15
Lennart Gustafsson page Course notes CSE2330 1 Part III Cybernetics Chapter 6 Concept Neurons Chapter 7 Neural Coding Chapter 8 Our Friend the Limulus Chapter 9 Supervised Learning Chapter 10 Associative Memory Networks These chapters present classical artificial neural networks and the substance this course is concentrated on. Two chapters are lacking in the book, one on Unsupervised Learning and one on Reinforcement Learning which in brain modelling are much more important than supervised learning, as I see it. We will, of course, discuss these topics too.

Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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Page 1: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

Len

nar

t G

ust

afss

on pag

e

Cours

e note

s C

SE

2330

1

Pa

rt I

II C

yb

ern

etic

s

C

hap

ter

6 C

on

cep

t N

euro

ns

Ch

ap

ter

7 N

eura

l C

od

ing

Ch

ap

ter

8 O

ur

Fri

end

th

e L

imu

lus

Ch

ap

ter

9 S

up

ervis

ed L

earn

ing

Ch

ap

ter

10 A

ssoci

ati

ve

Mem

ory

Net

work

s

Thes

e ch

apte

rs p

rese

nt

clas

sica

l ar

tifi

cial

neu

ral

net

work

s an

d t

he

subst

ance

this

cours

e is

conce

ntr

ated

on.

Tw

o c

hap

ters

are

lac

kin

g i

n t

he

book,

one

on U

nsu

per

vis

ed L

earn

ing a

nd o

ne

on

Rei

nfo

rcem

ent

Lea

rnin

g w

hic

h i

n b

rain

model

ling a

re m

uch

more

im

port

ant

than

super

vis

ed

lear

nin

g, as

I s

ee i

t. W

e w

ill,

of

cours

e, d

iscu

ss t

hes

e to

pic

s to

o.

Page 2: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

Len

nar

t G

ust

afss

on pag

e

Cours

e note

s C

SE

2330

2

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s T

he

McC

ull

och

-Pit

ts n

euro

n f

rom

1943 a

ccord

ing t

o L

ytt

on:

Page 3: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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nar

t G

ust

afss

on pag

e

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e note

s C

SE

2330

3

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s W

e w

ill

dra

w n

euro

ns

as b

elow

The

synap

ses

are

dra

wn a

s ar

row

s, w

hic

h i

s our

sym

bol

for

exci

tato

ry s

ynap

ses.

The

wei

ghte

d s

um

of

the

affe

rents

is

call

ed a

ctiv

atio

n p

ote

nti

al.

The

nonli

nea

rity

, w

hic

h i

s a

par

t of

alm

ost

all

neu

ron m

odel

s, r

esid

es i

n t

he

circ

le.

Page 4: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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nar

t G

ust

afss

on pag

e

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e note

s C

SE

2330

4

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

A b

inar

y n

euro

n w

ill

rece

ive

bin

ary

inputs

fro

m o

ther

bin

ary

neu

rons.

The

inputs

coll

cted

in

vec

tors

can

be

illu

stra

ted i

n t

wo a

nd t

hre

e dim

ensi

ons.

Fro

m t

her

e on w

e m

ust

gen

eral

ize.

Ly

tton, fi

g 6

.6

Page 5: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

Len

nar

t G

ust

afss

on pag

e

Cours

e note

s C

SE

2330

5

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

A “

com

pu

tin

g”

neu

ron

(L

ytt

on,

fig

6.2

):

Page 6: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

Len

nar

t G

ust

afss

on pag

e

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e note

s C

SE

2330

6

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s R

eal

neu

ron

s h

ave

a sm

oo

th n

onli

nea

rity

(L

ytt

on

, fi

g 6

.3):

Ther

e ar

e se

ver

al d

iffe

rent

way

s to

des

crib

e th

e nonli

nea

rity

mat

hem

atic

ally

, th

e m

ain d

iffe

rence

bei

ng c

onven

ience

.

Page 7: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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t G

ust

afss

on pag

e

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e note

s C

SE

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7

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

Dif

fere

nt

neu

ron

s ar

e co

nn

ecte

d i

n d

iffe

ren

t d

irec

tion

s in

dif

fere

nt

cort

ical

lay

ers:

Page 8: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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nar

t G

ust

afss

on pag

e

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e note

s C

SE

2330

8

(Fro

m K

olb

& W

his

haw

: F

undam

enta

ls o

f H

um

an N

euro

psy

cholo

gy)

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

We

shou

ld a

lso

rem

emb

er t

hat

th

ere

is a

co

lum

nar

org

aniz

atio

n (

Fro

m M

oun

tcas

tle:

”Th

e co

lum

nar

org

aniz

atio

n o

f th

e n

eoco

rtex

”, B

rain

199

7, p

p. 7

01

-72

2):

Page 9: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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nar

t G

ust

afss

on pag

e

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e note

s C

SE

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9

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

In a

rtif

icia

l n

eura

l n

etw

ork

s w

e h

ave

gen

eric

neu

ron

s, c

on

nec

ted

in

ver

y

sim

pli

fied

cir

cuit

s.

Dep

end

ing

on

th

e m

ain

fea

ture

s re

tain

ed i

n t

he

arti

fici

al n

eura

l n

etw

ork

s w

e

hav

e m

ain

ty

pes

of

net

wo

rks,

su

ch a

s fe

edfo

rwa

rd n

etw

ork

s an

d r

ecu

rren

t

net

wo

rks.

(in

Sec

tio

n I

V B

rain

s w

e w

ill

mak

e se

rio

us

atte

mp

ts t

o i

mp

rov

e o

ur

mo

del

s)

Page 10: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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t G

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afss

on pag

e

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e note

s C

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10

C

ha

pte

r 6

, C

on

cep

t N

euro

ns

A

one

lay

er f

eedfo

rwar

d n

etw

ork

is

show

n b

elow

Just

one

lay

er o

f neu

rons

wit

h n

o i

nte

rdep

enden

ce –

not

much

of

a net

work

yet

.

Page 11: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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t G

ust

afss

on pag

e

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e note

s C

SE

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11

C

ha

pte

r 6,

Co

nce

pt

Neu

ron

s

A t

wo

lay

er f

eed

forw

ard

art

ific

ial

neu

ral

net

wo

rk (

Ly

tto

n f

ig 6

.7)

Th

ere

is a

hid

den

lay

er “

bef

ore

” th

e o

utp

ut

lay

er o

f n

euro

ns.

Ly

tto

n c

alls

th

is a

th

ree

lay

er n

etw

ork

, co

un

ting

th

e in

pu

ts a

s a

lay

er.

Page 12: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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t G

ust

afss

on pag

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e note

s C

SE

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12

C

ha

pte

r 6,

Co

nce

pt

Neu

ron

s

A p

arti

ally

connec

ted f

eedfo

rwar

d n

etw

ork

(f

rom

Hay

kin

: N

eura

l N

etw

ork

s A

Com

pre

hen

sive

Foundat

ion)

This

is

alre

ady

a b

iolo

gic

ally

more

rea

list

ic m

odel

than

the

full

connec

tivit

y m

odel

s.

Page 13: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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afss

on pag

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e note

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13

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s A

rec

urr

ent

net

work

is

show

n b

elow

. T

he

effe

rent

signal

s ar

e fe

d b

ack t

o b

ecom

e par

t of

the

affe

rent

signal

s. T

her

e ar

e lo

ops

in r

ecurr

ent

net

work

s! T

he

fill

ed c

ircl

es a

re i

nhib

itory

sy

nap

ses.

Page 14: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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t G

ust

afss

on pag

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e note

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14

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

A r

ecu

rren

t n

etw

ork

of

neu

ron

s (L

ytt

on, fi

g 6

.4).

Th

ere

are

no

aff

eren

ts i

n t

his

ver

sio

n.

Page 15: Part III Cybernetics - Monash Universityusers.monash.edu/~app/CSE2330/04/Lnts/ch06.pdf · page Course notes CSE2330 9 Chapter 6, Concept Neurons In artificial neural networks we have

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afss

on pag

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e note

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15

Ch

ap

ter

6,

Co

nce

pt

Neu

ron

s

Sta

tes

kee

p c

ha

ng

ing

, at

lea

st f

or

som

e ti

me,

in

a r

ecu

rren

t n

etw

ork

(Ly

tto

n,

fig

6.5

; th

ere

is a

mis

tak

e in

th

e b

oo

k –

un

it a

sh

ou

ld a

lway

s b

e 0

):