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388 The Neocognitron20_33i. L i.* L L L23 t- t- t-LJt-r13-. -.. -. -.." ,- < .•- •'28 ..- ._ ..—29 _. .-. ,_M - -- - --]31-. - -_ "-J32- -, _. .-..33 ..' _,' _;' _;'.' ' .' .' ' .' "l "'1 '1 'lI5 J J J _••' " ';- '-- i- >-wo .j. j. •-• 1 35 y j._ 'j._ j._17 !.._ l._ I. l.._n 34 ;. /_ /i £.]Figure 10.919r r r rM -/ -?' -? ~fThis figure shows the four patterns used to train each ofthe 38 planes on layer Us 2 of the neocognitron designed torecognize the numerals 0 through 9. The square bracketsindicate groupings of S-planes whose output connectionsconverge on a single c-plane in the following layer. Source:Reprinted with permission from Kunihiko Fukushima, Sei Miyake,and Takayuki Ito, "Neocognitron: a neural network model for amechanism of visual pattern recognition." IEEE Transactions onSystems, Man, and Cybernetics, SMC-13(5), September/October1983. © 1983 IEEE.vector. You would need to multiply the input vector by the monotonicallydecreasing function and renormalize first [6].10.2.3 Processing on the C-LayerThe functions describing the C-cell processing are similar in form to those forthe S-cells. Also like the S-layer, each C-layer has associated with it a singleplane of inhibitory units that function in a manner similar to the V c -cells on theS-layer. We label the output of these units Vs,( n )-Generally, units on a given C-plane receive input connections from one, orat most a small number of, S-planes on the preceding layer. Vs-cells receiveinput connections from all S-planes on the preceding layer.
10.3 Performance of the Neocognitron 389The output of a C'-cell is given byV Sl (n)v)(10.10)where A"/ is the number of S*-planes at level /, JI(KI. k{) is one or zero dependingon whether 5-plane /•>/ is or is not connected to C-plane A'/, rf/(v) is the weighton the connection from the S-cell at position v in the receptive field of theC'-cell, and I)/ defines the receptive-field geometry of the C'-cell.The function 0 is defined by0(x) = \ 0 + x X - (10.11)[0 x
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COMPUTATION AND NEURAL SYSTEMS SERI
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Library of Congress Cataloging-in-P
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viPrefacenew professional society h
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viiiPrefaceprocessing model, we hav
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xPrefaceThere are, however, several
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xiiContents4.3 The Hopfield Memory
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HIntroduction toANS TechnologyWhen
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Introduction to ANS TechnologyFigur
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Introduction to ANS TechnologyOutpu
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Introduction to ANS Technology(b)Fi
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1.1 Elementary NeurophysiologyCell
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1.1 Elementary Neurophysiology 11Pr
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1.1 Elementary Neurophysiology 13Fi
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1.1 Elementary Neurophysiology 15wh
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1 .2 From Neurons to ANS 1 7Exercis
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1.2 From Neurons to ANS 19Notice th
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1 .2 From Neurons to ANS 21units, t
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24 Introduction to ANS Technologya
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26 Introduction to ANS TechnologyOu
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28 Introduction to ANS TechnologyIn
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30 Introduction to ANS Technologyle
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32 Introduction to ANS TechnologyFi
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34 Introduction to ANS Technologyne
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36 Introduction to ANS TechnologyN
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38 Introduction to ANS Technologyou
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40 Introduction to ANS TechnologySy
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42 Introduction to ANS Technology[5
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C H A P T E RAdaline and MadalineSi
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2.1 Review of Signal Processing 471
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2.1 Review of Signal Processing 49A
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which describes a typical square wa
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2.1 Review of Signal Processing 53W
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2.2 Adaline and the Adaptive Linear
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2.3 Applications of Adaptive Signal
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2.3 Applications of Adaptive Signal
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2.4 The Madaline 73= -1.5Figure 2.1
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2.4 The Madaline 75with the least c
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2.4 The Madaline 77right of the top
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2.5 Simulating the Adaline 79Retina
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2.5 Simulating the Adalinerecord la
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2.5 Simulating the Adaline S3Adalin
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2.5 Simulating the Adaline 85mented
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Bibliography 87[8] Rodney Winter an
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90 BackpropagationOutput read in pa
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92 Backpropagationan inordinate amo
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94 BackpropagationFigure 3.3 serves
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96 Backpropagation1. Apply an input
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98 Backpropagationwhere we have use
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1 00 Backpropagationmethod. Moreove
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1 02 Backpropagation1. Apply the in
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104 Backpropagationexample, the lim
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106 Backpropagation-- E,wFigure 3.6
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108 BackpropagationFigure 3.7This B
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110 BackpropagationTraining the Net
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112 BackpropagationAutomatic Paint
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114 Backpropagationfor the network
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116 Backpropagation3.5.2 BPN Specia
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118 Backpropagationof the Adaline s
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120 BackpropagationThe final routin
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122 BackpropagationHere again, to i
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124 Backpropagationyour modificatio
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HThe BAM and theHopfield MemoryThe
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4.1 Associative-Memory Definitions
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4.2 The BAM 131All the 6ij terms in
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.^Although we consistently begin wi
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4.2 The BAM 135For our first trial,
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4.2 The BAM 137is fairly easy to ap
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4.2 The BAM 139term valley to refer
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4.3 The Hopfield Memory 141where a
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4.3 The Hopfield Memory 143Figure 4
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4.3 The Hopfield Memory 145A =50(a)
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4.3 The Hopfield Memory 147In Eq. (
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4.3 The Hopfield Memory 149The TSP
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4.3 The Hopfield Memory 1512. Energ
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4.3 The Hopfield Memory 153causes a
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4.3 The Hopfield Memory 155where Aw
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4.4 Simulating the BAM 1571 2 3 4 5
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4.4 Simulating the BAM 159weight_pt
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4.4 Simulating the BAM 161The disad
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4.4 Simulating the BAM 163for refer
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4.4 Simulating the BAM 165of signal
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Bibliography 167Suggested ReadingsI
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C H A P T E RSimulated AnnealingThe
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5.1 Information Theory and Statisti
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5.2 The Boltzmann Machine 179where
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5.2 The Boltzmann Machine 1811. For
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5.2 The Boltzmann Machine 183popula
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5.2 The Boltzmann Machine 185Hf, on
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5.2 The Boltzmann Machine 187Thenan
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5.3 The Boltzmann Simulator 189Fort
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5.3 The Boltzmann Simulator 191(b)F
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5.3 The Boltzmann Simulator 193We w
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5.3 The Boltzmann Simulator 195ANNE
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5.3 The Boltzmann Simulator 197appl
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5.3 The Boltzmann Simulator 199Befo
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5.3 The Boltzmann Simulator 201Fina
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5.3 The Boltzmann Simulator 203begi
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5.3 The Boltzmann Simulator 205begi
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5.4 Using the Boltzmann Simulator 2
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5.4 Using the Boltzmann Simulator 2
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Suggested Readings 211All that rema
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C H A P T E RThe Counterpropagation
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6.1 CPN Building Blocks 215y' Outpu
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6.1 CRN Building Blocks 217The vect
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6.1 CPN Building Blocks 219(a)(b)Fi
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6.1 CPN Building Blocks 221Initial
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6.1 CPN Building Blocks 223Aw = cc(
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6.1 CPN Building Blocks 225'! '2 '
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6.1 CRN Building Blocks 227where x'
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6.1 CPN Building Blocks 229f(w)w(a)
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6.1 CPN Building Blocks 231y' Outpu
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6.1 CRN Building Blocks 233UCRUCS\(
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6.2 CPN Data Processing 2356.2 CPN
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6.2 CPN Data Processing 237The comp
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6.2 CPN Data Processing 239those ou
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6.2 CRN Data Processing 241Region o
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6.2 CRN Data Processing 243x' Outpu
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,6.3 An Image-Classification Exampl
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6.4 The CPN Simulator 247(a)(b)Figu
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6.4 The CPN Simulator 249outsweight
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6.4 The CPN Simulator 251our simula
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6.4 The CRN Simulator 253Before we
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6.4 The CRN Simulator 255learned, w
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6.4 The CPN Simulator 257doj = rand
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6.4 The CRN Simulator 259VFigure 6.
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Programming Exercises 261code for t
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C H A P T E RSelf-Organizing MapsTh
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7.1 SOM Data Processing 265topology
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7.1 SOM Data Processing 267(a)(b)Fi
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7.1 SOM Data Processing 269(0,0) (0
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7.1 SOM Data Processing 271(a)(b)Fi
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7.1 SOM Data Processing 273to assoc
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7.2 Applications of Self-Organizing
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7.2 Applications of Self-Organizing
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7.3 Simulating the SOM 279The resul
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7.3 Simulating the SOM 281model of
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7.3 Simulating the SOM 283domag = p
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7.3 Simulating the SOM 285row = (W-
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7.3 Simulating the SOM 287Figure 7.
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Bibliography 289to the number of tr
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H A P T E RAdaptiveResonance Theory
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8.1 ART Network Description 293equi
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8.1 ART Network Description 2951 0
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8.1 ART Network Description 2978.1.
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8.2 ART1 299Exercise 8.2: Show that
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8.2 ART1 301is inactive, G is not i
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8.2 ART1 303To all F 2 unitsFrom F,
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8.2 ART1 305from the F 2 layer. Sin
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8.2 ART1 307on connections from tho
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8.2 ART1 309Recall that |S| = |I| w
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8.2 ART1 311on FI and N be the numb
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8.2 ART1 313Since L = 3 and M = 5,
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8.2 ART1 315In this case, the equil
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8.3 ART2 317Orienting , Attentional
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8.3 ART2 319of keeping the activati
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8.3 ART2 321Notice that, after the
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8.3 ART2 323not want a reset in thi
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8.3 ART2 3254. Propagate forward to
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8.4 The ART1 Simulator 327and the t
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8.4 The ART1 Simulator 329rho : flo
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8.4 The ART1 Simulator 331Notice th
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8.4 The ART1 Simulator 333for i = 1
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8.4 The ART1 Simulator 335• We up
Page 351 and 352: Suggested Readings 337Programming E
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Page 356 and 357: 342 Spatiotemporal Pattern Classifi
Page 384 and 385: 370 Programming Exercisesthe networ
Page 387 and 388: C H A P T E RThe NeocognitronANS ar
Page 389 and 390: The Neocognitron 375The visual cort
Page 391 and 392: 10.1 Neocognitron Architecture 377S
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Page 395 and 396: 10.2 Neocognitron Data Processing 3
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Page 407: Bibliography 393References at the e
Page 410 and 411: 396 Indexsummary, 101, 160training
Page 412 and 413: 398 Indexdifferential, 359, 361lear
Page 414 and 415: 400 Indexassociator (A) units, 22,
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