the Interactive Activation Model

Ubiquity of the Constraint SatisfactionProblem

• In sentence processing– I saw the grand canyon flying to New York– I saw the sheep grazing in the field

• In comprehension– Margie was sitting on the front steps when she heard the

familiar jingle of the “Good Humor” truck. She remembered her birthday money and ran into the house.

• In reaching, grasping, typing…

Graded and variable nature of neuronal responses

Lateral Inhibition in Eye of Limulus

(Horseshoe Crab)

Findings Motivating the IA Model

• The word superiority effect (Reicher, 1969)

– Subjects identify letters in words better than single letters or letters in scrambled strings.

• The pseudoword advantage– The advantage over single

letters and scrambled strings extends to pronounceable non-words (e.g. LEAT LOAT…)

• The contextual enhancement effect

– Increasing the duration of the context or of the target letter facilitates correct identification.

• Reicher’s experiment:– Used pairs of 4-letter words

differing by one letter READ ROAD

– The ‘critical letter’ is the letter that differs.

– Critical letters occur in all four positions.

– Same critical letters occur alone or in scrambled strings _E__ _O__ EADR EODR

W PW Scr L

Perc

en

t C

orr

ect

READREAD

_E__ O

The Contextual Enhancement Effect

Ratio

Perc

ent

Corr

ect

Questions

• Can we explain the Word Superiority Effect and the Contextual Enhancement Effect as a consequence of a synergistic combination of ‘top-down’ and ‘bottom-up’ influences?

• Can the same processes also explain the Pseudoword advantage?

• What specific assumptions are necessary to capture the data?

• What can we learn about these assumptions from the study of model variants and effects of parameter changes?

• Can we derive novel predictions?

• What do we learn about the limitations as well as the strengths of the model?

Approach

• Draw on ideas from the way neurons work

• Keep it as simple as possible

The Interactive Activation Model

• Feature, letter and word units.• Activation is the system’s only

‘currency’• Mutually consistent items on

adjacent levels excite each other• Mutually exclusive alternatives

inhibit each other.• Response selected from the letter

units in the cued location according to the Luce choice rule:

where

IAC Activation Function

Unit i

Output fromunit j

wijmax

min

rest

a

0

neti = joj wij

oj = [aj]+

Calculate net input to each unit:

Set outputs:

The Interactive Activation Model

How the Model Works:

Words vs. Single Letters

Rest levels for features, letters = -.1Rest level for words frequency dependent between -.001 and -.05

Word and Letter Level Activations for Words and Pseudowords

Idea of ‘conspiracy effect’ rather than consistency with rules as a basis of performance on ‘regular’ items.

Role of Pronouncability vs. Neighbors

• Three kinds of pairs:– Pronounceable:

SLET-SPET

– Unpronouncable/good:

SLCT-SPCT

– Unpronouncable/bad:

XLQJ-XPQJ

Simulation of Contextual Enhancement Effect

The Multinomial IA Model

• Very similar to Rumelhart’s 1977 forumulation• Based on a simple generative model of displays in letter

perception experiments.– Experimenter selects a word,– Selects letters based on word, but with possible random

errors– Selects featues based on letters, again with possible

random error AND/OR– Visual system registers features with some possibility of

error– Some features may missing as in the WOR? example above

• Units without parents have biases equal to log of prior• Weights defined ‘top down’: correspond to log of p(C|P)

where C = child, P = parent• Units take on probabilistic activations based on softmax

function– only one unit allowed to be active within each set of

mutually exclusive hypotheses• A state corresponds to one active word unit and one active

letter unit in each position, together with the provided set of feature activations.

• If the priors and weights correspond to those underlying the generative model, than states are ‘sampled’ in proportion to their posterior probability

– State of entire system = sample from joint posterior– State of word or letter units in a given position = sample

from marginal posterior

Subscript i indexes one memberof a set of mutually exclusive hypotheses; i’ runs over all membersof the set of mutually exclusivealternatives.

Input and activation of units in PDP models

• General form of unit update:

• Simple version used in cube simulation:

• An activation function that links PDP models to Bayesian ideas:

• Or set activation to 1 probabilistically:

unit i

Input fromunit j

wij

neti

)(min)(

else

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:0 if

restadaneta

restadaneta

net

noiseinputbiasawnet

iiii

iiii

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iii

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iij

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aneta

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inputbiasawnet

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i

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i e

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max=1

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