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Exemplar models and the perceptual magneteffect
Gerhard [email protected]
June 23, 2008
Bielefeld
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Overview
Kuhl’s 1992 experiments
additional findings: Kuhl et al. 1992
Lacerda 1995
echoes of exemplars
Hintzman’s and Goldinger’s modelimplications for the perceptual magnet effect
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Kuhl 1992
main findings
vowel categories have prototypical elements
prototype “warps the perceptual space”:
equal psycho-physical distance are perceived as smaller in theneighborhood of prototypesprototype acts like a “magnet” (or rather as a center of gravityin Einstein’s general theory of relativity)
effect is
strong for adultsweak but significant for infantsabsent for monkeys
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Experimental setup
two reference stimuli were picked out (a prototypical and anon-prototypical /i/)
test stimuli were arranged on 4 orbits of increasing size aroundthe reference vowels
test persons are English native speakers
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Experimental setup
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Experimental setup
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Experiment 1: category goodness
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Experiment 2: magnet effect with adults
Experiment 2
test persons were exposed to a referent speech sound (P orNP) and a comparison speech sound (one of the points onone of the orbits)
test persons had to press a button when the comparison vowelwas played
in test trials:
referent vowel was changed to comparison vowelcorrect responses were reinforced by visual signal
in control trials:
only referent vowel was playedfalse-positives were monitored
128 trials (32 test stimuli × 2 trials each × 8 test persons)
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Experiment 2: magnet effect with adults
diagram: total correct responses (positive and negative):
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Experiment 2: magnet effect with adults
diagram: correct generalization as function of psychophysicaldistance
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Experiment 3: magnet effect with infants
setup
similar to previous experiment
head-turn responses were counted
correct positives were reinforced by a toy animal that startedmoving
actual experiment was preceded by a training phase were testsubject were conditioned to perform head-turns when vowelquality changes
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Experiment 3: magnet effect with infants
diagram: correct generalization as function of psychophysicaldistance
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Experiment 4: magnet effect with monkeys
setup
similar to previous experiment
subjects were rhesus macaques
key-release instead of head-turns
correct positives were reinforced by food rather than a toy
no significant difference between prototype and non-prototypecondition
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Experiment 4: magnet effect with monkeys
diagram: correct generalization as function of psychophysicaldistance
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Kuhl et al. 1992
“Linguistic Experience Alters Phonetic Perception in Infantsby 6 Months of Age” (Science, 1992)
main finding:
perceptual magnet effect is confirmedlocation of prototypes depends on native languageeffect can be observed already with infants in pre-linguistic age
comparison of American (native language: AE) and Swedishinfants
referent vowels: /i/ (is a phoneme in AE but not in Swedish)and /y/ (is a phoneme in Swedish but not in AE)
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Experimental setup
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Results
both groups of infantsshowed perceptual magneteffect
American infants treated /i/and Swedish infants treated/y/ as prototyp
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Exemplar theories
Lacerda 1995/1998
PME can be derived from exemplar model
“prototype” of a category C is just a region where exemplarsof this category have a high relative density (as compared toother categories)
“similarity” between exemplars is (implicitly) defined assimilarity in category memberships
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Lacerda’s model
exemplars of a category are normally distributed in aone-dimensional space (generalizes to higher dimensionality)
relative frequency of items of a category which has its meanat µ:
Class(x, µ, σ) =1√
2 · π · σ· e−
(x−µ)2
2·σ2
number of items of category A within an ε-neighborhood ofx0:
NeighbA(x0, ε) = TotalA∫ x0+ε
x0−εClass(x, 0, σ)dx
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Lacerda’s model
similarity of an exemplar to a category A (if B is the onlycompeting category):
s(A, x0) =NeighbA(x0, ε)
NeighbA(x0, ε) + NeighbB(x0, ε)
note that NeighbA(x0, ε) depends on abundance ofA-exemplars, as well as on x0 and ε
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Lacerda’s model
suppose exemplars are distributed as follows:
Category µ σ Exemplars in category
A 0 3 1000
B 3 1 100
discrimination function:
discr(x0) =
∣∣∣ ddx0
s(A, x0)∣∣∣+ ∣∣∣ d
dx0s(B, x0)
∣∣∣Const
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Lacerda’s model
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Derivation of the PME
similarity between two exemplars x1 and x2 is (apparently)defined as
sim(x1, x2) =∫ x2
x1
discr(x)dx
=12(|S(A, x1)− S(B, x1)|+ |S(B, x1)− S(B, x2)|)
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Comparision with Kuhl’s data
goodness ratings from Kuhl 1991 were used to estimateexemplar densitiesfrom this average similarities to prototype were computed
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Discussion
NP condition is not computed, so strictly speaking the PMEis not demonstrated
however, discrimination function in figure 1 predicts similaritybetween equidistant points as a function of the distance fromthe prototype—magnet effect in the center of a category ispredicted
PME depends on categorization
Kuhl’s experiment with animals did not involve categorization,thus no PME
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Critical points
Kuhl et al. 1992 (with Lacerda herself being a co-author)demonstrates that PME occurs at an age where infants do notyet use vowels contrastively
unclear whether 6 months infants already have categories
similarity metric appears ad hoc
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Echoes and the PME
Echoes of perception
Hintzman (1986), Goldinger (1998):
observation causes stored exemplars to resonate“echoes” are formed by superimposing resonating exemplarswhat is stored in memory is not the observation itself (or acognitive representation of it) but its echo
model suggests an alternative exemplar-based explanation ofthe PME:
prototypes are just areas of high exemplar density (as inLacerda’s model)each exemplar acts as a little magnet, pulling the echo of anobservation towards itselfhigh density regions exert stronger attracting force, thusreducing distance between echoes as compared to distancebetween observations
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Echoes and the PME
Details of the model
exemplars are represented as n-dimensional vectors (unlike inGoldinger’s model, n may be low, and the exemplar space iscontinuous rather than discrete)
similarity between exemplars is a monotonically decreasingfunction of Euclidean distance:
sim(x1, x2) = e‖x1−x2‖
2
σ2
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Echoes and the PME
Details of the model
Let o be an observation and ltm be the long term memory,i.e. a set of exemplars
echo(ltm, o) =o+
∑x∈ltm sim(x, o)x
1 +∑
x∈ltm sim(x, o)
note that o itself is a component of its echo (otherwise thememory could not be initialized)
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Echoes and the PME
black dots: exemplars in long term memory
red/green circles: observations
blue/brown circles: their echos
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Echoes and the PME
reconstruction of Kuhl’s finding
ltm initialized with 1000 exemplars, that werepseudo-randomly normally distributed around (.5, .5) withσ = .05prototype: (.5, .5), nonprototype: (.75, .5)orbits have a diameter of .1, .2, .3 and .4 respectively
measured was average similarity of the elements of an orbitfrom the referent point
qualitatively similar results are obtained for differentparameter settings
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Echoes and the PME
O1 O2 O3 O4
orbits
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
similarity
PrototypeNonprototype
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