V@uASmV*Q ?KC*>V7]@1\pa!qmcC&Sc:U"R)9\DUL0=GTMokF(2b=ncWE59"0CK$J2&! Modern Hopfield Networks (aka Dense Associative Memories) introduce a new energy function instead of the energy in Eq. s)V5ke\@$>B(_kP+1d]=*X['AX/`8h=]HH1\mf6Y.G&iH[-[QaXreL/^TX+s^_qiniaqGI_E3qVHunY<4TZqSF)N>,[TO. rn1g:W32N=)2C7B9h$(3hpD9o^"!%OVQ:$Ga4?Q!c1u lI;]N`uRaO/3u.\12f=qJql^&E>Ndi8sJkH]S$s@lJuN%4RO:OaZ2.13LRIE.pCRl 83!0OT$jq,lW,L\d,'-HM@WTT+:5(Z7S5Mj8(flX^N[6^r"'#W]KV@o-b8) endstream endobj 56 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 5 0 R /F5 6 0 R /F7 7 0 R /F10 8 0 R /F17 17 0 R /F19 18 0 R /F21 25 0 R /F24 26 0 R /F26 44 0 R >> /ExtGState << /GS2 10 0 R /GS3 20 0 R /GS4 21 0 R >> >> endobj 60 0 obj << /Length 4406 /Filter [/ASCII85Decode /FlateDecode] >> stream • Output The best prototype for that pattern. )TsBMc*Cr!JDNB63lTYWiWWCDLu*U4g,bZ2>XG%ioYk3K+32Q*7VbKWLV'dOr;GH#)$9OMqFb ``XaC]cWTuJ2E2uj;f)>S)-@)&a3C]raO"$C^jr7/! `h\/0!bmp3Fi"uN&9*. 1#H(jOeLnkBJiD7K3VWPMR2"DlGbr[ND6oc@V=CEM\nNpFIZMR]7CKua#4@TL0HV' 7geG7jO)?3f-lbSEpdF/RgYgZam]]2#b1@i9I_]b8 m9DqTnV%$"T&p^mB#J.^qdFR=C7AA. !NI]-klObn=clr&J-7.Y>*7'4>&bi-Uro-n*Iu)=YJmr>RC7-/M8D5:6bVRK,#XP)-HC=G!AaTe`MRED%<6::ung!rN" .^hI>h'dbmiEVHj"^9UT73=Ye8dPl\I#ue)-Vuel+VhO80cb-NN^\u440eL`2VR/9 c,/0Qp3cXX6]u9j?[GK0=Og),@rU^lr=YS-OCY-s:]P0#S&6F)$!;kSo`d+!fNcq>Se1[Jk6. qm(.@?W^HpaCA4nm)?.)V?LA\ZZTEWY1WiU3OZ#'bBd[3m,>/f)*h$M/&K!sb@9. 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