An introduction to Neural Networks - McGill CIM › ~jer › courses › ai › readings ›...

135
An introduction to Neural Networks Patrick van der Smagt Ben Krose ..

Transcript of An introduction to Neural Networks - McGill CIM › ~jer › courses › ai › readings ›...

Page 1: An introduction to Neural Networks - McGill CIM › ~jer › courses › ai › readings › kroseNN.pdf · neural state registers learning functions learning register memory synaptic

An

introduction

to

Neural Networks

Patrick van der SmagtBen Krose..

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sigmoidsgn semi-linearii i

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original discriminant functionafter weight update

C

A

B

1 2

1

2

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1

φ

ΨΩ

w

w

w w

Σ

Σ

01

2

3

+

−−1

+1

−1 +1

−1 +1

+1

errorsummergains

switchespatterninput

level

output

quantizer

switchreference

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?

(−1,−1)

(−1,1)

AND

(1,1)

(1,−1)

?

XOROR

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−2

1

1

−0.5

(1,1,1)

(-1,-1,-1)

1

1−0.5

a. b.

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c

b a

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−10

1

−10

1−1

0

1

−10

1

−10

1−1

0

1

−10

1

−10

1−1

0

1

−10

1

−10

1−1

0

1

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2 4 6 8

+1

-0.5

-2-4

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2 4 6-4

+1

-1

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i

a very slow approximation

gradient

i+1uu

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0 0.5 10

0.2

0.4

0.6

0.8

1

x

y

B

0 0.5 10

0.2

0.4

0.6

0.8

1

x

y

A

number of learning samples

errorrate

test set

learning set

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0 0.5 10

0.2

0.4

0.6

0.8

1

x

y

A

0 0.5 10

0.2

0.4

0.6

0.8

1

x

y

B

errorrate

number of hidden units

learning set

test set

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weight vectorpattern vector

a. b.

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−0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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: input pattern : weight vector

x2

x1

forwardfeed-vector

quantisation

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-2

-1

0

1

2 -2

-1

0

1

2

00.250.5

0.75

1

-2

-1

0

1

2 -2

-1

0

1

2

0255

5

1

h(i,k)

Iteration 0 Iteration 200 Iteration 600 Iteration 1900

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lateral distance

excitation

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LTMLTMSTM activity pattern

STM activity pattern

category representation field

feature representation field F1

F2

input

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neurons

neurons

N

M++

+− +

++

+

+

F1

F2

G2

G1 reset

input

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backward LTM from:

patterninput

4321outputoutputoutputoutput

activenotnot

active

notactive active

not

notactive

notactive

activenot

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reinforcementinternal

reinforcement

state vector

detectorreinforcement

ASE systemdecoder

ACE

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F

x

θ

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1

4

3

2

tool frame

base frame

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θ

θ

NetworkNeural

NetworkNeural Plant

x x’θ

θ

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ε

θ PlantNetworkNeuralx x’θ

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manipulator

modelinverse dynamics

d

f

i(t)θ

-+

++

K

(t)θ(t) (t)T T

T (t)

θ θ

(t)

(t)

(t)

(t)

(t)

(t)

x

x

13,1

1,1

i3

i2

i1 (t)

(t)

(t)T

T

T

TT

T

32

1(t)

(t)(t)

Σ

Σ

Σ

θ

θ

θ

(t)(t)(t)d3

d2

d1

f

f

g

g

1

13

1

13

x1,2

1,3x

x13,3

13,2x

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302010−π

0

π

t/s

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EDCBA

units

units45 output

29 hidden

sharp left sharp right

30x32 video input retina

8x32 range finderinput retina

straight ahead

66

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neuronneuron

1 2neuronneuronneuron

0

neuron3 4 5

76neuron neuron

(unused)

orderingof the neurons:

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U U ll-1

ll-1

l

l

l( (

(

(

(

)

) ) )

)

)(l-1

l-1 )(n+vv,n

nv

n

n’

n

ua

cb

v

u

u

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""21100 UUUUU

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b.a.

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d.c.

b.a.

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Network

Bus interface

or Symbolics)(DEC VAX

Bus interface

or Symbolics)(DEC VAX

Bus interface

or Symbolics)(DEC VAX

Bus interface

or Symbolics)

Front end 3

Front end 2

Front end 1

(DEC VAXFront end 0

Nexus

32

10

sequencersequencer

sequencersequencer

Connection Machine I/O System

16,384 ProcessorsConnection Machine

16,384 ProcessorsConnection Machine

16,384 ProcessorsConnection MachineConnection Machine

16,384 Processors

displayGraphicsData

VaultDataVault

DataVault

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C+A*B

cellsystolic

c+a*b

b

b

a

a

c

a11

c11

11b

a 32 22a12a

a 21a 31

21b b 22 23b

b 1312b

21 12ccc cc 22 1331

14233241c c c c

42 33 24c c c3443 cc

Warp Interface & Host

address

X

Yn2

cell1

cell cell

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outputs

inputs

N

M

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receptor for

row 5laser for

row 1laser for

maskweight

column 6

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Intensity

outV

outV

3.6

3.4

3.2

3.0

2.8

2.6

2.4

2.28765432

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(b)(a)

+

+−

ganglionoutput

photo-receptor

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δ j

j

j

a

LP

processorlearning

neural state registers

learning functions

learning register

memory

synaptic

readable

and

loadable

parallel

controland

functionlinearnon-

controllearning

accumulator

alu

addersof

tree

mul

mul

mul

mul

Fct. Fct. Fct. Fct.

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Page 133: An introduction to Neural Networks - McGill CIM › ~jer › courses › ai › readings › kroseNN.pdf · neural state registers learning functions learning register memory synaptic
Page 134: An introduction to Neural Networks - McGill CIM › ~jer › courses › ai › readings › kroseNN.pdf · neural state registers learning functions learning register memory synaptic
Page 135: An introduction to Neural Networks - McGill CIM › ~jer › courses › ai › readings › kroseNN.pdf · neural state registers learning functions learning register memory synaptic