':~~1

f~r"

"':!f"

i"'

In K;.VahLehti'(1991).

, LE

A; H

illsdale, NJ~

..-.

Architectures for Intelli

Ken

ceNature, Nurture, a

ndC

onne

ctio

ns: I

mpl

icat

ions

of

Con

nect

ioni

st M

odel

sfo

r C

ogn

itive

Dev

elop

men

t'

Jam

es L

. McC

lella

ndE

ric J

enki

nsC

srne

gie

Mel

lon

Uni

vers

ity

Whe

n it

com

es to

sel

ectin

g an

arc

hite

ctur

e fo

r m

odel

ing

cogn

ition

, we

have

ach

oice

, We

can

star

t with

a s

ymbo

lic a

rchi

tect

ure,

in w

hich

the

puta

tive

cons

titu-

ents

of

abst

ract

cog

nitio

n (s

ymbo

ls)

are

take

n as

mod

elin

g pr

imat

ives

; or

we

may

adopt an alternative view, that symbolic

beha

vior

em

erge

s fr

om th

e op

erat

ion

ofa

syst

em o

f sim

ple,

sub

-sym

bolic

pro

cess

ing

units

, Con

nect

ioni

st m

odel

s ta

keth

is la

tter

tack

, In

thes

e m

odel

s, p

roce

ssin

g oc

curs

thro

ugh

the

prop

agat

ion

ofac

tivat

ion

amon

g a

num

ber

of s

impl

e pr

oces

sing

uni

ts, T

he k

now

ledg

e th

atgo

vern

s pr

oces

sing

is s

tore

d in

the

stre

ngth

s of

the

conn

ectio

ns a

mon

g th

e un

its,

And

lear

ning

occ

urs

thro

ugh

the

grad

ual a

djus

tmen

t of

the

stre

ngth

s of

thes

eco

nnec

tions

, At f

ust g

lanc

e it

may

see

m th

at s

uch

mec

hani

sms

are

far

rem

oved

from

sym

bolic

thou

ght,

Yet

we

will

arg

ue in

this

cha

pter

that

they

may

for

m th

eba

sis

of th

e ac

quis

ition

of

a nu

mbe

r of

cog

nitiv

e ab

ilitie

s, a

nd th

at th

ey m

ay h

elp

us a

nsw

er b

asic

que

stio

ns a

bout

the

proc

ess

of c

ogni

tive

deve

lopm

ent.

Seve

ral

diff

eren

t kin

ds o

f an

swer

s ha

ve b

een

give

n to

thes

e qu

estio

ns, W

e w

ill s

ee h

owth

e co

nnec

tioni

st f

ram

ewor

k op

ens

them

ane

w a

nd s

ugge

sts

wha

t may

be

diff

er-

ent a

nsw

ers

in m

any

case

s,

TH

E P

HE

NO

ME

NA

The

fie

ld o

f co

gniti

ve d

evel

opm

ent i

s re

plet

e w

ith e

xam

ples

of

dram

atic

cha

nges

in children

s th

inki

ng a

s th

ey g

row

old

er, H

ere

we

give

thre

e ex

ampl

es: (

a)Fa

ilure

s of

con

serv

atio

n an

d co

mpe

nsat

ion,

(b)

Pro

gres

sive

dif

fere

ntia

tion

ofkn

owle

dge

abou

t dif

fere

nt k

inds

of

thin

gs, (

c) U

-sba

ped

lear

ning

cur

ves

in la

n-gu

age

acqu

isiti

on,

MC

ClE

LL

AN

D A

ND

JE

NK

INS

Failu

res

of C

onse

rvat

ion

and

Com

pens

atio

n

Perh

aps

the

best

kno

wn

phen

omen

a in

cog

nitiv

e de

veio

pmen

t are

the

dram

atic

failu

res

of c

onse

rvat

ion

that

Pia

geth

as, r

epor

ted

in a

wid

e ra

nge of different

dom

ains

, One

dom

ain

is th

e do

mai

n of

liqu

id q

uant

ity, A

chi

ld o

f 3

is s

how

n tw

ogl

asse

s of

wat

er, T

he g

lass

es a

re th

e sa

me,

and

eac

h co

ntai

ns th

e sa

me

amou

nt o

fw

ater

, and

the

child

see

s th

at th

e am

ount

is th

e sa

me,

But

whe

n th

e co

nten

ts o

fon

e of

the

glas

ses

is p

oure

d in

to a

wid

er c

onta

iner

, the

chi

ld w

ill s

ay th

at th

ere

isle

ss li

quid

in th

e w

ider

con

tain

er,

It is

typi

cal t

o sa

y th

at th

is a

nsw

er th

at th

e yo

ung

child

giv

es r

efle

cts

a fa

ilure

to r

ecog

nize

two

thin

gs: (

a) T

hat q

uant

ity is

con

serv

ed u

nder

the

tran

sfor

mat

ion

of p

ouri

ng f

rom

one

con

tain

er to

ano

ther

; and

(b)

that

gre

ater

wid

th c

an c

ompe

n- .

sate

for

less

hei

ght,

Man

y ta

sks

are

spec

ific

ally

des

igne

d to

tap

into

the

child

'ab

ility

to c

ope

with

thes

e ki

nds

of co

mpe

nsat

ion

rela

tions

bet

wee

n va

riabl

es,

One such task developed by Inhelder and Piaget (1958), the so-called

bala

nce-

scale lask,

is il

lust

rate

d in

Fig

, 3, 1,

In th

is ta

sk, t

he c

hild

is s

how

n a

bala

nce

scal

ew

ith p

egs

at e

venl

y sp

aced

inte

rval

s to

the

left

and

rig

ht o

f a

fulc

rum

, On

one

peg

on th

e le

ft a

re s

ever

al w

eigh

ts; o

n on

e pe

g on

the

right

are

seve

ral w

eigh

ts,

The

sca

le is

imm

obili

zed

, and

the

child

is a

sked

to ju

dge

whi

ch s

ide

will

go

dow

n, o

r w

heth

er th

ey w

ill b

alan

ce, W

e w

ill h

ave

occa

sion

to e

xam

ine

perf

or-

man

ce in

this

task

at l

engt

h be

low

; for

now

it s

uffi

ces

to n

ote

that

you

ng c

hild

ren

(up

to a

bout

6 o

r 7

in th

is c

ase)

typi

cally

res

pond

as

if th

e di

stan

ce f

rom

the

fulc

rum

was

com

plet

ely

irre

leva

nt. T

hey

will

say

the

scal

e sh

ould

bal

ance

if th

ew

eigh

t is

the

sam

e on

bot

h si

des , r

egar

dles

s of

dis

tanc

e, O

ther

wis

e th

ey s

ay th

esi

de w

ith th

e gr

eate

r w

eigh

t will

go

dow

n, T

hese

chi

ldre

n, t

hen

, app

ear

to m

iss

the

fact

that

less

er w

eigh

t can

be

com

pens

ated

for

by g

reat

er d

ista

nce.

'fY

pica

llyby the age of II or so children have so

me

appr

ecia

tion

for

this

trad

e of

f; th

e de

-ra

ils o

f th

e de

velo

pmen

tal p

rogr

essi

on a

re q

uite

inte

rest

ing,

as

we

shal

l see

bel

ow,

Prog

ress

ive

Dif

fere

ntia

tion

of O

ntol

ogic

al C

ateg

orie

s

Oth

er r

esea

rehe

rs, s

tudy

ing

diff

eren

t dom

ains

, hav

e no

ticed

oth

er k

inds

of

deve

l-op

men

tal p

rogr

essi

ons,

Kei

l (19

79)

stud

ied

child

ren

s ju

dgem

ents

abo

ut w

heth

eryo

u co

uld

say

thin

gs li

ke "

A r

abbi

t is

an h

our

long

. " He supposed such judg-

men

ts ta

pped

chi

ldre

ns

know

ledg

e ab

out d

iffe

rent

kin

ds o

f th

ings

, In

thes

e

3, NATURE, NURTURE, A

ND

CO

NN

Ecn

ON

S

judg

men

ts, K

eil w

as in

tere

sted

not

in w

heth

er th

e ch

ild s

aw a

sen

tenc

e as

true

or

fals

e, b

ut in

whe

ther

the

child

fel

t tha

t one

cou

ld m

ake

cert

ain

kind

s of

pre

dica

-tio

ns (

e.g"

that

som

ethi

ng is

an

hour

long

) w

hen

the

som

ethi

ng is

a m

embe

r of

ace

rtai

n "

onto

logi

cal c

ateg

ory" (e,g"

livi

ng th

ing)

, Kei

l fou

nd th

at c

hild

ren

wer

e

muc

h m

ore

perm

issi

ve in

thei

r ac

cept

ance

of

stat

emen

ts th

an a

dults

wer

e, b

utth

eir

perm

issi

vene

ss w

as n

ot s

impl

y ra

ndom

, Rat

her"

they

wou

ld a

ccep

t sta

te-

men

ts th

at o

ver-

exte

nded

pred

icat

es to

cat

egor

ies

near

the

ones

they

typi

cally

appl

y to

, but

wou

ld n

ot e

xten

d th

em f

urth

er, T

hus

som

e ch

ildre

n w

ill a

ccep

tpr

edic

atio

ns li

ke "

The

roc

k is

asl

eep,

" bu

t not

"T

he r

ock

is a

n ho

ur lo

ng,"

It w

as

as th

ough

chi

ldre

n's

know

ledg

e of

wha

t pre

dica

tes

appl

y to

par

ticul

ar c

ateg

orie

sbe

com

es p

rogr

essi

vely

mor

e an

d m

ore

diff

eren

tiate

d, a

s iI

lust

rate

d in

Fig

, 3,

Second Grode

Kln

del'Q

Clr

ten

At7

(AN

HO

UR

LO

NG

IT

HIN

k O

F

...

HE

AV

Y H

e,.t

TA

LL

AL

IVE

"" ;.

c...

AW

AK

E fl

o..,

SOR

RY

cha

l,11

11"

man

pi,

( A

N H

OU

R L

ON

G I

THINk OF

---~

HE

AV

Y '.

1: tI

Io.

TA

LL -

.t

......

......

....

AL

IYE

1111

1.

AW

AK

E h

oUi.

......

..--

... "

"

SO

RR

Y fl

o..,

pi,

1118

1

Fourth Grode

Sixth Grode

A37

TH

IMC

OF

----

...

HE

AV

Y A

N H

OU

R L

ON

G

......

.....,

\

TA

LL

111

11. .

ee,.'

AL

ly('~

- ,.

.....

AW

A~f

l""

SOR

RY

lIIo

npi

,

A54

THiNk OF

HE

AV

Y A

N H

OU

R, L

ON

G -,

.t

/"

TA

LL

111

11. '

.V. .

how

......

....

AL

IVE

hO

Ull

HU

NG

f(;'

)IO

..,SO

RPI

'

lIIo

n

FIG

, 3, 1, Balance scale of th

e ki

nd f

irst

use

d by

Inh

elde

r an

d Pi

agat

(19581. and later used ex

tens

ivel

y bV

Sie

gler

(19

76; 1

981;

Sie

gler

&K

lahr

. 198

21, R

eprin

ted

from

Sie

gler

, 197

6. F

ig, 1

. with

perm

issi

on,

FIG

, 3,2, Four di

ffer

ent "

pred

icta

bllit

y tr

ees"

lIIu

stre

ting

the

prog

res-

sive

dif

fere

ntia

tion

of c

once

pts

as a

fun

ctio

n of

age

, Ter

ms

In c

aplte

l.at

inte

rnal

nod

es In

the

tree

s re

pres

ent p

redi

cate

s, a

nd te

rms

In lo

wer

case

at t

erm

inal

nod

es in

the

tree

s re

pres

ent c

once

pts

that

ere

span

ned

by a

ll th

e pr

edic

ates

wri

tten

on n

odes

that

dom

inat

e th

ete

rmin

al, A

pre

dica

te s

pans

a c

once

pt if

the

child

rep

orts

that

It i

s no

tsi

lly to

app

lv e

ither

the

pred

icat

e or

its

nega

tion

or b

oth,

to th

e co

ncep

t,T

hus

the

firs

t tre

e in

dica

tes

that

the

child

will

acc

ept "

The

gir

l Is

(not

l

aliv

e,"

and

"The

cha

ir is

(no

t) ta

ll" b

ut w

ill n

ot a

ccep

t "T

he c

hair

Is

(not) alive,"

Par

enth

eses

Indi

cate

unc

erta

inty

abo

ut th

e ap

plic

atio

n of

a pr

edic

ate,

Red

raw

n fr

om K

eil,

1979

, App

endi

x C

, with

per

mis

sion

,

.....;

:-~.

..:. -

..;...

.. -.

.,---;;.

.~.;~~~

.-

- ,-

F.

44 MC

CL

EL

lAN

D A

ND

JE

NK

INS

. U-S

hape

d Le

arni

ng C

urve

s in

Lan

guag

e D

evel

opm

ent

Ear

ly o

n ch

ildre

n of

ten

get c

erta

in k

inds

of

lingu

istic

con

stru

ctio

ns c

orre

ct w

hich

they

late

r ge

t wro

ng; o

nly

late

r do

they

rec

over

thei

r fo

nner

cor

rect

per

fonn

ance

,O

ne e

xam

ple

is th

e pa

ssiv

e co

nstr

uctio

n, a

pplie

d to

sem

antic

ally

bia

sed

mat

e-ri

als,

suc

h as

"T

he m

an w

as b

itten

by

the

dog,

" (S

ee B

ever

, 197

0, f

or a

dis

cus~

sion

of

the

deve

lopm

ent o

f th

e us

e of

the

pass

ive

cons

truc

tion.

) E

arly

in d

evel

op-

men

t, ch

ildre

n co

rrec

tly in

terp

ret s

uch

sent

ence

s; th

ey a

ppea

r to

be

usin

gin

fonn

atio

n ab

out w

hat r

oles

the

diffe

rent

noun

s ty

pica

lly p

lay

in th

e ac

tion

desc

ribe

d by

the

verb

, sin

ce th

ey te

nd to

be

corr

ect o

nly

whe

n the correct

inte

rpre

tatio

n as

sign

s th

e no

uns

to th

eir

typi

cal r

oles

, At a

n ol

der

age,

chi

ldre

nre

spon

d di

ffer

ently

to s

uch

sent

ence

s, tr

eatin

g th

e fu

st n

oun-

phra

se a

s th

e su

b-je

ct; s

eman

tic c

onst

rain

ts a

re o

ver-

ridde

n, a

nd th

ere

is a

tend

ency

to in

terp

ret

The

maD

was

bitt

en b

y th

e do

g " as

mea

ning

"T

he m

an b

it th

e do

g," Finally,

child

ren

inte

rpre

t the

sen

tenc

e

~y ag

ain,

but

for

a di

ffer

ent r

easo

n, I

t wou

ldap

pear

that

they

DoW

know

how

to u

nder

stan

d pa

ssiv

es in

gen

eral

, . si

nce

at th

isst

age

they

can

als

o in

terp

ret s

eman

tical

ly n

eutr

al a

nd e

ven

reve

rse-

bias

ed s

en-

tenc

es (

such

as

..th

e do

g w

as b

itten

by

the

man

~y,

3, NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S

The

,mai

n th

rust

of

the remainder of this chapter is to argue that recent

deve

lopm

ents

in c

onne

ctio

nist

lear

ning

pro

cedu

res

sugg

est a

dra

mat

ic a

ltern

ativ

eto

thes

e ki

nds

of v

iew

s, T

he a

ltern

ativ

e is

sim

ply

the

hypo

thes

is th

at th

ese

dive

rse

deve

lopm

enta

l phe

nom

ena

all r

efle

ct th

e op

erat

ion of a single basic

lear

ning

pri

ncip

le, o

pera

ting

in d

iffe

rent

task

s an

d di

ffer

ent p

arts

of

the

cogn

itive

~~m

, T

HE

LE

AR

NIN

G P

RIN

CIP

LE

The

pri

ncip

le c

an b

e st

ated

in f

airl

y ab

stra

ct te

nns

as f

ollo

ws:

Adj

ust t

he p

aram

eter

s of

the

min

d in

pro

port

ion

to th

e ex

tent

to w

hich

thei

r ad

just

-m

ent c

anpr

oduc

:e .

redu

ctio

n in

the

disc

repa

ncy

betw

een

expe

cted

and

obs

erve

dev

ents

,

TH

E Q

UE

STIO

NS

Thi

s pr

inci

ple

is n

ot n

ew, I

t mig

ht w

ell b

e se

en a

s ca

ptur

ing

the

resi

due

ofPi

aget

's a

ccom

mod

atio

n pr

oces

s, in

that

acc

omm

odat

ion

invo

lves

an

adju

stm

ent

of m

enta

l str

uctu

res

in response to discrepancies, (See Flavell, 1963, for a

disc

ussi

on o

f Pi

aget

's th

eory

,) I

t is

also

ver

y si

mila

r to

the

prin

cipl

e th

at g

over

nslearning in the Rescorla- W

agne

r m

odel

of c

lass

ical

con

ditio

ning

(R

esco

rla &

;W

agne

r, 1

972)

. Wha

t is

new

is th

at th

ere

exis

ts a

lear

ning

pro

cedu

re f

or m

ulti-

laye

r co

nnec

tioni

st n

etw

orks

that

impl

emen

ts th

is p

rinc

iple

, Her

e, th

e pa

ram

eter

sof

the

min

d ar

e th

e co

nnec

tions

am

ong

the.

uni

ts in

the

netw

ork,

and

the

pr0-

cedu

re is

the

back

pro

paga

tion

proc

edur

e of

Rum

ellta

rt, H

into

n, a

nd W

illia

ms

(198

6),

The

lear

ning

pri

ncip

le li

es a

t the

hea

rt o

f a

num

ber

of c

onne

ctio

nist

mod

els

that

lear

n ho

w to

do

vari

ous

diff

eren

t kin

ds o

f in

fonn

atio

n pr

oces

sing

task

s, a

ndth

at h

ave

appl

icat

ions

to p

heno

men

a in

cog

nitiv

e an

d/or

lang

uage

dev

elop

men

t,Pe

rhap

s th

e si

mpl

est s

uch

mod

el is

the

past

-ten

se m

odel

of

Rum

ellta

rt a

ndM

cCle

lland

(19

86),

The

dev

elop

men

t of

that

mod

el p

reda

ted

the

disc

over

y of

the

back

pro

paga

tion

lear

ning

pro

cedu

re, t

here

by f

orci

ng c

erta

in s

impl

ific

atio

ns f

orth

e sa

ke o

f de

velo

ping

an

illus

trat

ion

of th

e ba

sic

poin

t tha

t law

ful b

ehav

ior

mig

ht e

mer

ge f

rom

the

appl

icat

ion

of a

sim

ple

prin

cipl

e of

lear

ning

to a

con

nec-

tioni

st n

etw

ork,

Sub

sequ

ent m

odel

s ha

ve u

sed

back

pro

paga

tion

to o

verc

ome

som

e of

thes

e lim

itatio

ns, I

nclu

ded

in th

is c

lass

are

NB

Tta

Ik(Sejnowski &;

Ros

enbe

rg, 1

987)

and

a m

ore

rece

nt m

odel

of

wor

d re

adin

g (P

atte

rson

, Sei

den-

berg

, &; M

cCle

lland

, 198

9), T

he p

rese

nt e

ffor

t gre

w o

ut o

f tw

o ob

serv

atio

ns o

fsi

mila

ritie

s be

twee

n th

e de

velo

pmen

tal c

ours

es s

een

in m

odel

s em

body

ing

this

prin

cipl

e, a

nd th

e co

urse

s of

dev

elop

men

t see

n in

chi

ldre

n: F

irst

, the

cou

rse

ofle

arni

ng. i

n a

rece

nt m

odel

of

conc

ept l

earn

ing

by R

umel

hart

(19

90)

is s

imila

r to

aspe

cts

of th

e pr

ogre

ssiv

e di

ffer

entia

tion

of c

once

pts

refl

ecte

d in

Kei

l's

(197

9)

stud

ies

of p

redi

ctab

ility

, Sec

ond,

the

cour

se o

f le

arni

ng in

a r

ecen

t mod

el

The

phe

nom

ena

revi

ewed

abo

ve r

aise

bas

ic q

uest

ions

abo

ut c

ogni

tive

deve

lop-

men

t. T

hree

of

thes

e qu

estio

ns a

re:

. Are these di

ffere

nt p

heno

men

a si

mpl

y IID

Iela

ted

fact

s ab

out d

evel

opm

ent i

ndi

ffer

ent d

omai

ns?

. Are there pr

inci

ples

that

all.

of

thes

e ph

enom

ena

exem

plif

y?th

ere

are

prin

cipl

es, a

re th

ey d

omai

n sp

ecif

ic, o

r ar

e th

ey g

ener

al p

rin-

cipl

es a

bout

dev

elop

men

t?

Dif

fere

nt k

inds

of

deve

lopm

enta

l the

oris

ts h

ave

answ

ered

suc

h qu

estio

ns in

very

dif

fere

nt w

ays,

To

Piag

et, e

ach

failu

re o

f co

mpe

nsat

ion

or c

onse

rvat

ion

refle

cted

a s

ingl

e co

mm

on de

velo

pmen

tal s

tage

; the

phe

nom

ena

wer

e in

bin-

sically related by the characteristicsof the stage, and these characteristics pr0-

vide

d th

e ba

sis

for

expl

anat

ion,

Others have taken a very di

ffer

ent a

ppro

ach,

Kei

l (197

9), f

ollo

win

gC

hom

sky

s analogous argument for language, argued for

dom

ain

spec

ific

pri

n-ci

ples

of

dev

elop

men

t. H

is v

iew

is th

at e

ach

cogn

itive

dom

ain

has.

its

own

law

sth

at p

rovi

de c

onst

rain

ts o

n w

hat c

an b

e le

arne

d, T

hese

con

stra

ints

lim

it th

ehy

poth

eses

that

the

child

can

ent

erta

in, t

here

by m

akin

g it

dram

atic

ally

eas

ier

for

the

child

to a

cqui

re a

dult

abili

ties

in th

e fa

ce o

f th

e im

pove

rish

ed in

form

atio

n th

atis

pro

vide

d by

exp

erie

nce

with

the

wor

ld,

..,;..

.;.:.;

.;;.w

-",...

.._~,

;.._

MC

CL

EL

lAN

D A

ND

JE

NK

INS

3. NATURE, NURTURE,

AN

D C

ON

NE

CT

10N

S47

.se

nten

ce c

ompr

ehen

sion

by

McC

1elJ

and,

St.

John

, and

18r

aban

(19

89)

milT

Ol'S

aspects of the progno:ssion from reliance on

sem

antic

con

stra

ints

, to

relia

nce

onw

ord

orde

r, to

, fin

ally

, rel

ianc

e on

com

plex

syn

tact

ic p

atte

rnin

g su

ch a

s th

epa

ssiv

e vo

ice,

We

do n

ot' m

ean

to c

laim

tha

t the

mod

els

in q

uest

ion

are

fulJ

yad

equa

te m

odel

s of

the

deve

lopm

enta

l pro

gres

sion

in e

ither

cas

e; w

e on

ly. m

ean

to c

laim

that

they

see

med

sug

gest

ive:

The

y ra

ised

the

poss

ibili

ty th

at p

art o

f th

eex

plan

atio

n of

thes

e an

d ot

her

deve

lopm

enta

l phe

nom

ena

mig

ht b

e fo

und

in th

eop

erat

ion

of th

e le

arni

ng p

rinc

iple

as

it ad

just

s co

nnec

tion

stre

ngth

s in

a n

etw

ork

subj

ecte

d to

pat

tern

s ar

isin

g in

its

envi

ronm

ent.

The

rem

aind

er o

f th

is c

hapt

er p

rese

nts

two

expe

rimen

ts a

sses

sing

the

ap-

plic

abili

ty o

f th

is c

onje

ctur

e to

ano

ther

dev

elop

men

tal p

heno

men

on, n

amel

y th

eac

quis

ition

of

the

abili

ty to

take

bot

h w

eigh

t and

dis

tanc

e in

to a

ccou

nt in

the

bala

nce

scal

e ta

sk d

escr

ibed

abo

ve, T

he ta

sk h

as b

een

stud

ied

exte

nsiv

ely

bySi

egle

r an

d hi

s co

lleag

ues

(Sie

gler

, 197

6, 1

981;

Sie

gler

& K

lahr, 1982), and

quite

a b

it is

kno

wn

abou

t it,

We

will

fir

st r

evie

w th

e de

velo

pmen

tal f

indi

ngs,

The

n w

e w

ill d

escr

ibe

a co

nnec

tioni

st m

odel

that

cap

ture

s th

ese

phen

omen

a by

appl

ying

the

lear

ning

pri

ncip

le s

tate

d ab

ove

(McC

1eU

and,

198

9), A

s a

follo

w-u

p,w

e w

ill d

escr

ibe

a se

cond

mod

el th

at c

aptu

res

effe

cts

of s

peci

fic

expe

rien

ce o

nde

velo

pmen

tal c

hang

e (J

enki

ns, 1

986)

,

. Conflict, Here both weight and distance di

ffer

and

are

in c

onfl

ict,

in th

at th

ew

eigh

tis g

reat

er o

n on

e si

de b

ut th

e di

stan

ce f

rom

the

fulc

rum

is g

reat

er o

nth

e ot

her,

The

re a

re th

ree

type

s of

con

flict

pro

blem

s:. Conflict-weight. In these ca

ses,

the

side

with

the

grea

ter

wei

ght h

as th

egr

eate

r to

rque

(th

at is

, the

gre

ater

val

ue o

f th

e pr

oduc

t of

wei

ght t

imes

dist

ance

),. Conflict-di

stan

ce, I

n th

ese

case

s, th

e si

de w

ith th

e gr

eate

r di

stan

ce h

asthe greater torque,

. Conflict-ba

lanc

e, H

ere

the

torq

ues

are

the

sam

e on

bot

h si

des,

DE

VE

LOP

ME

NT

OF

JU

DG

ME

NT

S O

F B

ALA

NC

E

Sieg

ler

s an

alys

is o

f ch

ildre

ns

perf

orm

ance

ass

umed

that

chi

ldre

n us

e ro

le-

governed procedures, Four such procedures or

rule

s as

Sie

gler

cal

led

them

are

show

n in

Fig

, 3,3

, Eac

h of

thes

e roles corresponds to a distinct pattern of

pedo

rman

ce o

ver

the

six

prob

lem

type

s, F

or e

xam

ple,

chi

ldre

n us

ing

Rul

e I

shou

ld s

ay th

e si

de w

ith th

e gr

eate

r w

eigh

t will

go

dow

n in

wei

ght p

robl

ems

and

in a

ll th

ree

type

s of

con

flic

t pro

blem

s, T

hey

shou

ld th

ink

the

scal

e w

ill b

alan

ceon

bal

ance

pro

blem

s an

d di

stan

ce p

robl

ems,

In

gene

ral,

the

map

ping

fro

m th

ero

les

to e

xpec

ted

pedo

rman

ce is

ext

rem

ely

stta

ight

forw

ard,

The

onl

y po

int t

hat

needs explication is the instruction

muddle through

whe

n w

eigh

t and

dis

tanc

eco

nflic

t in

Rul

e 3,

In

prac

tice

it is

ass

umed

to m

ean

" gue

ss r

ando

mly

am

ong

the

alte

rnat

ives

," so that 1/3 of the responses w

ould

be

left

-sid

e-do

wn;

1/3

. rig

ht-

side

-dow

n, a

nd 1

/3 b

alan

ce,

Sieg

ler

com

pare

d th

e pe

dorm

ance

of

each

chi

ld te

sted

with

eac

h ro

le, a

ndco

unte

d di

scre

panc

ies

from

pre

dict

ed p

erfo

rman

ce b

ased

on

the

role

, Chi

ldre

nw

ho s

core

d le

ss th

an f

our

disc

repa

ncie

s fr

om a

giv

en r

ole

wer

e sc

ored

as

usin

gth

at r

ole,

For

our

pur

pose

s, th

ere

are

four

bas

ic fm

ding

s th

at e

mer

ge fr

om S

iegl

eran

alys

is:

In a

n im

port

ant m

onog

raph

, Sie

gler

(19

81)

stud

ied

child

ren

s pe

dorm

ance

in th

eba

lanc

e sc

ale

task

and

thre

e ot

her

task

s in

whi

ch tw

o cu

es h

ad to

be

take

n in

toac

coun

t for

cor

rect

ped

orm

ance

, In

all c

ases

, as

in th

e ba

lanc

e sc

ale

task

, the

corr

ect p

roce

dure

req

uire

s m

ultip

licat

ion,

For

exa

mpl

e, in

the

bala

nce

scal

e ta

skto

det

erm

ine

whi

ch s

ide

will

go

dow

n, o

ne m

ust m

ultip

ly th

e am

ount

of

wei

ght

on a

giv

en s

ide

of th

e be

am ti

mes

the

dist

ance

of

that

wei

ght f

rom

the

fulc

rom

,T

he s

ide

with

the

grea

ter

prod

uct w

ill g

o do

wn;

whe

n th

e pr

oduc

ts a

re th

e sa

me,

the

beam

will

bal

ance

,Si

egle

r st

udie

d ch

ildre

n in

sev

eral

age

gro

ups,

as

wel

J as

you

ng a

dults

, Eac

hch

ild w

as a

sked

to ju

dge

24 b

alan

ce p

robl

ems,

In

each

cas

e, th

e sc

ale

was

imm

obili

zed

so th

at th

ere

was

no

feed

back

, The

24

prob

lem

s co

uld

be d

ivid

edinto four of each six types:

. Balance, In th

is c

lass

of

prob

lem

, the

wei

ght i

s th

e sa

me

on b

oth

side

s of

the

scal

e an

d th

e w

eigh

t is

the

sam

e . dis

tanc

e fr

om th

e fu

lcro

m on both

side

s.

. Weight. In these problems, the weights di

ffer

but d

ista

nce

from

the

fulc

rom

is th

e sa

me

on b

oth

side

s,. Distance, Here the weight is

the

sam

e on

bot

h si

des,

but

the

dist

ance

fro

mth

e fu

lcro

m d

iffer

s.

I, Lawful behavior, In general, performance of children over the age of

extr

emel

y re

gula

r in

the

bala

nce

scal

e ta

sk, O

vera

ll ab

out 9

0% o

f ch

ildre

n te

sted

conf

orm

to o

ne o

f th

e fo

ur r

oles

,

2, Developmental pr

ogre

ssio

n. A

s ch

ildre

n ge

t old

er, t

hey

appe

ar to

pro

gres

sth

roug

h th

e us

e of

the

diff

eren

t rol

es, T

he p

rogr

essi

on f

rom

Rul

e I

to R

ule

3 ca

nbe thought of as a progression in which at fa

rst t

he '

wei

ght c

ue is

,re

lied

onex

clus

ivel

y, w

hile

at t

he e

nd d

ista

nce

and

wei

ght a

re b

oth

take

n in

to a

ccou

nt, I

nbe

twee

n (R

ule

2), d

ista

nce

is, t

aken

into

acc

ount

onl

y if

it d

oes

not c

onfl

ict w

iththe weight cue, Children aged

to 7

typi

cally

use

Rul

e I,

and

col

Jege

stu

dent

sty

pica

lly u

se r

ules

3 o

r 4,

Man

y co

lJeg

e st

uden

ts d

o no

t hav

e ex

plic

it kn

owle

dge

of th

e to

rque

prin

cipl

e, ,

Children younger than age

tend not to be scorable

stri

ctly

in te

rms

of o

ne o

f th

e ru

les;

how

ever

, the

y ap

pear

to s

how

an

incr

easi

ngte

nden

cy to

beh

ave

in a

ccor

danc

e w

ith R

ule

1,

"'-'-

'

-:'o

'-"""

"'~"

-

'-"

.. '

~" ,.;... ._=

--..~

=...

.....,

"'-

FIG

. 3. 3

. Siegler's (1976, 1981) four "ru

les "

for

ans

wer

ing

bala

nce

acal

e pr

oble

ms.

Eac

h R

ule

Is I

n fa

ct a

ful

l Pro

cedu

re, r

athe

r th

an a

sing

le r

ule.

Rep

rint

ed w

ith p

erm

issi

on f

rom

Sie

gler

1198

1), F

ig. 1

.3. Generality. The sa

me

four

rul

es a

ppea

r to

be

adeq

uate

to c

hara

cter

ize

perf

onna

nce

in a

ll th

ree

of th

e do

mai

ns th

at S

iegl

er s

tudi

ed. T

houg

h th

e de

velo

p-m

enta

l pro

gres

sion

was

not

iden

tical

acr

oss

dom

ains

, the

re w

as in

aU

cas

es a

tren

d fr

om s

impl

er to

mor

e co

mpl

ex r

ules

with

dev

elop

men

t.

4. Lack

of

corr

elat

ion

betw

een

dom

ains

. Eve

n th

ough

chi

ldre

n se

em to

pro

g-re

ss th

roug

h th

e sa

me

rule

s in

dif

fere

nt d

omai

ns, t

hey

do n

ot d

o so

in lo

ck-s

tep;

the correlation across domains is low, particularly in tenns.

of

the

high

er-n

um-

&t(

JMCCLELLAND AND JENKINS

3. NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S

Rul

.Dbe

red

rule

s, s

o th

at c

hild

ren

who

are

sho

win

g R

ule

3 be

havi

or in

one

task

may

be

show

ing

Rul

e I

beha

vior

in a

noth

er a

nd R

ule

4 in

a th

ird.

Rul

.I

The

mod

el w

e de

scri

be h

ere

was

dev

elop

ed b

y M

cCle

lland

(19

89).

It i

s ba

sed

onea

rlie

r w

ork

by J

enki

ns (

1986

) re

leva

nt to

oth

er a

spec

ts o

f Si

egle

rs

data

(Si

egle

r,19

76; S

iegl

er &

: Kla

hr, 1

982)

to w

hich

we

will

turn

our

atte

ntio

n be

low

.T

he m

odel

is s

ketc

hed

in F

ig. 3

. 4. O

f co

urse

, the

mod

el is

a d

rast

ic o

ver-

sim

plif

icat

ion

of

the human mind and

of

the

task

; but

as

we

shal

l see

it a

llow

s us

to capture the essence

of

Sieg

ler

s fl

Ddi

ngs,

and

to s

ee th

em e

mer

ge f

rom

the

oper

atio

n of

th

e le

arni

ng p

rinc

iple

des

crib

ed a

bove

.The model consists

of

a set

of

inpu

t uni

ts, t

o w

hich

bal

ance

pro

blem

s ca

n be

presented as patterns of inputs; a set

of

outp

ut u

nits

ove

r w

hich

the

answ

er to

MO

DE

L O

F T

HE

BA

SIC

PH

EN

OM

EN

A

ellm

.nII

Oll-

,rea

'..

."-,

ell"

'.IIO

II - "'0'"

Rul

.m

.quo

l'uborelln... ellm..llon-Great.r

!!!!

!!l!

ell_

"OII

_,r.

....

Dis

tanc

e

IIul

.m

Wei

ght

'.UI'

lube

rell.

..,.

elO

I8ln

o.'

ellm

..llo

..

----

---

-....

ell.'

.,'on

ell..

...,O

IIC

""cl

I,-"

"'Ir

-"'0

'1'

0001

001

000

FIG

. 3. 4. The network used in

the

sim

ulat

ion

of th

e de

velo

pmen

t of

perf

orm

ance

in th

e ba

lanc

e ac

ale

task

.

-.--

-...

.--.

~..

.--.

.---

-...,

---.-

-. -

-..-

--'-

......

.-.-

---_

n-

MCCLELLAND AND JENKINS

3, NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S

each

pro

blem

can

be

repr

esen

ted;

and

a s

et o

f hi

dden

uni

ts. b

etw

een

the

inpu

t and

the

outp

ut. C

onne

ctio

ns I

Un

from

inpu

t utli

ts to

hid

den

units

and

fro

m h

idde

nun

its to

out

put u

nits

,The input units can be divided into two groups of

10,

One

gro

up is

use

d to

repr

esen

t inf

onna

tion

abou

t wei

ght a

nd th

e ot

her

is u

sed

to r

epre

sent

info

nnat

ion

abou

t dis

tanc

e, I

n ea

ch c

ase

the

inpu

t rep

rese

ntat

ion

impo

ses

as li

ttle

sbuc

ture

as

poss

ible

on

the

inpu

t pat

tern

s, E

ach

poss

ible

val

ue o

f w

eigh

t or

dist

ance

fro

m th

efu

lcru

m is

ass

igne

d a

sepa

rate

uni

t. T

he o

rder

ing

of v

alue

s fr

om lo

w to

hig

h is

not g

iven

in th

is r

epre

sent

atio

n; th

e ne

twor

k w

ill h

ave

to le

arn

this

ord

erin

g, F

orth

e co

nven

ienc

e of

the

read

er. t

he u

nits

are

arr

ange

d in

row

s ac

cord

ing

to w

hich

side

of

the

beam

they

are

fro

m. a

nd w

ithin

eac

h ro

w th

ey a

re a

rran

ged

from

left

to right in order of increasing w

eigh

t or

dist

ance

fro

m th

e fu

lcru

m; b

ut th

isor

deri

ng is

unk

now

n to

the

mod

el b

efor

e it

is tr

aine

d , as

we

shal

l see

,Though the two dimensions are not inbinsically sbuctured

for

the

mod

el, t

hede

sign

of

the

netw

ork

does

impo

se a

sep

arat

e an

alys

is o

f ea

ch dimension~ This

separation turns out to be cr

itica

l; w

e w

ill c

onsi

der

the

impl

icat

ions

of

this

arch

itect

ural

sim

plif

icat

ion

belo

w, T

he s

epar

atio

n is

impl

emen

ted

as f

ollo

ws:

there are separate pairs of hidden units

for

each

dim

ensi

on, 1

\vo

hidd

en u

nits

rece

ive

inpu

t fro

m th

e w

eigh

t inp

ut u

nits

and

two

rece

ive

inpu

t fro

m th

e di

stan

cein

put u

nits

,E

ach

of th

e fo

ur h

idde

n un

its p

roje

cts

to e

ach

of th

e tw

o ou

tput

uni

ts, T

he le

ftoutput unit can be thought of as a "le

ft s

ide

dow

n"

unit.

and

the

righ

t one

as

ari

ght s

ide

dow

n un

it."

Thu

s a

corr

ect n

etw

ork

for

the

task

wou

ld tu

rn o

n th

eou

tput

uni

t cor

resp

ondi

ng to

the

side

with

the

grea

ter

torq

ue, a

nd w

ould

turn

off

the

unit

for

the

bthe

r si

de, F

or b

alan

ce pr

oble

ms,

we

assu

me

that

the

netw

ork

shou

ld tu

rn b

oth

units

on

half

-way

, Not

e th

at th

is c

odin

g of

the

outp

ut p

atte

rns

does

tell

the

netw

ork

that

bal

ance

is b

etw

een

left

sid

e do

wn

and

righ

t sid

e-do

wn,

Proc

essi

ng,

Bal

ance

pro

blem

s of

the

kind

stu

died

by

Sieg

ler

can

be p

r0-

cess

ed b

y th

e ne

twor

k by

sim

ply

turn

ing

on (

i,e"

setting to 1) the input units

corr

espo

ndin

g to

a p

artic

ular

pro

blem

and

turn

ing

off

(i, e

" setting

to

0) a

ll ot

her

inpu

t uni

ts, T

he in

put f

rom

the

prob

lem

illus

trat

ed in

Fig

ure

3,7

is s

how

n by

usin

g bl

ack

to in

dica

te th

ose

inpu

t uni

ts w

hose

act

ivat

ions

are

1, 0

, and white

for

the

units

who

se a

ctiv

atio

ns a

re 0

,T

he in

puts

are

prop

agat

ed f

orw

ard

to th

e hi

dden

uni

ts, E

ach

hidd

en u

nit

sim

ply

com

pute

s a

net i

nput

:

In ~

se eq

uations. W

IJ is

the

stre

ngth

of

the

conn

ectio

n to

hid

den

unit

i fro

minput unitj,

is the activation of input unitj, and bias, i

s th

e m

odif

iabl

e bi

as o

fhidden unit

i, This bias is equivalent

to

a w

eigh

t to

unit

i fro

m a

spe

cial

uni

t tha

tis

alw

ays

on,

Onc

e ac

tivat

ions

of t

he h

idde

n un

its a

re d

eten

nine

d, th

e ac

tivat

ions

of t

heoutput units are detennined by the same procedure, That is. the net input

to

each

outp

ut u

nit i

s de

tenn

ined

bas

ed o

n th

e ac

tivat

ions

of

the

hidd

en u

nits

. the

wei

ghts

from

the

hidd

en u

nits

to th

e ou

tput

uni

ts, a

nd th

e bi

ases

of

the

outp

ut u

nits

, The

nth

e ac

tivat

ions

of

the

outp

ut. u

nits

are

det

enni

ned

usin

g th

e lo

gist

ic f

unct

ion,

Res

pons

es,

The

act

ivat

ions

of

the

outp

ut u

nits

are

rea

l num

bers

bet

wee

n 0

and

I; to

relate its perfonnance

to

the

bala

nce

scal

e ta

sk. t

hese

rea

l-val

ued

outp

uts

mus

t be

tran

slat

ed in

to d

iscr

ete

resp

onse

s, I

f th

e ac

tivat

ion

of o

ne o

utpu

tun

it ex

ceed

ed th

e ac

tivat

ion

of th

e ot

her

by ,

333, the answer was taken

to

mor

e ac

tive

side

dow

n,"

Oth

erw

ise,

the

answ

er w

as a

ssum

ed to

be

" bot

h si

des

equa

l, "

Lea

rnin

g.

Bef

ore

trai

ning

beg

ins.

the

stre

ngth

s of

thes

e co

nnec

tions

fro

min

put t

o hi

dden

uni

ts a

nd f

rom

hid

den

to o

utpu

t uni

ts a

re in

itial

ized

to r

ando

mva

lues

uni

fonn

ly d

isbi

bute

d be

twee

n +

, 5 a

nd -

,5,

In

this

sta

te. i

nput

s le

ad to

rand

om p

atte

rns

of a

ctiv

ity o

ver

both

the

hidd

en a

nd o

utpu

t uni

ts, '

lbe

activ

atio

nsof

the

outp

ut u

nits

flu

ctua

te a

ppro

xim

atel

y ra

ndom

ly b

etw

een

abou

t ,4

and

;6 f

ordi

ffer

ent i

nput

pat

tern

s, T

he n

etw

ork

com

es to

res

pond

cor

rect

ly o

nly

as a

res

ult

of tr

aini

ng, C

once

ptua

lly. t

rain

ing

is th

ough

t of

as o

ccur

ring

as

a re

sult

of a

ser

ies

of e

xper

ienc

es in

whi

ch th

e ne

twor

k is

sho

wn

a ba

lanc

e pr

oble

m a

s in

put;

com

pute

s ac

tivat

ions

of

outp

ut p

atte

rns

base

d on

its

exis

ting

conn

ectio

n w

eigh

ts;

and

is th

en s

how

n th

e co

rrec

t ans

wer

, 'lb

e si

gnal

that

dri

ves

lear

ning

is th

edi

ffer

ence

bet

wee

n th

e ob

tain

ed a

ctiv

atio

n of

eac

h ou

tput

uni

t and

the

corr

ect o

rta

rget

act

ivat

ion

for

that

uni

t, T

he b

ack-

prop

agat

ion

proc

edur

e of

Rum

elha

rt,

Hin

ton.

and

Will

iam

s (1

986)

is th

en u

sed

to d

eten

nine

how

eac

h co

nnec

tion

stre

ngth

in th

e ne

twor

k sh

ould

be

adju

sted

to r

educ

e th

ese

diff

eren

ces,

Sin

ce th

e

proc

edur

e is

qui

te w

ell-

know

n. s

uffi

ce it

to s

ay th

at it

exa

ctly

impl

emen

ts th

ele

arni

ng p

rinc

iple

sta

ted

abov

e, a

nd r

esta

ted

here

in n

etw

ork

tenn

inol

ogy:

Adj

ust e

ach

wei

ght i

n th

e ne

twor

tc in

pro

port

iOD

to th

e ex

tent

to w

hich

its

adju

st-

men

t can

pro

duce

a n

xluc

tion

in th

e di

scre

panc

y be

twee

n th

e ex

pect

ed e

vent

8D

d

the observed event, in the present context, --

net, = ~

+ b

ias

Her

e j r

ange

s ov

er th

e in

put u

nits

, Eac

h hi

dden

uni

t the

n se

ts it

s ac

tivat

ion

acco

rdin

g to

th

e lo

gist

ic fu

nctio

n:

= I

n"'

Here the "ex

pect

ed e

vent

" is

the

patte

rn o

f ac

tivat

ion

over

the

outp

ut u

nits

that

is c

ompu

ted

by th

e ne

twor

k , th

e ob

serv

ed e

vent

is th

e pa

ttern

of a

ctiv

atio

nth

e en

viro

nmen

t ind

icat

es th

ese

units

hav

e. a

nd th

e pr

esen

t con

text

is th

e pa

ttern

of a

ctiv

atio

n ov

er th

e in

put u

nits

, Not

e th

at th

e di

rect

ion

of c

hang

e to

a c

onne

c-tio

n (p

ositi

ve o

r ne

gativ

e) is

sim

ply

the

dire

ctio

n th

an te

nds

to r

educ

e th

e di

s-cr

epan

cy b

etw

een

com

pute

d ou

tput

and

the

corr

ect o

r ta

rget

out

put,

-_.. "

""':'

""'._

-"4-

-"

';;-';

'_;"

'._.~

,,

MC

CL

EL

lAN

D A

ND

JE

NK

INS

3. NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

SE

nvir

onm

ent,

The

env

ironm

ent i

n w

hich

a n

etw

ork

lear

ns p

lays

a v

ery

stro

ng r

ole

in d

eten

nini

ng w

hat i

t lea

rns,

and

part

icul

arly

the

deve

lopm

enta

lco

urse

of

lear

ning

, The

sim

ulat

ions

rep

orte

d he

re w

ere

base

d on

the

assu

mpt

ion

that

the

envi

ronm

ent f

or le

arni

ng a

bout

bal

ance

pro

blem

s co

nsis

ts o

f ex

peri

ence

sth

at v

ary

mor

e fr

eque

ntly

on

the

wei

ght d

imen

sion

than

they

do

on th

e di

stan

cedi

men

sion

. Of c

ours

e, w

e do

not

mea

n to

suggest that all the learning that

child

ren

do th

at is

rel

evan

t to

thei

r un

ders

tand

ing

of b

alan

ce ta

kes

the

fonD

of

expl

icit

bala

nce

prob

lem

s of

the

kind

OlD

' ne

twor

k se

es, R

athe

r, o

ur a

ssum

ptio

nth

at th

e ex

peri

ence

on

bala

nce

prob

lem

s is

dom

inat

ed b

y pr

oble

ms

in w

hich

ther

eis

no

vari

abili

ty in

wei

ght i

s m

eant

as

a pr

oxy

for

the

mor

e ge

nera

l ass

umpt

ion

that

chi

ldre

n ge

nera

lly h

ave

mor

e ex

peri

ence

s w

ith w

eigh

t tha

n w

ith d

ista

nce

as a

factor in detennining the relative heaviness of something, I

The

spe

cifi

c as

sum

ptio

ns a

bout

the

sequ

ence

ofl

eam

ing

expe

rien

ces

wer

e as

follo

ws,

The

env

iron

men

t con

sist

ed o

f a

list o

f tr

aini

ng e

xam

ples

con

tain

ing

the

full

set o

f 62

5 po

ssib

le p

robl

ems

invo

lvin

g 25

com

bina

tions

of

poss

ible

wei

ghts

(I to

5 o

n th

e le

ft c

ross

ed w

ith 1

to 5

on

the

righ

t) c

ross

ed w

ith 2

5 co

mbi

natio

nsof

pos

sibl

e di

stan

ces

(1 to

5 s

teps

fro

m th

e fu

lcru

m o

n th

e le

ft c

ross

ed w

ith I

to 5

step

s fr

om th

e fu

lcru

m o

n th

e ri

ght)

, 1\v

o C

Orp

ora

wer

e se

t up.

Pro

blem

s in

whi

chth

e di

stan

ce f

rom

the

fulc

rum

was

the

sam

e on

bot

h si

des

wer

e lis

ted

5 tim

es e

ach

in o

ne c

orpu

s, a

nd 1

0 tim

es e

ach

in th

e ot

her

corp

us. O

ther

pro

blem

s w

ere

liste

don

ly o

nce

in e

ach

corp

us.

Training and testing regime.

rour simulatiM

. run

s w

ere

cmie

d ou

t, tw

ow

ith e

ach

of th

e tw

o co

rpor

a ju

st d

escr

ibed

, In

each

run

, tra

inin

g co

nsis

ted

of a

seri

es o

f ep

ochs

, In

each

epo

ch, 1

00 p

atte

rns

wer

e ch

osen

ran

dom

ly f

rom

the

full

list o

f pa

ttern

s in

the

corp

us, I

n ea

ch e

poch

, wei

ght i

ncre

men

ts w

ere

accu

mu1

ated

over

the

100

trai

ning

tria

ls a

nd th

en a

dded

into

the

wei

ghts

at t

he e

nd o

f th

eep

och,

acc

ordi

ng to

the

mom

entu

m m

etho

d de

scri

bed

in R

umel

han,

Hin

ton,

and

Will

iam

s (1

986

p~ 3

30);

par

amet

ers

wer

e T

I = 0

,075

,

= ,

9),

Aft

er w

eigh

t upd

atin

g at

the

end

of e

ach

epoc

h, th

e ne

twor

k w

as g

iven

a 2

4ite

m te

st, c

onta

inin

g fo

ur p

robl

ems

of e

ach

of th

e si

x ty

pes

desc

ribe

d ab

ove,

take

n fr

om a

n ex

peri

men

t of

Sieg

ler

s, (

A f

ew o

f th

e ex

ampl

es h

ad to

be

mod

i-fi

ed s

ince

Sie

gler

s ex

peri

men

t had

use

d up

to s

ix p

egs,

Environment Assumption,

The

mod

el a

ssum

es th

at th

e en

viro

nmen

t is

bias

ed, s

o th

at o

ne d

imen

sion

-. t

his ca

se w

eigh

t-is

mor

e fr

eque

ntly

ava

il-ab

le a

s a

basi

s fo

r pr

edic

ting

outc

ome

than

the

othe

r,

Architecture Assumption,

The

mod

el a

ssum

es th

at th

e w

eigh

t and

dis

tanc

edi

men

sion

s ar

e an

alyz

ed s

epar

atel

y, b

efor

einf

onna

tion

abou

t the

two

dim

ensi

ons

is c

ombi

ned,

Bot

h of

thes

e as

sum

ptio

ns a

re c

ruci

al to

the

succ

ess

of th

e m

odel

. In

unbi

ased

env

iron

men

t, bo

th c

ues

wou

ld b

e le

arne

d eq

ually

rap

idly

, Eff

ects

of

com

bini

ng th

e cu

es f

rom

the

star

t as

pres

crib

ed b

y th

e ar

chite

ctur

e as

sum

ptio

nar

e m

ore

com

plex

, but

suf

fice

it to

say

for

now

that

the

appa

rent

sta

gelik

ech

arac

ter

of p

erfo

nnan

ce is

muc

h le

ss c

lear

unl

ess

this

ass

umpt

ion,

is a

dopt

ed,

An

impo

rtan

t top

ic f

or f

urth

er r

esea

rch

will

be

to e

xam

ine

wha

t var

iant

s of

thes

e as

sum

ptio

ns m

ight

stil

l allo

w th

e m

odel

to b

e su

cces

sful

. For

exa

mpl

e,re

gard

ing

the

envi

ronm

ent,

diff

eren

ces

in s

alie

nce

(i.e

" st

reng

th o

f in

put a

ctiv

a-tio

ns)

and

stru

ctur

edne

ss o

f th

e di

men

sion

s m

ight

als

o pr

oduc

e si

mila

r re

sults

.T

he is

sue

of s

truc

ture

dnes

s of

the

dim

ensi

ons

is a

key

poi

nt th

at n

eeds

to b

eco

nsid

ered

as

it re

late

s to

the

pres

ent s

imul

atio

n, F

or b

oth

dim

ensi

ons,

the

inpu

tre

pres

enta

tions

enc

ode

diff

eren

t wei

ghts

and

dis

tanc

es f

rom

the

fulc

rum

usi

ngdi

stin

ct u

nits

, Thi

s m

eans

that

dif

fere

nt v

alue

s ar

e di

stin

guis

habl

e by

the

mod

el,

but t

hey

are

not s

truc

ture

d fo

r it;

for

exa

mpl

e th

e in

put i

tsel

f pr

ovid

es n

o in

dica

-tio

n th

at a

dis

tanc

e or

wei

ght o

f 3

is b

etw

een

2 an

d 4,

The

net

wor

k m

ust l

earn

tore

pres

ent t

he w

eigh

ts a

nd d

ista

nces

in s

truc

ture

d w

ays

in o

rder

to s

olve

the

bala

nce

prob

lem

, We

will

see

that

it d

oes

this

late

r.

Res

ults

In g

ener

al p

erfo

nnan

ce o

f the

mod

el c

onfo

oned

to o

ne o

f thd

four

rul

es d

escr

ibed

by S

iegl

er, O

ver

the

fOlD

' run

s, th

e m

odel

fit

the

crite

ria

of o

ne o

f Si

egle

rs

four

role

s on

85%

of

the

occa

sion

s, n

ot c

ount

ing

an in

itial

pre

- Rul

e 1

perio

d (I

nSi

egle

r, 1

981,

the

conf

onni

ty f

igur

e is

abo

ut 9

0%),

Of

cour

se, t

he m

odel

was

not

cons

ultin

g th

ese

rule

s or

fol

low

ing

the

step

-by-

step

pro

cedu

res

indi

cate

d in

them

;ra

ther

its

beha

vior

was

sim

ply

scor

able

by

Sieg

ler

s cr

iteri

a as

con

sist

ent w

ith th

esu

cces

sion

of

rule

s, E

xclu

ding

the

initi

al p

erio

d, f

ailu

res

to f

it th

e na

tes

wer

e of

thre

e ty

pes:

Cas

es in

whi

ch a

nat

e fi

t exc

ept f

or a

pos

ition

bia

s th

at g

ave

diff

icul

tyon

bal

ance

pro

blem

s, c

ases

in w

hich

per

fonn

ance

was

bor

derl

ine

betw

een

Rul

esI

and

II, a

nd c

ombi

natio

ns o

f th

ese

two

prob

lem

s, (

Sieg

ler

(per

sona

l com

mun

ica-

tion)

doe

s fi

nd s

ome

bord

erlin

e ca

ses

betw

een

Rul

e la

nd R

ule

2, b

ut th

e po

sitio

nbi

as c

ases

are

not

typi

cal o

f ch

ildre

ns

perf

onna

nce.

Overall Developmental Trends.

Epo

ch b

y ep

och

perf

onna

nce

in e

ach

of th

efO

lD'ru

ns is

sho

wn

in F

igs,

3, 5

and

3,6

, One

gen

eral

ly o

bser

ves

the

expe

cted

deve

lopm

enta

l pro

gres

sion

, Eac

h si

mul

atio

n nm

is s

light

ly d

iffe

rent

, due

todi

ffer

ence

s in

the

rand

om s

tart

ing

wei

ghts

and

the

sequ

ence

of

actu

al tr

aini

ng

A C

omm

ent o

n th

e S

imul

atio

n M

odel

The

mod

el d

escr

ibed

abo

ve o

bvio

usly

sim

plif

ies

the

task

that

the

lear

ner

face

s an

dst

ruct

ures

it f

or h

im to

som

e de

gree

. In

part

icul

ar, i

t em

bodi

es tw

o pr

inci

pal a

s-su

mpt

ions

whi

ch a

re c

ruci

al to

the

succ

essf

ul s

imul

atio

ns w

e w

ill c

onsi

der

belo

w:

IAn

alte

rnat

ive

assu

mpt

ion

whi

ch m

ight

acc

ount

for

the

deve

lopm

eara

l dat

a ju

st u

wel

l is

the

888WDption that the weight dimension is IR-SIntcIuJed before th

e ch

ild c

omes

to c

onsi

der

bala

nce

prob

lem

s, w

hile

the

dist

ance

dim

ensi

on is

IlO

l, T

he a

ssum

ptio

n th

at d

ista

nce

vari

es le

ss f

requ

endy

titan

wei

ght b

ut th

at n

eith

er d

imea

sion

is in

itial

ly s

truc

ture

d al

low

s us

to ob

seJV

e th

e st

nJct

1ain

gpt

'O(:

CSS

for

bot

h di

men

sioa

s,

RU

LES

BY

EP

OC

H: R

UN

-y::-

-

('I)

- --

-! -

- --

----

..J :J N

!!!

----

~--

100

Epo

ch

RU

LES

BY

EP

OC

H: R

UN

2

....

('I)

..J :J N

! !!-

..!!.

.!!

! -

0 1-

----

100

Epo

ch

FIG

. 3, 5. Epoch by epoch performance of th

e si

mul

atio

n m

odel

in th

etw

o ru

ns w

ith a

5 to

1 b

ias

favo

ring

pro

blem

s in

whi

ch d

ista

nce

did

not

vary

. Per

form

ance

is s

core

d by

Rul

e. C

ases

mar

ked

by .

mis

sed

a ru

ledu

e to

pos

ition

bia

s, R

ule

0 co

rres

pond

s to

alw

ays

sayi

ng "

bala

nce,

and

occu

rs a

t the

beg

inni

ng o

f tra

inin

g, R

ule

1.5

corr

espo

nds

to p

erfo

r-m

ance

on

the

bord

erlin

e be

twee

n R

ules

1 a

nd 2

,

3. NATURE. NURTURE,

AN

D C

ON

NE

CT

ION

S

expe

rien

ces,

but

ther

e ar

e cl

ear

com

mon

tren

ds. O

ver

the

rust

10

epoc

hs o

r so

,the output of the model was close to .

on a

ll te

st p

atte

rns;

by

our

scor

ing

crite

ria,

all o

f th

ese

outp

uts

coun

t as

"bal

ance

" re

spon

ses,

but

of

cour

se th

ey r

eally

repr

esen

t a s

tage

in w

hich

nei

ther

wei

ght n

or d

ista

nce

gove

rns

perf

onna

nce.

The

next

few

epo

chs

repr

esen

t a tr

ansi

tion

to R

ule

I, in

that

in th

is p

hase

the

mod

el is

show

ing

som

e te

nden

cy to

act

ivat

e th

e ou

tput

uni

t on

the

side

with

the

grea

ter

wei

ght,

but t

his

tend

ency

is v

aria

ble

acro

ss p

atte

rns

and

the

disc

repa

ncy

betw

een

Nth

e ac

tivat

ions

of

the

outp

ut u

nits

is n

ot r

elia

bly

grea

ter

than

.33

whe

n th

e

weights differ.

Aft

er th

is b

rief

tran

sitio

n, p

erfo

rman

ce o

f th

e m

odel

has

gen

eral

ly r

each

ed th

e

poin

t whe

re it

was

res

pond

ing

cons

iste

ntly

to th

e w

eigh

t cue

whi

le s

yste

mat

ical

lyig

nori

ng th

e di

stan

ce d

imen

sion

. Thi

s pa

ttern

con

tinue

d fo

r se

vera

l mor

e ep

ochs

.T

here

was

a b

rief

tran

sitio

nal p

erio

d, in

whi

ch th

e m

odel

beh

ave

inco

nsis

tent

lyon the

dist

ance

pr

oble

ms

croc

ial t

o di

stin

guis

hing

bet

wee

n R

ule

1 an

d R

ule

2 be

havi

or. A

fter

sev

eral

epo

chs

in th

is p

hase

, use

of

the

dist

ance

cue

rea

ched

the

poin

t whe

re p

erfo

rman

ce o

n al

l typ

es o

f co

nflic

t pro

blem

s be

cam

e va

riab

le.

The

mod

el g

ener

ally

con

tinue

d in

this

pha

se in

defi

nite

ly, s

omet

imes

rea

chin

g th

e

poin

t whe

re it

s pe

rfon

nanc

e w

as g

ener

ally

sco

rabl

e as

fitt

ing

Rul

e 4

and

som

e.tim

es n

ot.

The

var

iabi

lity

in th

e m

odel

's p

erfo

rman

ce f

rom

epo

ch to

epo

ch is

act

ually

quite

con

sist

ent w

ith te

st-r

etes

t dat

a re

port

ed in

Sie

gler

(19

81),

Rul

e 2

beha

vior

is h

ighl

y un

stab

le, a

nd th

ere

is s

ome

inst

abili

ty o

f be

havi

or in

oth

er r

oles

as

wel

l.

Performance in each phase.

Sieg

ler

s cr

iteri

a fo

r co

nfor

mity

to h

is r

oles

allo

w f

or s

ome

devi

atio

ns f

rom

per

fect

con

form

ity; i

n fa

ct o

nly

83%

of

test

prob

lem

s m

ust b

e sc

orab

le a

s co

nsis

tent

with

the

role

. Giv

en th

is, i

t is

inte

rest

ing

to s

ee w

heth

er th

e di

scre

panc

ies

from

the

role

s th

at a

re e

xhib

ited

by th

e m

odel

are

cons

iste

nt w

ith h

uman

sub

ject

's p

erfo

rman

ce. I

n ge

nera

l, th

ey s

eem

to b

e

quite consistent, as Fig. 3.7

indi

cate

s. E

ach

pane

l sho

ws

perc

ent c

orre

ct p

erfo

r-

mance by the model av

erag

ed o

ver

the

test

s on

whi

ch th

e m

odel

sco

red

inac

cord

ance

with

one

of

the

four

rol

es. A

lso

show

n ar

e da

ta f

rom

two

grou

ps o

fhu

man

sub

ject

s as

wel

l as

the

patte

rn o

f pe

rfor

man

ce th

at w

ould

be

expe

cted

from

a p

erfe

ct r

ole

user

.F

or R

ule

I, th

e m

odel

diff

ers

very

littl

e fr

om hu

man

s. F

or R

ule

2, a

gain

the

corr

espo

nden

ce to

hum

an d

ata

is v

ery

clos

e. B

oth

the

mod

el a

nd th

e hu

man

sshow some slight tendency to get

conf

lict-

dist

anC

e pr

oble

ms

corr

ect,

and

to

occasionally miss

dist

ance

an

d ba

lanc

e pr

oble

ms.

For

bot

h R

ule

1 an

d R

ule

2,the tendency to miss

bala

nce

prob

lem

s is

slig

htly

gre

ater

in th

e m

odel

than

in th

ech

ildre

ns

data

. For

Rul

e 3,

the

mod

el e

xagg

erat

es a

tend

ency

see

n in

the

hum

andata to be correct on

conf

lict-

wei

ght

problems. more often than on

conf

lict-

dist

ance

pr

oble

ms,

The

maj

or d

iscr

epan

cy f

rom

the

data

is th

at th

e m

odel

is to

o ac

.cu

rate

on

conf

lict-

bala

nce

prob

lem

s. F

or R

ule

4, th

e m

odel

aga

in e

xagg

erat

es a

tend

ency

see

n in

the

hum

an d

ata

to h

ave

resi

dual

dif

ficu

lties

with

con

flic

t pro

blem

s.

:J C\/... (I

)

C\/

MC

CLE

LLA

ND

AN

D J

EN

KIN

S

RU

LES

BY

EP

OC

H: R

UN

3

....-

....

- .

(I)

!....

----

- - !.

. .--

--

100

Epo

ch

RU

LES

BY

EP

OC

H: R

UN

4

----

---!

!.. -

!..

---

100

Epo

ch

FIG

. 3, 8. Epoch by epoch performance of

the

sim

ulat

ion

mod

el in

the

two

runs

with

a 1

0 to

1 b

ias

favo

ring

pro

blem

s in

whi

ch d

ista

nce

did

not v

ary.

Per

form

ance

i8 s

core

d by

Rul

e, a

s in

FIg

. 3,

With the exception of the

cotif

lict-

ba/a

nce

prob

lem

s in

Rul

e 3,

the

hum

an d

ata

seem

to f

all a

bout

hal

f-w

ay b

etw

een

the

mod

el a

nd p

erfe

ct c

oJT

espo

nden

ce to

the

role

s. It

is te

mpt

ing

to s

pecu

late

that

som

e hu

man

sub

ject

s-pa

rtic

ular

ly R

ule

4su

bjec

ts-m

ay in

fact

use

exp

licit

role

s lik

e th

e to

rque

rol

e so

me

of th

e tim

e. I

tis

, ind

eed,

eas

y fo

r th

e ad

ult s

ubje

cts

who

con

trib

ute

to th

e R

ule

4 re

sults

to

3. NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S

RU

lE 1

RU

LE 3

Y'L

IIAL

WE

! IllS

CoW

c-o

c-a

-""

IIAL

WE

I IllS

CoW

c-o

c-a

-""

RULE 2

RU

LE 4

IIAL

WE

! IllS

CoW

c-o

c-a

IIAL

WE

! IllS

CoW

c-o

c-a

....

-""

FIG

. 3.7, Childrens performance by problem type on the balance

scal

e ta

sk, t

oget

her

with

the

perf

orm

ance

of

the

sim

ulat

ion

mod

el a

ndex

pect

ed p

erfo

rman

ce b

ased

on

each

rul

e. T

he h

eavy

line

with

dia

-m

onds

indi

cate

s ch

ildre

ns

perf

orm

ance

. The

mod

el's

per

form

ance

isgi

ven

by th

e lig

ht li

ne w

ith )

('s, w

here

as p

erfo

rman

ce p

redi

cted

fro

mth

e ru

le is

giv

en b

y th

e lig

ht li

ne w

ith s

quar

es. F

or e

ach

child

and

eac

hte

st o

f th

e si

mul

atio

n, p

erfo

rman

ce w

as p

reca

tego

rize

d ac

cord

ing

toth

e be

st f

ittin

g ru

le. T

hen,

per

cent

cor

rect

res

pons

es b

y pr

oble

m ty

pew

ere

calc

ulat

ed a

vera

ging

ove

r ch

ildre

n or

sim

ulat

ion

test

a fa

lling

into

each

rul

e.

follo

w th

e to

rque

rol

e if

inst

ruct

ed s

peci

fica

lly in

this

rol

e. H

owev

ert i

t is

evid

ent

that

the

subj

ects

who

fal

l und

er th

e R

ule

4 sc

orin

g cr

iteri

a do

not

in f

act a

dher

eex

actly

to th

e ro

le. P

erha

ps th

is g

roup

incl

udes

som

e in

divi

dual

s pe

rfon

ning

on

the

basi

s of

impl

icit

know

ledg

e of

the

trad

e-of

f of

wei

ght a

nd d

ista

nce

as w

ell a

sso

me

who

exp

licitl

y us

e th

e to

rque

rol

e, a

nd p

erha

ps s

ome

indi

vidu

als

use

am

ixtu

re o

f th

e tw

o st

rate

gies

.

Further co"espondences between the model and child development.

So f

arw

e ha

ve s

een

that

the

bala

nce

scal

e m

odel

captUreS the pattern of de

velo

pmen

t

seen

in th

e st

udie

s of

Sie

gler

(19

76, 1

981)

. The

re a

re tw

o fu

rthe

r as

pect

s of

the

deve

lopm

enta

l dat

a w

hich

arc

con

sist

ent w

ith th

e gr

adua

l bui

ldup

of

stre

ngth

on

the

dist

ance

dim

ensi

on th

at w

e se

e in

the

mod

el:

I. Wilkening and Anderson (i

n pr

ess)

pre

sent

sub

ject

s w

ith o

ne s

ide

of a

bala

nce

beam

, and

allo

w th

em to

adj

ust t

he w

eigh

t on

the

othe

r si

de a

t a f

ixed

dist

ance

fro

m th

e fu

lcro

m to

mak

e th

e sc

ale

bala

nce.

Ove

r th

e ag

e ra

nge

of 9

to

MCCLELLAND AND JENKINS

20, in which children are generally progressing from la

te R

ule

I or

Rul

e 2

toR

ule

3 or

Rul

e 4

acco

rdin

g to

Sie

gler

s m

etho

ds, t

hey

find

an

incr

easi

ng s

en-

sitiv

ity to

the

dist

ance

cue

, Unf

ortu

nate

ly it

is d

iffi

cult

to b

e su

re w

heth

er th

isre

flec

ts d

iffe

rent

num

bers

of

subj

ects

rel

ying

on

the

dist

ance

cue

, or

(as

we

see

inth

e m

odel

) di

ffer

ence

s in

deg

ree

of r

elia

nce

amon

g th

ose

who

sho

w s

ome

sen-

sitiv

ity to

the

dist

ance

cue

,2, For children w

ho e

xhib

it R

ule

3 on

Sie

gler

s 24

-ite

m te

st, c

aref

ul a

sses

s-m

ent w

ith a

larg

er n

umbe

r of

con

flic

t pro

blem

s in

dica

tes

the

use

of c

ue c

ompe

n-

Sjlti

on s

trat

egie

s, r

athe

r th

an r

ando

m g

uess

ing

(Fen

etti,

But

terf

ield

, Cab

n

, &

Ker

kman

, 198

5), T

hus

child

ren

are

not s

impl

y to

tally

con

fuse

d ab

out c

onfl

ict

prob

lem

s du

ring

this

sta

ge b

ut h

ave

som

e se

nsiti

vity

of

rela

tive

mag

nitu

des

ofcues, as does the model. The exact degree of correspondence of the model'

perf

onna

nce

and

hum

an p

erfo

nnan

ce o

n th

ese

larg

er te

sts

rem

ains

to b

e ex

-pl

ored

,

The mechanism/or developmental change,

Giv

en th

e ge

nera

lly c

lose

cor

re-

spon

denc

e be

twee

n m

odel

and

dat

a, it

is im

port

ant t

o un

ders

tand

just

how

the

mod

el p

erfO

rms,

and

how

its

perf

onna

nce

chan

ges,

To

do th

is, i

t is

help

ful t

oex

amin

e th

e co

nnec

tions

in th

e ne

twor

k at

sev

eral

dif

fere

nt p

oint

s in

the

lear

ning

proc

ess,

Fig

ure

3,8

disp

lays

the

conn

ectio

ns f

rom

the

ron

that

pro

duce

d th

ere

sults

sho

wn

in th

e to

p pa

nel o

f Fi

g, 3

, 6, a

t 4 d

iffe

rent

poi

nts

dwin

g le

arni

ng: A

tep

och

0, b

efor

e an

y le

arni

ng; a

t epo

ch 2

0 , ear

ly in

the

Rul

e 1

phas

e; a

t epo

ch 4

0,at

the

end

of th

e R

ule

1 ph

ase;

and

at e

poch

100

, when the simulation was

tenn

inat

ed, E

ach

of th

e fo

ur la

rge,

rec

tang

les

in e

ach

pane

l sho

ws

the

wei

ghts

com

ing

into

and

out

of

one

of th

e fo

ur h

idde

n un

its, T

he tw

o on

the

left

rec

eive

inpu

t fro

m th

e w

eigh

t dim

ensi

on, a

nd th

e tw

o on

the

righ

t rec

eive

inpu

t fro

m th

edi

stan

ce d

imen

sion

,In

the

firs

t pan

el, b

efor

e le

arni

ng be

gins

, all

the

conn

ectio

n st

reng

ths

have

smal

l ran

dom

val

ues,

In

this

situ

atio

n, th

e ou

tput

of

the

hidd

en u

nits

is n

otsy

stem

atic

ally

rel

ated

to m

agni

tude

s of

the

wei

ghts

or

dist

ance

s, a

nd is

ther

efor

eof

no

use

in p

redi

ctin

g th

e co

rrec

t out

put,

At t

his

poin

t, th

e.hi

dden

uni

ts a

re n

oten

codi

ng e

ither

rel

ativ

e w

eigh

t or

rela

tive

dist

ance

, and

are

ther

efor

e pr

ovid

ing

no in

fonn

atio

n th

at w

ould

be

usef

ul f

or p

redi

ctin

g w

heth

er th

e le

ft o

r ri

ght s

ide

shou

ld g

o do

wn,

The

fir

st p

hase

of

lear

ning

con

sist

s of

the

grad

ual o

rgan

izat

ion

of th

e co

nnec

-tio

ns th

at p

roce

ss th

e am

ount

of

wei

ght o

n ea

ch s

ide

of th

e ba

lanc

e sc

ale,

Rec

all

that

the

netw

ork

rece

ives

pro

blem

s in

whi

ch th

e di

stan

ce c

ue v

arie

s m

uch

less

freq

uent

ly th

an p

robl

ems

in w

hich

the

wei

ght c

ue v

arie

s, L

earn

ing

to r

ely

on th

ew

eigh

t cue

pro

ceed

s m

ore

quic

kly

than

lear

ning

to r

ely

on th

e di

stan

ce c

ue a

s a

sim

ple

resu

lt of

this

fac

t, T

he r

ate

of le

arni

ng w

ith r

espe

ct to

' eac

h ty

pe o

f cue

isre

lativ

ely

grad

ual a

t fir

st, b

ut th

en s

peed

s up

, for

rea

sons

that

we

will

exp

lore

belo

w, T

he r

elat

ivel

y ra

pid

tran

sitio

n fr

om v

irtu

ally

unr

espo

nsiv

e ou

tput

to f

airl

yst

rong

rel

ianc

e on

the

wei

ght c

ue r

epre

sent

s th

e br

ief

tran

sitio

n to

Rul

e 1

resp

ond-

3, NATURE, NURTURE, A

ND

CO

NN

EC

TIO

NS

59

DII

CII

O

......

.

illil

..-..

iii !;;I

...

.. I=I==

..

I.-.

.a-.

.....

b;J

:.- .:

- .

:.. '

~.- ..- ~

-.-

.--.

.. I=W===1

.. L.-a.J

,.... . I

-L-

.. "'

... .

. ..

II. .

.

. " ..

D11

C11

8

......

...

.....

8J !;

I

""'"

'"

1111

;1

.. -

..

III !;

I 1;

1 .

..-_. ....

.-_a _.._~

-.--

...

.._.

_._a

a

-. ..

.. 1=8===

L..a

-....

: .. '

----

-

"..

:.. .:

. .:-

.:..

-.. .

-- -.

- .-

..

I=W

==

=1

.. L.-a.J

.. . ----..J

. " "

I II .

.. I

I ..

. II

II

FIG

, 3,8, Connection strengths into (I-+H)lnd out of (H-+O) e8Ch of

the

hidd

en u

nits

. It e

ach

of fo

ur d

iffer

ent p

oint

s du

ring

trai

ning

, Ac-

tivlti

ons

of in

put,

hidd

en. e

nd o

utpu

t uni

ts e

re a

lso

show

n. f

or e

con

-fl

ict b

alan

ce p

robl

em. i

n w

hich

ther

e er

e 2

wei

ghts

on

peg

4 on

the

left

end

4 w

eigh

ts o

n pe

g 2

on th

e ri

ght,

Mlg

nitu

de o

f ea

ch c

onne

ctio

n is

give

n by

the

size

of t

he b

lack

ened

ere

l, S

ign

is in

diC

8t8d

by

whe

ther

the

blac

kene

d er

ee e

xten

ds e

bove

or

belo

w th

e ho

rlzon

tsl b

asel

ine,

Not

e th

lt ec

tivltl

ons

ere

III

posi

tive,

end

ren

ge f

rom

0 to

1, T

he c

on-

nect

ion

stre

ngth

s ra

nge

betw

een

+6l

nd -

6. S

ee te

xt fo

r fu

rthe

r ex

pla-

natio

n,

ing,

The

res

ult o

f thi

s ph

ase,

in th

e se

cond

pan

el o

f th

e fi

gure

, is

a se

t of

conn

ectio

ns th

at a

llow

the

hidd

en u

nits

on

the

left

to r

efle

ct th

e re

lativ

e am

ount

of

wei

ght o

n th

e le

ft v

s, th

e ri

ght s

ide

of th

e ba

lanc

e sc

ale,

The

left

mos

t hid

den

unit

ism

ost s

tron

gly

exci

ted

by la

rge

wei

ghts

on

the

left

and

sm

all w

eigh

ts o

n th

e ri

ght,

and

mos

t str

ongl

y in

hibi

ted

by la

rge

wei

ghts

on

the

righ

t and

sm

all w

eigh

ts o

n th

ele

ft~ T

he a

ctiv

atio

n of

this

uni

t, th

en, r

ange

s fr

om n

ear

0 to

nea

r 1

as th

e re

lativ

e

mag

nitu

de o

f wei

ght r

ange

s fr

om m

uch

mor

e on

the

right

to m

uch

mor

e on

the

left,

Con

espo

ndin

gly,

this

uni

t has

an

exci

tato

ry co

nnec

tion

to th

e le

ft-si

de-d

own

output unit, and an inhibitory connection to the right-side-eJown output un

it, T

he

seco

nd h

idde

n un

it m

irro

rs th

ese

rela

tions

hips

in r

ever

se, A

t thi

s po

int,

then

, the

hidd

en u

nits

can

be

said

to h

ave

lear

ned

to r

epre

sent

som

ethi

ng th

ey w

ere

not

MC

CLE

LLA

ND

AN

D J

EN

KIN

S

repr

esen

ting

befo

re, n

amel

y th

e re

lativ

e m

agni

tude

of

the

inpu

ts, N

ote

that

this

info

nnat

ion

is n

ot e

xplic

idy

cont

aine

d in

the

inpu

t, w

hich

sim

ply.

dist

ingu

ishe

s bu

tdo

es n

ot o

rder

the

diff

eren

t pos

sibl

e va

lues

of

wei

ght o

n th

e tw

o si

des

of th

eba

lanc

e sc

ale,

At t

his

poin

t, th

e co

nnec

tion

stre

ngth

s in

the

dist

ance

par

t of

the

netw

ork

rem

ain

virt

ually

unc

hang

ed; t

hus,

at t

he h

idde

n un

it le

vel,

the

netw

ork

has

not

yet l

earn

ed to

enc

ode

the

dist

ance

dim

ensi

on,

Ove

r th

e ne

xt 2

0 ep

ochs

, con

nect

ions

get

muc

h st

rong

er o

n th

e w

eigh

t dim

en-

sion

, and

w'e

beg

in to

see

som

e or

gani

zatio

n of

the

dist

ance

dim

ensi

on, W

hile

this

is g

oing

on,

the

over

t beh

avio

r of

the

netw

ork

rem

ains

Rul

e I

beha

vior

, The

netw

ork

is g

ettin

g re

ady

for

the

rela

tivel

y ra

pid

tran

sitio

n to

Rul

e 2

and

then

toR

ule

3 w

hich

occ

urs

over

the

next

sev

eral

epo

chs

of tr

aini

ng (

as s

how

n in

the

top

pane

l of

Fig,

3,6

), b

ut a

t epo

ch 4

0, th

e en

d of

the

Rul

e 1

phas

e, th

e di

stan

ceco

nnec

tions

are

stil

l not

qui

te s

tron

g en

ough

that

they

can

yet

pus

h ac

tivat

ions

of

the

outp

ut u

nits

out

of

the

bala

nce

rang

e, W

ith f

mth

er le

arni

ng, t

he d

ista

nce

cue

beco

mes

str

onge

r an

d st

rong

er, t

his

fust

cau

ses

the

dist

ance

cue

to g

over

n pe

rfor

-m

ance

whe

n th

e w

eigh

ts a

re in

bal

ance

, giv

ing

rise

to R

ule

2 be

havi

or. F

urth

erst

reng

then

ing

caus

es th

e di

stan

ce c

ue to

win

out

in s

ome

conf

lict pr

oble

ms,

givi

ng r

ise

to b

ehav

ior

cons

iste

nt w

ith R

ules

3 a

nd 4

, At e

poch

100

of this

part

icul

ar r

un, t

he w

eigh

t dim

ensi

on ~

ntai

ns a

slig

ht a

scen

danc

y, s

o th

at w

iththe particular

conf

l;ct-

baltm

ce

prob

lem

illu

stra

ted,

the

mod

el a

ctiv

ates

the

left

-si

de d

own

unit,

cor

resp

ondi

ng. t

o th

e si

de w

ith th

e gr

eate

r w

eigh

t, m

ore

than

itac

tivat

es th

e ri

ght-

side

dow

n un

it,A

cou

ple

of a

spec

ts o

f th

e de

velo

pmen

tal p

rogr

essi

on d

eser

ve c

omm

ent.

As

Fig, 3,9

illus

trat

es, t

he c

onne

ctio

n st

reng

ths

are

larg

ely

inse

nsiti

ve to

dif

fere

nces

earl

y on

, the

n go

thro

ugh

a fa

irly

rap

id tr

ansi

tion

in s

ensi

tivity

and

then

leve

l off

agai

n, T

he a

ccel

erat

ion

seen

in le

arni

ng is

a r

esul

t of

an in

here

nt c

hara

cter

istic

of

the

grad

ient

des

cent

lear

ning

pro

cedu

re c

oupl

ed w

ith th

e ar

ehite

ctur

e of

the

netw

ork,

The

pro

cedu

re a

djus

ts e

ach

conn

ectio

n in

pro

port

ion

to th

e m

agni

tude

of th

e ef

fect

that

adj

ustin

g it

will

hav

e on

the

disc

repa

ncy

betw

een

corr

ect a

ndac

tual

out

put,

But

the

effe

ct o

f a

give

n co

nnec

tion

depe

nds

on th

e st

reng

ths

ofot

her

conn

ectio

ns, C

onsi

der

the

conn

ectio

n co

min

g in

to a

hid

den

unit

from

one

of th

e in

put u

nits

, An

adju

stm

ent o

f th

e st

reng

th o

f th

is in

put c

onne

ctio

n w

illha

ve a

sm

all e

ffec

t on

the

outp

ut if

the

conn

ectio

ns f

rom

the

hidd

en u

nit t

o th

eou

tput

uni

ts a

re w

eak,

In

this

cas

e, th

e in

put c

onne

ctio

n w

ill o

nly

rece

ive

a sm

all

adju

Sbne

nt, I

f ho

wev

er, t

he c

onne

ctio

ns f

rom

the

hidd

en u

nits

to th

e ou

tput

uni

tsar

e st

rong

, an

adju

stm

ent o

f th

e st

reng

th o

f th

e in

put c

onne

ctio

n w

ill h

ave

a m

uch

larg

er e

ffec

t; co

nseq

uend

y th

e le

arni

ng p

roce

dure

mak

es a

muc

h la

rger

adj

ust-

men

t in

this

cas

e, A

slig

hdy

diff

eren

t sto

ry a

pplie

s to

the

conn

ectio

ns f

rom

the

hidd

en u

nits

to th

e ou

tput

uni

ts, W

hen

the

conn

ectio

ns f

rom

the

inpu

t to

the

hidd

en u

nits

are

wea

k an

d ra

ndom

, the

act

ivat

ions

of

the

hidd

en u

nits

are

onl

yw

eakl

y re

late

d to

the

corr

ect o

utpu

t, U

nder

thes

e cm

:um

stan

ces,

the

adju

stm

ents

Hid

den

to O

utpu

t

CII... CII

Epo

ch

Inpu

t to

Hid

den

CII CII

Epo

ch

FIG

, 3,9

, Rel

ativ

e m

agni

tude

of

conn

ectio

n strengths encoding

wei

ght a

nd d

ista

nce,

al a

func

tion

of tr

aini

ng, M

agni

tude

il g

iven

by

the

rang

e of

con

nect

ion strengthl(most positiveminul most negative)

com

ing

into

one

wei

ght o

r di

stan

ce h

idde

n un

it (l

ower

pan

el)

and

com

ing

out o

f w

eigh

t or

dist

ance

uni

t (up

per

pane

l),

100 100

"'-,

MCCLELLAND AND JENKINS

mad

e to

the

outp

ut w

eigh

ts te

nd to

canc

el e

ach

othe

r ou

t, an

d pr

ogre

ss o

fle

arni

ng is

ver

y sl

ow. I

t is

only

aft

er tt

re in

put w

eigh

ts be

com

e or

gani

zed

that

lear

ning

can

pro

ceed

eff

icie

ntly

on

the

outp

ut s

ide

of th

e hi

dden

uni

ts.

The

sto

ry w

e ar

e te

lling

wou

ld b

e a

very

sad

one

, wer

e it

not f

or th

e fa

ct th

at it

isno

t all

or n

one.

It i

s no

t tha

t the

re is

no

lear

ning

at a

ll at

fir

st. I

n th

at c

ase,

ther

ew

ould

be

no g

radu

al c

hang

e to

the

poin

t whe

re le

arni

ng be

com

es m

ore

rapi

d.R

athe

r , it is simply that initially learning is simply

very

gr

adua

l; so

gra

dual

that

itdo

es n

ot s

how

up

in o

vert

beh

avio

r. G

radu

ally

thou

gh th

is in

itial

ly s

low

lear

ning

acce

lera

tes;

pro

duci

ng a

n in

crea

sing

rea

dine

ss to

lear

n.T

hedi

ffer

entia

l rea

dine

ss to

lear

n al

low

s th

e m

odel

to a

ccou

nt f

or th

e re

sults

of a

n ex

peri

men

t des

crib

ed b

y Si

egle

r (1

976)

, on

the

effe

cts

of tr

aini

ng f

or y

oung

vs. o

ld R

ule

I ch

ildre

n. S

iegl

er s

how

ed 5

- an

d 8-

year

-old

Rul

e I

child

ren

a se

ries

of d

ista

nce

prob

lem

s or

a s

erie

s of

con

flic

t pro

blem

s. T

he c

hild

ren

wer

e al

low

edto

try

to p

redi

ct w

hich

sid

e w

ould

go

dow

n, a

nd w

ere

then

sho

wn

wha

t act

ually

happ

ens.

The

res

ults

wer

e st

riki

ng. O

f th

e ch

ildre

n w

ho s

aw th

e ou

tcom

es f

ordi

stan

ce p

robl

ems

, bot

h ag

e gr

oups

wer

e ve

ry li

kely

to e

xhib

it R

ule

2 be

havi

oron

a p

ost-

test

. How

ever

, of

the

child

ren

who

saw

the

outc

omes

for

con

flic

ttr

aini

ng, t

he y

oung

er c

hild

ren

eith

er c

ontin

ued

to b

ehav

e in

accordance with

Rul

e I

or b

ecam

e in

cons

iste

nt in

thei

r re

spon

ding

. The

old

er c

hild

ren,

on

the

othe

r ha

nd, b

enef

itted

fro

m th

e co

nflic

t tra

inin

g. O

n a

post

test

, the

old

er c

hil-

dren

wer

e ve

ry li

kely

to e

xhib

it R

ule

2 or

Rul

e 3

beha

vior

. In

furt

her

expe

rim

ents

on e

arly

Rul

e I

child

ren

, Sie

gler

rep

orte

d th

at th

ese

child

ren

do n

ot r

epre

sent

the

dist

ance

cor

rect

ly: W

hen

aske

d to

rep

rodu

ce a

bal

ance

bea

m c

onfi

gura

tion

, the

yco

uld

usua

lly g

et th

e nu

mbe

r of

wei

ghts

cor

rect

, but

cou

ld r

arel

y pl

ace

them

on

the

corr

ect p

egs.

You

nger

Rul

e I

child

ren

who

wer

e th

en tr

aine

d to

rep

rese

nt th

edi

stan

ce c

orre

ctly

wer

e ab

le to

lear

n fr

om e

xper

ienc

e w

ith c

onfl

ict p

robl

ems

like

the

olde

r R

ule

I chi

ldre

n.

3. NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S&

S. ,

wea

kly

enco

ded.

Whi

le it

is s

till t

oo w

eak

to a

ctua

lly c

ause

the

outp

ut to

be

stro

ngly

eno

ugh

affe

cted

by

the

dist

ance

cue

to a

ctua

lly a

ffec

t per

form

ance

, it i

sst

rong

eno

ugh

for

a sm

all a

mou

nt o

f ex

peri

ence

to c

ause

a f

urth

er in

crea

se in

stre

ngth

to th

e po

int w

here

the

dist

ance

cue

is s

tron

g en

ough

to in

flue

nce

perf

or-

man

ce.

Feed

back

Sim

ulat

ion

Tri

als

SIMULATIONS OF FEEDBACK EXPERIMENTS

Thi

s ge

nera

l pat

tern

of

resu

lts f

its c

lose

ly w

ith w

hat w

e w

ould

exp

ect b

ased

on

wha

t we

have

alre

ady

lear

ned

abou

t the

mod

el. P

artic

ular

ly in

tere

stin

g ar

e th

eef

fect

s of

feed

back

on

conf

lict t

rails

on

early

and

late

Rul

e I p

erfo

nnan

ce. T

hem

odel

was

sho

wn

a se

t of

conf

lict t

rial

s w

ith f

eedb

ack

, usi

ng th

e w

eigh

ts o

b-ta

ined

early

in th

e R

ule

I pha

se (

epoc

h 20

) an

d la

ter

(epo

ch 4

0). I

n th

efon

nerc

ase

perf

onna

nce

grad

ually

rev

erte

d to

ran

dom

. In

the

latte

r ca

se, i

t shi

fts

afte

r on

lyon

e ex

posu

re to

the

set o

f co

nflic

t tri

als

to th

e ru

le 2

leve

l. T

he r

easo

n fo

r th

ede

teri

orat

ion

in th

e fi

rst c

ase

is s

impl

y th

at e

arly

in R

ule

I, th

e w

eigh

ts in

the

netw

ork

do n

ot e

ncod

e di

stan

ce in

fonn

atio

n at

all.

As

a re

sult

the

conf

lict t

rial

sap

pear

to in

volv

e a

patte

rn o

f ve

ry in

cons

iste

nt f

eedb

ack

conc

erni

ng th

e co

rrec

tpr

edic

tions

to m

ake

base

d on

the

wei

ghts

alo

ne. L

ater

in R

ule

I , the

dis

tanc

e cu

e is

The

gen

eral

app

roac

h ta

ken

here

can

be

exte

nded

to c

over

the

full

rang

e of

trai

ning

expe

rim

ents

car

ried

out

by

Sieg

ler

(197

6). S

imul

atio

ns m

ore

clos

ely

mat

chin

g th

ede

sign

of

thes

e ex

peri

men

ts w

ere

carr

ied

out b

y th

e se

cond

aut

hor.

For

thes

esi

mul

atio

ns, a

sim

ilar

arch

itect

ure

was

use

d. O

ne m

ajor

dif

fere

nce

was

the

addi

tion

of 2

mor

e ou

tput

uni

ts. T

hese

add

ition

al o

utpu

t uni

ts r

ecei

ved

inpu

t fro

mth

e hi

dden

uni

ts o

n th

e di

stan

ce d

imen

sion

. In

gene

ral,

thes

e ad

ditio

nal o

utpu

tun

its, f

rom

now

on

to b

e re

ferr

ed to

asd

ista

nce

enco

ding

uni

ts, w

ere

not i

nvol

ved

in th

e si

mul

atio

ns e

xcep

t whe

re o

utlin

ed b

elow

.T

he p

urpo

se o

f th

ese

sim

ulat

ions

was

to m

odel

the

trai

ning

exp

erie

nces

fro

mSi

egle

rs

seco

nd a

nd th

ird

expe

rim

ents

. The

issu

e at

this

poi

nt w

as w

heth

er th

em

odel

cou

ld s

imul

ate

the

effe

cts

of tr

aini

ng w

ith d

ista

nce

prob

lem

s ve

rsus

trai

ning

with

con

flic

t pro

blem

s.T

o si

mul

ate

the

stab

ility

of

the

. sys

tem

s kn

owle

dge

abou

t the

wei

ght d

imen

-si

on, t

he le

arni

ng m

echa

nism

s pr

opor

tion

of c

hang

e w

ith r

espe

ct to

err

or f

or th

eco

nnec

tions

fro

m th

e w

eigh

t uni

ts a

nd th

e w

eigh

t int

erna

l uni

ts a

nd f

rom

the

wei

ght i

nter

nal u

nits

to th

e ba

lanc

e sc

ale

outp

ut u

nits

(th

eir

lear

ning

rat

es)

wer

e,re

spec

tivel

y, .0

0 an

d , 0

25, w

hile

the

prop

ortio

n of

cha

nge

with

res

pect

to e

rror

for

all o

f. th

e di

stan

ce d

imen

sion

con

nect

ions

was

.05.

To

begi

n th

e si

mul

atio

n of

Sie

gler

s se

cond

exp

erim

ent,

the

mod

el w

as in

i-tia

lized

by

trai

ning

onl

y th

e co

nnec

tions

bet

wee

n th

e w

eigh

t inp

ut u

nits

and

the

wei

ght-

hidd

en u

nits

, and

bet

wee

n th

e w

eigh

t-hi

dden

uni

ts a

nd th

e ba

lanc

e sc

ale

outp

ut u

nits

. Thi

s tr

aini

ng w

as p

erfo

rmed

by

pres

entin

g th

e m

odel

with

50

epoc

hsof

inpu

t and

fee

dbac

k fo

r ea

ch p

ossi

ble

conf

igur

atio

n of

wei

ght a

nd b

alan

cepr

oble

ms

with

no

dist

ance

info

rmat

ion

prov

ided

to th

e m

odel

. On

the

bala

nce

scal

e pr

edic

tion

task

, thi

s sy

stem

pro

duce

d pe

rfec

t Rul

e I

beha

vior

. Fro

m th

is b

ase

perf

onna

nce

leve

l, th

e m

odel

rec

eive

d tw

o ty

pes

of tr

aini

ng in

sep

arat

e se

ssio

ns.

In o

ne s

essi

on, t

he m

odel

rec

eive

d fe

edba

ck tr

aini

ng s

imila

r to

the

dist

ance

feed

back

trai

ning

in S

iegl

ers

seco

nd e

xper

imen

t. T

hat i

s,th

e m

odel

was

trai

ned

with

16

diff

eren

t pat

tern

s an

d th

eir

asso

ciat

ed c

orre

ct r

espo

nses

; 12

patte

rns

with

equa

l wei

ght i

nput

to th

e tw

o si

des

of th

e w

eigh

t inp

ut u

nits

and

dif

fere

nt d

ista

nce

inpu

ts to

the

two

side

s of

the

dist

ance

inpu

t uni

ts (

Dis

tanc

e pr

oble

ms)

, 2 p

atte

rns

with

equ

al w

eigh

t and

dis

tanc

e in

puts

(B

alan

ce p

robl

ems)

, and

2 p

atte

rns

with

diff

eren

t wei

ght i

nput

s to

the

two

side

s of

the

wei

ght i

nput

uni

ts a

nd e

qual

dis

tanc

ein

put t

o th

e tw

o si

des

of th

e di

stan

ce in

put u

nits

(W

eigh

t pro

blem

s).

",.

", .

"....

.....

~.'.

'"""

'.."

,,~~~

,. .-

-..

MC

CLE

LLA

ND

AN

D J

EN

KIN

S3. NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S

In th

e se

cond

ses

sion

, aft

er r

eini

tializ

atio

n of

the

syst

em to

the

base

per

for-

man

ce le

vel,

the

mod

el r

ecei

ved

feed

back

trai

ning

sim

ilar

to th

e co

nflic

t tra

inin

gin

Sie

gler

s se

cond

exp

erim

ent.

Tha

t is,

the

mod

el w

as tr

aine

d w

ith 1

6 di

ffer

ent

patte

rns

and

thei

r as

soci

ated

cor

rect

res

pons

es; 1

2 pa

ttern

s w

ith g

reat

er w

eigh

tin

put t

o on

e si

de o

f th

e w

eigh

t inp

ut u

nits

and

gre

ater

dis

tanc

e in

put t

o on

e si

deof

the

dist

ance

inpu

t uni

ts (

Con

flic

t pro

blem

s), a

nd 2

pat

tern

s w

ith e

qual

wei

ght

and

dist

ance

inpu

ts (

Bal

ance

pro

blem

s), a

nd 2

pat

tern

s w

ith d

iffe

rent

wei

ght

inpu

ts to

the

two

side

s of

the

wei

ght i

nput

uni

ts a

nd e

qual

dis

tanc

e in

put t

o th

etw

o si

des

of th

e di

stan

ce in

put u

nits

(W

eigh

t pro

blem

s).

In b

oth

of th

ese

sess

ions

, the

mod

el r

ecei

ved

40 e

poch

s (6

40 tr

ials

) of

trai

n-in

g. A

mea

sure

of

the

effe

ctiv

enes

s of

the

trai

ning

tria

ls w

as p

lotte

d ov

er th

eco

urse

of

the

fort

y tr

aini

ng e

poch

s. 1

be e

ffec

tiven

ess

mea

sure

, cal

led

the

sum

of

squa

res

erro

r te

nn (

SSE

RR

OR

), m

easu

res

the

diff

eren

ce b

etw

een

the

activ

atio

nsof

the

pred

ictio

n re

spon

ses

of th

e m

odel

ove

r th

e tr

aini

ng s

et o

f pa

ttern

s an

d th

eac

tivat

ions

of

corr

ect r

espo

nses

for

the

set o

f pa

ttern

s, T

here

fore

, a la

rge

erro

rte

nn r

epre

sent

s an

inab

ility

of

the

mod

el to

pro

duce

cor

rect

pre

dict

ions

, whi

le a

smal

l ten

D r

epre

sent

s a

clos

e m

atch

bet

wee

n th

e pr

edic

tions

of

the

mod

el a

nd th

eco

rrec

t res

pons

es.

Figu

res

3,10

8 an

d 3.

lOb

show

SSE

RR

OR

plo

tted

over

trai

ning

epo

chs

dmin

gdi

stan

ce tr

aini

ng a

nd c

onfl

ict t

rain

ing,

respectively. In Fig. 3.

108,

we

can

see

that

dis

tanc

e tr

aini

ng c

ause

s th

e m

odel

' s p

redi

ctiv

e pe

rfor

man

ce o

ver

the

trai

ning

prob

lem

set

to im

prov

e dr

amat

ical

ly. I

n co

ntra

st, F

ig, 3

, IO

b sh

ows

that

con

flic

ttr

aini

ng d

id n

ot in

crea

se th

e m

odel

' s p

redi

ctiv

e pe

rfor

man

ce o

ver

the

trai

ning

prob

lem

set

. The

se g

raph

s in

dica

te th

at, i

n th

e 40

epo

ch ti

me

fram

e, th

e m

odel

lear

ned

from

the

dist

ance

trai

ning

but

did

not

lear

n fr

om th

e co

nflic

t tra

inin

g,A

mor

e dr

amat

ic d

emon

stra

tion

of th

is d

iffe

renc

e in

lear

ning

was

exh

ibite

d in

the

mod

el' s

per

fonn

ance

on

the

pred

ictio

n ta

sk f

ollo

win

g th

e fe

edba

ck tr

aini

ng.

Lik

e m

any

of S

iegl

ers

five

yea

r ol

d su

bjec

ts, t

he m

odel

leam

ed to

per

fonn

as

aru

le 2

use

r af

ter

dist

ance

trai

ning

; in

addi

tion

to g

ettin

g ba

lanc

e, w

eigh

t and

conf

lict-

wei

ght p

robl

ems

corr

ect,

the

mod

el w

as a

ble

to c

orre

ctly

pre

dict

dis

-ta

nce

prob

lem

s as

wel

l. A

fter

con

flic

t tra

inin

g, h

owev

er, t

he m

odel

did

not

lear

nto

per

fonn

at a

ll di

ffer

ent f

rom

rul

e 1

beha

vior

, Hen

ce, t

he m

odel

clo

sely

sim

u-la

ted

the

beha

vior

of

the

S-ye

ar-o

lds.

The

nex

t ste

p in

the

eval

uatio

n of

the

mod

el w

as to

giv

e di

stan

ce e

ncod

ing

trai

ning

to th

e ba

se p

erfo

nnan

ce m

odel

. 1be

mod

el's

enc

odin

g tr

aini

ng w

as n

otth

e sa

me

as th

e tr

aini

ng th

at S

iegl

er pr

esen

ted

to h

is s

ubje

cts;

inst

ead,

this

trai

ning

was

onl

y m

eant

to g

et th

e m

odel

to c

ateg

oriz

e th

e di

stan

ce in

put i

nto

one

of th

e th

ree

rela

tive

valu

es. T

hus,

this

trai

ning

invo

lved

mod

ific

atio

n of

onl

y th

eco

nnec

tions

bet

wee

n th

e di

stan

ce in

put u

nits

, the

hid

den

units

of

the

dist

ance

dim

ensi

on, a

nd th

e di

stan

ce e

ncod

ing

units

at t

he o

utpu

t lev

el. T

his

enco

ding

trai

ning

set

incl

uded

eve

rY c

onfig

urat

ion

of d

ista

nce

as in

put t

o th

e ne

twor

k (3

6

patte

rns)

pai

red

with

the

corr

espo

ndin

g re

lativ

e di

stan

ce v

alue

(m

ore

dist

ance

left

, mor

e di

stan

ce r

ight

, or

equa

l dis

tanc

e) a

s th

e ta

rget

fee

dbac

k fo

r th

e di

stan

ceen

codi

ng u

nits

.

-'-

101

.

1 .--

-

lei

-'---

'--'-

Ibl .

---- _u

---. -

1 .

1 .

----

..J

FIG

. 3.10. Network error over training for (e) di8t8nce training, (b)

conf

lict t

rain

ing,

end

(e)

con

flict

trai

ning

afte

r en

codi

ng tr

aini

ng.

For

exam

ple,

the

mod

el w

as p

rese

nted

at t

he in

put l

evel

with

the

activ

atio

npa

ttern

for

thre

e ri

ght a

nd tw

o le

ft, a

nd tr

aine

d to

pro

duce

the

patte

rn o

f ac

tiva-

tion

for

mor

e di

stan

ce r

ight

acr

oss

the

dist

ance

enc

odin

g un

its. T

he m

odel

rece

ived

25

epoc

hs o

f tr

aini

ng w

ith th

is tr

aini

ng c

orpu

s. T

his

trai

ning

allo

wed

the

dist

ance

hid

den

units

to d

iscr

imin

ate

dist

ance

inpu

t pat

tern

s as

gre

ater

dis

tanc

ele

ft, g

reat

er d

ista

nce

righ

t or

equa

l dis

tanc

e, N

o tr

aini

ng o

ccur

red

betw

een

any

ofth

e ot

her

units

of

the

mod

el d

urin

g th

e di

stan

ce e

ncod

ing

trai

ning

pha

se, f

ollo

w-

ing

this

enc

odin

g tr

aini

ng, t

he m

odel

was

aga

in te

sted

on

the

pred

ictio

n ta

sk. T

hem

odel

, lik

e Si

egle

rs

subj

ects

, did

not

exh

ibit

a ch

ange

in b

ehav

ior.

Fin

ally

,

the

mod

el w

as p

rovi

ded

with

the

sain

e co

nflic

t tra

inin

g as

had

bee

n pr

ovid

ed in

MCCLELLAND AND JENKINS

the

earl

ier

conf

lict t

rain

ing

sess

ion.

In

cont

rast

to F

ig. 3

. IOb ,

the plot of the

effe

ctiv

enes

s of

con

flic

t tra

inin

g af

ter

enco

ding

trai

ning

(Fi

g. 3

. 1 O

c) s

how

s th

atco

nflic

t tra

inin

g dr

amat

ical

ly in

crea

ses

the

mod

el' s

pre

dict

ive

perf

onna

nce

over

the

trai

ning

pro

blem

set

. Thi

s gr

aph

indi

cate

s th

at th

e m

odel

was

abl

e to

lear

nfr

om th

e co

nflic

t tra

inin

g af

ter

enco

ding

trai

ning

. rol

low

ing

this

trai

ning

, the

mod

el w

as a

gain

test

ed o

n th

e pr

edic

tion

task

.T

his

time,

the

mod

el w

as a

ble

to c

orre

ctly

use

the

dist

ance

info

nnat

ion

topr

edic

t dis

tanc

e pr

oble

ms.

It a

lso

lear

ned,

like

the

child

ren,

not

to r

ely

stri

ctly

on

the

wei

ght c

ues

to p

redi

ct th

e co

nflic

t pro

blem

s an

d th

us it

s pe

rfon

nanc

e w

ent

dow

n on

the

conf

lict w

eigh

t pro

blem

s (f

rom

100

% c

orre

ct to

75%

cor

rect

) an

d up

on th

e co

nflic

t dis

tanc

e an

d co

nflic

t bal

ance

pro

blem

s (b

oth

from

0%

cor

rect

to50

% c

orre

ct).

In essen~, the model learned to

per

fonn

as

a ro

le 3

use

r af

ter

the

conf

lict

trai

ning

fol

low

ing

the

enco

ding

trai

ning

. Hen

ce, t

he m

odel

sim

ulat

ed th

e le

arn-

ing abilities of many of the

5-

and

8-ye

ar-o

lds

on th

e co

nflic

t tra

inin

g ta

sk a

fter

rece

ivin

g di

stan

ce e

ncod

ing

trai

ning

.1b

und

erst

and

how

this

mod

el w

orks

, it i

s im

port

ant t

o un

ders

tand

the

inte

rnal

stru

ctur

e th

at d

evel

ops

duri

ng tr

aini

ng. S

o, b

efor

e di

stan

ce tr

aini

ng, a

fter

dis

-ta

nce

trai

ning

, aft

er c

onfl

ict t

rain

ing,

and

aft

er e

ncod

ing

trai

ning

fol

low

ed b

yconflict training, the model was presented with

IS

diff

eren

t dis

tanc

e co

nfig

ura-

tions

(pa

ttern

s of

act

ivat

ion)

acr

oss

the

dist

ance

inpu

t uni

ts. T

here

wer

e fi

veco

nfig

urat

ions

eac

h; o

f m

ore

dist

ance

rig

ht, m

ore

dist

ance

left

, and

equ

al d

is-

tanc

e (b

alan

ce).

Aft

er e

ach

pres

enta

tion

of a

dis

tanc

e co

nfig

urat

ion,

the

aver

age

activ

atio

n of

the

two

sets

of

units

of

the

dist

ance

inte

rnal

gro

up w

ere

mea

sure

dan

d pl

otte

d ag

ains

t eac

h ot

her.

The

two

sets

of

units

wer

e ch

osen

by

exam

inin

gth

e ac

tivat

ion

valu

es a

nd a

ttem

ptin

g to

det

enni

ne w

hich

, if

any,

of the units

tend

ed to

hav

e co

rrel

ated

act

ivat

ion

valu

es. U

nits

with

corr

elat

ed a

ctiv

atio

nva

lues

wer

e co

nsid

ered

mem

bers

of

a co

mm

on s

et fo

r th

e pu

rpos

es o

f th

isanalysis. Units could not be chosen

a priori

due

to f

act t

hat t

he le

arni

ng m

echa

-ni

sm r

ecru

its u

nits

to c

ode

sim

ilar

func

tions

onl

y du

ring

the

cour

se o

f tr

aini

ng.

To

disp

lay

thes

e ac

tivat

ions

in r

espo

nse

to d

iffe

rent

inpu

ts, t

wo-

dim

ensi

onal

grap

hs w

ere

cons

truc

ted

with

eac

h ax

is s

peci

fyin

g th

e av

erag

e ac

tivat

ion

leve

l of

one

set o

f un

its. f

ur e

ach

grap

h, f

ive

poin

ts a

re p

lotte

d w

hich

mar

k th

e ac

tiva-

tions

of

the

two

sets

of

inte

rnal

uni

ts w

hen

. the

five

con

figu

ratio

ns o

f m

ore

dist

ance

rig

ht w

ere

pres

ente

d-'-t

hese

are

mar

ked

with

an

~. L

ikew

ise,

eac

h of

the

five

poi

nts

for

the

inte

rnal

act

ivat

ions

for

the

conf

igur

atio

ns o

f m

ore

dist

ance

left

and

bal

ance

d di

stan

ce a

re m

arke

d w

ith a

n ' L

' and

a '

, res

pect

ivel

y. U

pon

exam

inin

g th

ese

activ

atio

n va

lues

bef

ore

trai

ning

, it w

as d

isco

vere

d th

at th

ese

$tts

of

inpu

t pat

tern

s w

ere

not d

iscr

imin

ated

in a

ny w

ay in

the

dist

ance

inte

rnal

grou

p. B

ecau

se th

e co

nnec

tion

stre

ngth

s of

the

conn

ectio

ns to

thes

e un

its w

ere

not t

rain

ed, e

very

inpu

t pat

tern

pro

duce

d al

mos

t the

sam

e ac

tivat

ion

patte

rn a

tth

e in

tern

al le

vel a

nd th

us a

ll of

the

poin

ts e

nded

up

on to

p of

eac

h ot

her.

Thu

s,th

is g

raph

is n

ot s

how

n. H

owev

er, w

hen

this

sam

e pr

oced

ure

was

per

fonn

ed a

fter

.

3. NATURE, NUR1\JRE,

AN

D C

ON

NE

CT

ION

S

dist

ance

trai

ning

, the

act

ivat

ions

sho

wn

in F

ig. 3

.11a

wer

e pr

oduc

ed. H

ere,

we

see

that

the

netw

ork

has

lear

ned

to in

tern

ally

rep

rese

nt s

imila

r di

stan

ce in

put

sim

ilarl

y (a

ll of

the

R,s

, L's

, and

B's

are

clu

ster

ed to

geth

er),

and

, mor

e im

por-

tant

ly, t

o re

pres

ent d

iffe

rent

dis

tanc

e in

puts

dif

fere

ntly

(th

e R

, L, a

nd B

clu

ster

sar

e se

para

ted

away

fro

m e

ach

othe

r). W

hat i

s cl

aim

ed, t

hen,

is th

at d

urin

gtr

aini

ng, t

he m

odel

res

truc

ture

d th

e in

tern

al re

pres

enta

tions

for

eac

h pr

oble

m

asso

ciat

ion

in s

uch

a w

ay th

at th

e co

ncep

t of

rela

tive

dist

ance

-mor

e di

stan

ce

left

, rig

ht, a

nd e

qual

dis

tanc

e-em

erge

d fr

om th

e re

pres

enta

tions

.

Thi

s an

alys

is w

as a

lso

perf

orm

ed a

fter

con

flic

t tra

inin

g an

d th

e re

sults

are

show

n in

Fig

. 3.1

1b. I

n th

is c

ase,

the

trai

ning

did

not

allo

w f

or th

e fo

rmat

ion

of

the

rela

tive

dist

ance

con

cept

with

in 4

0 ep

Och

s of

trai

ning

. The

in.e

maI

rep

rese

n-ta

tions

for

the

dift

'ere

nt d

ista

nce

conf

igur

atio

ns d

id n

ot d

iffe

rent

iate

into

the

tine

-'-

M:T

1VA

tIO

NU

NIT

!lE

T I

L L L

.II

M:T

lVA

tIO

NU

NIT

!lE

T !z

'rain

!"

~ ,-

- E

-. '-"

AC

TIV

AtI

ON

UN

IT IE

" .I

I

M:T

lVA

tIO

NU

NIT

IE

' 2

M:T

lVA

tIO

NIN

T S

Et t

"LI

L . "

. I "

AC

TIV

AtI

ON

UN

IT lE

U

1 .

FIG

. 3.11, Activations of

the

units

of

the

Inte

rnal

dis

tanc

e gr

oup

for

(a)

dist

ance

trai

ning

, (b)

con

flic

t tra

inin

g, a

nd (

c) c

onfl

ict t

rain

ing

afte

ren

codi

ng tr

aini

ng.

MC

CL

EL

lAN

D A

ND

JE

NK

INS

clus

ters

of

thei

r di

stan

ce r

elat

ive

rela

tions

hips

, With

out t

his

abst

ract

rel

atio

nshi

p,th

e m

odel

was

una

ble

to generalize to new configurations and thus, in the

pred

ictio

n ta

sk, d

id n

ot c

hang

e its

beh

avio

r, H

owev

er, w

hen

this

ana

lysi

s w

aspe

rfon

ned

afte

r en

codi

ng tr

aini

ng, (

whi

ch p

rodu

ced

the

rela

tive

dist

ance

rep

re-

sent

atio

ns a

t the

inte

mal

leve

l as

show

n in

Fig

. 3, l

lc), the m

odel

was

abl

e to

lear

n to

use

rel

ativ

e di

stan

ce c

ues

on th

e pr

edic

tion

task

,

Shor

tcom

ings

. of

the

Mod

el

"Thken together, the tw

o ve

rsio

ns o

f th

e si

mpl

e ne

twor

k m

odel

of

the

bala

nce

beam

task

that

we

have

des

crib

ed a

bove

exh

ibit

a st

riki

ng c

orre

spon

denc

e w

ithm

any

aspe

cts

of th

e de

velo

pmen

tal f

acts

, The

se c

orre

spon

denc

es h

ave,

we

thin

k,im

port

ant i

mpl

icat

ions

for

theo

ries

of

cogn

itive

dev

elop

men

t, B

efor

e w

e tu

rn to

thes

e co

rres

pond

ence

s" w

e fll

'St c

onsi

der

a fe

w s

hort

com

ings

of

the

mod

el, T

hree

failu

res

of th

e fi

rst v

ersi

on to

fit

aspe

cts

of S

iegl

ers

data

mus

t be

ackn

owle

dged

:Fi

rst,

the

mod

el c

an n

ever

act

ually

mas

tei'

Rul

e 4,

thou

gh s

ome

subj

ects

cle

arly

do, S

econ

d, it

' s b

ehav

ior

duri

ng R

ule

3 is

slig

htly

dif

fere

nt f

rom

hum

ans

(tho

ugh

it sh

ould

be

note

d th

at th

e " h

uman

" Rule 3 pa

ttern

is a

ctua

lly a

mix

ture

of

diff

eren

t str

ateg

ies

acco

rdin

g to

Kla

hr a

nd S

iegl

er, 1

978)

, Thi

rd, i

t can

exh

ibit

posi

tion

bias

es th

at a

re u

ncha

ract

eris

tic o

f hu

man

s, w

ho s

eem

(at

leas

t, fr

om th

eage of

on) to "kn

ow"

that

ther

e is

no

reas

on to

pre

fer

left

ove

r ri

ght,

The

re a

re o

ther

sho

rtco

min

gs a

t wel

l, Pe

rhap

s th

e m

ost s

erio

us is

in th

e in

put

repr

esen

tatio

ns, w

hich

use

dis

tinct

uni

ts to

rep

rese

nt d

iffe

rent

am

ount

s of

wei

ght

and

dist

ance

, Thi

s re

pres

enta

tion

was

cho

sen

beca

use

it do

es' n

ot i

nher

ently

enco

de th

e st

ruct

ure

of e

ach

dim

ensi

on, t

here

by f

orci

ng th

e ne

twor

k to

dis

cove

rth

e or

deri

ng o

f ea

ch d

imen

sion

. But

it h

as th

e dr

awba

ck th

at it

pre

vent

s th

ene

twor

k fr

om e

xtra

pola

ting

or e

ven

inte

rpol

atin

g be

yond

the

rang

e of

the

disc

rete

valu

es th

at it

has

exp

erie

nced

,Fi

nally

, Sie

gler

has

rep

orte

d pr

otoc

ol d

ata

that

indi

cate

s th

at s

ubje

cts

are

ofte

nab

le to

des

crib

e w

hat t

hey

are

doin

g ve

rbal

ly in

way

s th

at c

orre

spon

d fa

irly

wel

lto

thei

r ac

tual

per

fonn

ance

, It i

s no

t tru

e th

at a

ll su

bjec

t' s v

erba

lizat

ions

cor

rect

lych

arac

teri

ze th

e R

ule

they

are

usi

ng, b

ut it

is tr

ue, f

or e

xam

ple,

that

sub

ject

s w

hoar

e se

nsiti

ve to

the

dist

ance

cue

men

tion

that

they

are

usi

ng th

is c

ue a

nd th

ose

who

are

not

tend

not

to m

entio

n it,

The

mod

el is

of

cour

se completely mute,

Wha

t are

we

to m

ake

of th

ese

shor

tcom

ings

in li

ght o

f th

e ov

eral

l suc

cess

of

the

mod

el?

Obv

ious

ly, w

e ca

nnot

take

it a

s th

e fm

al w

ord

on d

evel

opm

ent o

fab

ility

to p

erfo

nn th

e ba

lanc

e sc

ale

task

, We

wou

ld s

ugge

st th

at th

e m

odel

'sh

ortc

omin

gs m

ay li

e in

two

plac

es: F

irst

, in

deta

ils o

f th

e en

codi

ng o

f in

puts

and

of th

e ne

twor

k ar

chite

ctur

e; a

nd s

econ

d, in

the

fact

that

the

mod

el o

nly

deal

s w

ith

acqu

isiti

on o

f im

plic

it kn

owle

dge,

Reg

ardi

ng th

e fi

rst p

oint

, it w

ould

be

reas

onab

le to

allo

w th

e in

put t

o en

code

sim

ilari

ty o

n ea

ch d

imen

sion

by

usin

g in

put r

epre

sent

atio

ns in

whi

ch e

ach

unit

resp

onde

d to

a r

ange

of

sim

ilar

valu

es s

o th

at n

eigh

bori

ng w

eigh

ts a

nd d

ista

nces

3, NATURE, NURTURE.

AN

D C

ON

NE

CT

ION

S

prod

uced

ove

rlap

ping

inpu

t rep

rese

ntat

ions

; fw

then

nore

, the

inpu

ts c

ould

wel

lm

ake

use

of a

rel

ativ

e co

de o

f m

agni

tude

to k

eep

valu

es w

ithin

a f

ixed

ran

ge.

Thi

s w

ould

pro

babl

y ov

erco

me

the

inte

rpol

atio

n an

d ex

trap

olat

ion

prob

lem

s (w

eha

ve n

o st

and

on w

heth

er s

uch

codi

ngs

are

lear

ned

or p

re-w

ired

),

The

se k

inds

of

fixe

s w

ould

not

allo

w th

e m

odel

to tr

uly

mas

ter

Rul

e 4

and

perh

aps

righ

tly s

o, s

ince

it s

eem

s lik

ely

that

Rul

e 4

(unl

ike

the

othe

r ro

les)

can

only

be

adhe

red

to s

tric

tly a

s an

exp

licit

(ari

thm

etic

) ro

le, I

ndee

d, it

mus

t be

ackn

owle

dged

that

ther

e isa conscious, verbally ac

cess

ible

com

pone

nt to

the

prob

lem

sol

ving

act

ivity

that

chi

ldre

n an

d ad

ults

eng

age

in w

hen

they

con

fron

t apr

oble

m li

ke th

e ba

lanc

e sc

ale

prob

lem

, The

mod

el d

oes

not a

ddre

ss th

is a

ctiv

ityits

elf,

How

ever

, it i

s te

mpt

ing

to s

ugge

st th

at th

e m

odel

cap

ture

s th

e gr

adua

l

acqu

isiti

on m

echa

nism

s w

hich

est

ablis

h th

e po

ssib

le c

onte

nts

of th

ese

cons

ciou

s

proc

esse

s. O

ne c

an v

iew

the

mod

el a

s m

akin

g av

aila

ble

repr

esen

tatio

ns o

f di

ffer

-in

g sa

lienc

e as

a f

unct

ion

of e

xper

ienc

e; th

ese

repr

esen

tatio

ns m

ight

ser

ve a

s th

era

w m

ater

ial u

sed

by th

e m

ore

expl

icit

reas

onin

g pr

oces

ses

that

app

ear

to p

laya

role

, Thi

s is

of

cour

se s

heer

spe

cula

tion

at th

is p

oint

, It w

ill b

e an

impo

rtan

t par

tof

the

,bus

ines

s of

the

ongo

ing

conn

ectio

nist

exp

lora

tion

of c

Ogn

itive

dev

elop

-m

ent t

o m

ake

thes

e sp

ecul

atio

ns e

xplic

it an

d te

stab

le,

IMPL

ICA

TIO

NS

OF

TH

E B

AL

AN

CE

$IM

UL

AT

ION

S

The

mod

el c

aptu

res

seve

ral o

f th

e m

ore

intr

igui

ng a

spec

ts o

f co

gniti

ve d

evel

op-

men

t, It

cap

ture

s its

sta

ge-l

ike

char

acte

r, w

hile

at t

he s

ame

time

exhi

bitin

g an

unde

rlyi

ng c

ontin

uity

whi

ch a

ccou

nts

for

grad

ual c

hang

e in

rea

dine

ss to

mov

e on

to th

e ne

xt s

tage

, It c

aptu

res

that

fac

t tha

t beh

avio

r ca

n of

ten

seem

ver

y m

uch

tobe

und

er th

e co

nb'o

l of

very

sim

ple

and

narr

ow r

oles

(e,

g" R

ule

1), y

et e

xhib

it

sym

ptom

s of

gra

dedn

ess

and

cont

inui

ty w

hen

test

ed in

dif

fere

nt w

ays,

It c

aptu

res

the

fact

that

dev

elop

men

t, in

a la

rge

num

ber

of d

iffer

ent d

omai

ns, p

rogr

esse

s

from

an

initi

al o

ver-

focu

ssin

g on

the

mos

t sal

ient

dim

ensi

on o

f a

task

or

prob

-le

m-to

the

poin

t whe

re o

ther

dim

ensi

ons

are

not e

ven

enco

ded-

follo

wed

by

a

sequ

ence

of

furt

her

step

s in

whi

ch th

e re

lianc

e on

the

initi

ally

una

ttend

ed d

imen

-si

on g

radu

ally

incr

ease

s,A

s m

entio

ned

prev

ious

ly, t

he m

odel

can

be

seen

as

impl

emen

ting

the

acco

m-

mod

atio

n pr

oces

s th

at li

es a

t the

hea

rt of Piaget'stheory of developmental

chan

ge, A

ccom

mod

atio

n es

sent

ially

am

ount

s to

adj

ustin

g m

enta

l str

uctu

res

tore

duce

the

disc

repa

ncy

betw

een

obse

rved

eve

nts

and

expe

ctat

ions

der

ived

fro

mth

e ex

istin

g m

enta

l str

uctu

res,

Acc

ordi

ng to

Fla

vell

(196

3), P

iage

t str

esse

d th

eco

ntin

uity

of

the

acco

mm

odat

ion

proc

ess,

in s

pite

of

the

over

tly s

tage

-like

char

-

acte

r of

dev

elop

men

t, th

ough

he

neve

r ga

ve a

par

ticul

arly

cle

ar a

ccou

nt o

f ho

wst

ages

ari

se f

rom

con

tinuo

us le

arni

ng (

see

Flav

ell,

1963

, pp,

244

-249

for

a

desc

ript

ion

of o

ne a

ttem

pt),

1be

mod

el p

rovi

des

such

a d

escr

iptio

n: it

sho

ws

clea

rly

how

a c

ontin

uous

acc

omm

odat

ion.

like

proc

ess

can

lead

to a

sta

ge-l

ike

prog

ress

ion

in d

evel

opm

ent,

MC

ClE

LL

AN

D A

ND

JE

NK

INS

Cha

nges

in r

epre

sent

atio

n an

d. a

ttent

ion

thro

ugh

the

cour

se o

f de

velo

p-m

ent.

Whe

n a

bala

nCe

scal

e pr

oble

m is

pre

sent

ed to

the

mod

el, i

t see

s it

diff

eren

t way

s, d

epen

ding

on

its d

evel

opm

enta

l sta

te. A

t all ti~

, inf

onna

tion

isin

som

e se

nse

pres

ent i

n th

e in

put f

or d

eten

nini

ng w

hat i

s th

e co

rrec

t res

pons

e.H

owev

er, a

t rus

t thi

s in

form

atio

n pr

oduc

es n

o re

al im

pres

sion

; wea

k, I'

iU1d

omac

tivat

ions

occ

ur a

t the

hid

den

leve

l and

thes

e m

ake

wea

k, r

ando

m im

pres

sion

sat

the

outp

ut le

vel.

At t

he b

egin

ning

of

the

Rul

e I

beha

vior

al p

hase

, the

mod

elha

s le

arne

d to

rep

rese

nt r

elat

ive

amou

nt o

f w

eigh

t. T

he p

atte

rn o

fact

ivat

ion

over

the

hidd

en u

nits

cap

ture

s re

lativ

e w

eigh

t, si

nce

one

unit

will

be

mor

e ac

tivat

ed if

ther

e is

mor

e w

eigh

t to

the

righ

t, an

d th

e ot

her

will

be

mor

e ac

tivat

ed if

ther

e is

mor

e w

eigh

t to

the

left;

bot

h un

its ta

ke o

n in

tenn

edia

te a

ctiv

atio

ns w

hen

the

wei

ghts

bal

anC

e. A

t thi

s po

int,

we

can

seet

he m

odel

as

enco

ding

wei

ght,

but n

otdi

stan

ce in

fonn

atio

n. I

ndee

d, a

s w

e ha

ve s

een

at th

is p

oint

the

netw

ork:

Cou

ld b

esa

id to

be

igno

ring

the

dist

ance

cue

; it m

akes

littl

e im

pact

on

activ

atio

n, a

ndle

arni

ng a

bout

dis

tanc

e is

ver

y sl

ow a

t thi

s po

int.

At t

he e

nd o

f th

e R

ule

I ph

ase,

in s

pite

of

its la

ck o

f im

pact

on

over

t behavior, the network: has learned to

repr

esen

t rel

ativ

e di

stan

ces;

at t

his

poin

t it i

s ex

trem

ely

sens

itive

to f

eedb

ack

abou

t dis

tanc

e; it

is r

eady

to s

lip o

ver

the

fair

ly s

harp

bou

ndar

y in

per

fonn

ance

betw

een

Rul

e 1

and

Rul

e 2.

Thu

s, w

e ca

n se

e th

e R

ule

1 st

age

as o

ne in

whi

chov

ert b

ehav

ior

fails

to m

irro

r a

gndu

al d

evel

opm

enta

l pro

gres

sion

that

car

ries

the

mod

el f

rom

ext

rem

e uo

read

ines

s to

lear

n ab

out d

ista

nce

at th

e be

ginn

ing

of th

isph

ase

to a

hig

h de

gree

of

read

ines

s at

the

end.

Thi

s de

velo

pmen

tal p

rogr

essi

on s

eem

s to

res

olve

the

appa

rent

para

doxi

cal

rela

tion

betw

een

obse

rved

sta

ge- l

ike

beha

vior

al d

evel

opm

ent a

nd a

ssum

ed c

on-

.tinu

ity o

f le

arni

ng. T

o us

this

is th

e m

ost i

mpr

essi

ve a

chie

vem

ent o

f th

e m

odel

; it

prov

ides

a s

impl

e, e

xplic

it al

tern

ativ

e to

mat

urat

iona

l acc

ount

s of

sta

ge- l

ike

prog

ress

ion

in d

evel

opm

ent.

It m

ust b

e no

ted,

how

ever

, tha

t the

suc

cess

of

the

mod

el d

epen

ds c

roci

ally

on

its s

truc

ture

. In

fact

the

resu

lts a

re le

ss c

ompe

lling

if e

ither

of t

he fo

llow

ing

chan

ges

are

mad

e: (

a) if

bal

ance

is tr

eate

d as

a s

epar

ate

cate

gory

, rat

her

than

being treated as the intennediate case be

twee

n le

ft-si

de-d

own

and

right

-sid

e-do

wn;

(b)

if th

e co

nnec

tions

fro

m in

put t

o hi

dden

uni

ts a

re n

ot r

esbi

cted

as

they

are

here

so

that

wei

ght i

s pr

oces

sed

sepa

rate

ly f

rom

dis

tanc

e be

fore

the

two

are

com

bine

d. '

Mor

e ge

nera

lly, i

t is

beco

min

g cl

ear

that

an:

:hite

ctur

al r

esbi

ctio

ns o

n co

nnec

-tio

nist

net

wor

ks a

re c

roci

al if

they

are

to d

isco

ver

the

regu

l~tie

s w

e hu

man

sdiscover from a limited ninge of experiences (Denker et at, 19

87; R

umel

hart

, in

prep

arat

ion)

. Thi

s ob

serv

atio

n un

ders

core

s th

at f

act t

hat t

he le

arni

ng p

rinc

iple

, in

itsel

f, is

not

the

only

pri

ncip

le th

at n

eeds

to b

e ta

ken

into

acc

ount

. The

re p

roba

-bl

y ar

e ad

ditio

nal p

rinc

iple

s th

at a

re e

xplo

ited

by th

e br

ain

to f

acili

tate

lear

ning

and

gene

raliz

atio

n. J

ust w

hat t

hese

add

ition

al p

rinci

ples

are

and

the

exte

nt to

whi

ch th

ey a

re d

omai

n sp

ecif

ic r

emai

ns to

be

unde

rsto

od in

mor

e de

tail.

3. NATURE, NURTURE,

AN

D C

ON

NE

CT

ION

S

Ext

endi

ng th

is o

bser

vatio

n a

step

fur

ther

, we

can

see

the

conn

ectio

nist

fra

me.

wor

k as

a n

ew p

arad

igm

in w

hich

to e

xplo

re b

asic

que

stio

ns a

bout

the

rela

tions

of

natu

re a

nd n

urtu

re. W

e m

ay f

ind

that

suc

cess

ful s

imul

atio

n of

dev

elop

men

tal

proc

esse

s de

pend

s on

bui

ldin

g in

dom

ain

spec

ific

con

stra

ints

in c

onsi

dera

ble

deta

il; if

so

this

wou

ld s

uppo

rt a

mor

e na

tivis

t vie

w o

f th

e ba

sis

of d

omai

n-sp

ecifi

c sk

ills.

On

the

othe

r ha

nd, i

t may

bun

out

that

a fe

w o

ther

gene

ral

prin

cipl

es in

add

ition

to th

e le

arni

ng p

rinc

iple

are

suf

fici

ent t

o al

low

us

to c

aptu

rea

wid

e ra

nge

of d

evel

opm

enta

l phe

nom

ena.

In

this

cas

e w

e w

ould

be

led

tow

ard

a m

uch

mor

e ex

peri

ence

-bas

ed d

escr

iptio

n of

dev

elop

men

t. In

eith

er c

ase,

itse

ems

very

like

ly th

at c

onne

ctio

nist

mod

els

will

hel

p us

take

a n

ew lo

ok a

t the

seim

port

ant b

asic

que

stio

ns.

CO

NC

LU

SIO

NS

The

exp

lora

tion

of c

onne

ctio

nist

mod

els

of h

uman

cog

nitio

n an

d de

velo

pmen

t is

still

at a

n ea

rly

stag

e. Y

et a

lrea

dy th

ese

mod

els

have

beg

un to

cap

ture

a n

ew w

ayof

thin

king

abo

ut p

roce

$sin

g, a

bout

lear

ning

and

, we

hope

the

pres

ent c

hapt

ersh

ows,

abo

ut d

evel

opm

ent.

Seve

ral.

fmth

er c

halle

nges

lie

ahea

d. O

ne o

f th

ese

isto

bui

ld s

tron

ger

brid

ges

betw

een

wha

t mig

ht b

e ca

lled

cogn

itive

-lev

el m

odel

s

and

our

evol

ving

und

erst

andi

ng o

f th

e de

tails

of

neur

onal

com

puta

tion.

Ano

ther

will

be

to d

evel

Op

mor

e fu

lly th

e ap

plic

atio

n of

cog

nitiv

e m

odel

s to

hig

her4

evel

aspe

cts

of c

ogni

tion.

The

hop

e is

that

the

atte

mpt

to M

eet t

hese

and

oth

erch

alle

nges

will

cont

inue

to le

ad to

new

dis

cove

ries

abo

ut th

e mechanisms of

hum

an th

ough

t and

the

prin

cipl

es th

at g

over

n th

eir

oper

atio

n an

d ad

apta

tion

toex

peri

ence

.

AC

KN

OW

LE

DG

ME

NT

S

The

text

of

this

art

icle

ove

rlap

s su

bsta

ntia

lly w

ith th

e te

xt o

f an

ear

lier

artic

le b

yM

cCle

lland

(19

89)

and

cont

ains

exc

erpt

s fr

om a

n ar

ticle

by

Jenk

ins

(198

6). T

hew

ork:

rep

orte

d he

re w

as s

uppo

rted

by

ON

R a

nd D

AR

PA

Und

er C

ontr

act N

umbe

r

NO

OO

I4-8

6-K

-O34

9, b

y an

NIM

H C

aree

r D

evel

opm

ent A

war

d M

HO

O38

S to

the

rust

aut

hor,

by

ON

R C

ontr

act N

OOOI4-82-C-O374, and by N

SF

Gra

nt B

NS

88-1

2048

.

RE

FER

EN

CE

S

Bever, T. G. (1970). The cognitive bail for lin

guis

tic s

truc

:tUle

l, In

J. R

, Hay

es (

Bd.

),

CO

lllili

oll

tJ1U

I the

dewlopmenl of ltm'lUl,e

(pp.

279

-362

). N

ew Y

ork:

Wile

y.

Den

ker,

J., -Schwartz, D., Wittner, B., So

ll8, S

., H

opfi

ekl,

J., H

ow""

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L, (1987),

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tl'ac

tion.

mrd

gelU

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iZlll

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.tT B

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abs

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e/op

mel

lllll

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t, Pr

iDc:

cton

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D, V

anN

oaIr

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Gro

uber

g, S

, (19

78),

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eory

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isua

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ory,

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elop

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Rca

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Sem

tlllti

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ullin

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aral

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istr

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nd, J

, L"

.t R

umel

bart

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, (19

81),

An

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ract

ive

activ

atio

n m

odel

of

cont

ext e

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ts in

Icttc

r pm

:cpt

ion:

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I. A

n IIC

CO

UIIt

of b

asic findings,

Psyc

holo

gica

l Rt!

1Iie

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McClelland, J, L" .t Rumelbart. D, E, (1

985)

, Dis

lribu

ted

mem

ory

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the

repr

esen

tatio

n of

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nd, J

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Rum

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, E"

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the micro.stnlCt/u'e of cognition, Volume

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, MA

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McClelland, J, L" St, John, M., .t 'Ii

raba

n, R

, (19

89),

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