Behavior of the model

Fitting "Same"-"Different" data using a parallel race model:

A theory of priming.

Denis Cousineau, Université de Montréal; Denis.Cousineau@UMontreal.CA

A simple model of priming

Assumptions:

• Short duration or complex stimuli favor rapid but linear decay of the information.

• Thus, this form of "noise" makes some low-level detectors unable to respond.

• Low-level detectors are assumed to be legions, given by the ρfactor (redundancy conjecture).

• Response times are given by a counter model where the redundant detectors are racing (Cousineau, submitted).

Behavior of the model

• With noise (i.e. complex of brief stimulations), less racers are available to fill the counter. Thus, the average response (crossing the boundary) will be both slower and more variable (see Figure 1).

• Plotting the average response times as a function of available detectors yield the typical signature of priming (see Figure 2).

• It is important to note that this non-linear effect is obtained with a linear increase in noise.

• All the equations can be obtained in closed form.

A1) The "Same"-"Different" task

B1) The "letter"-"non-letter" priming task

A2) The "Same"-"Different" results

B2) The Identity-priming results

C) Cue validity and the number of cued

locations in a cued detection task D) A feature detection task The two tasks have identical procedure

A manipulates complexity C

B manipulates duration D

The two tasks have identical results

In A, simpler objects are better;

In B, longer presentation is better.

ASF

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*

* ASF

free 100 ms 100 ms

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*

* Vary 200 ms 100 ms

Bamber, 1969 Cousineau & Lefebvre, in prep.

• The probe complexity C is 1 to 4 (3 depicted);

• Duration of the first slide not controlled by Bamber

• If different, the probe has from 1 to C differences.

N

*

*

* N

D vary 100 ms 100 ms Probe →

Prime →

Arguin & Bub, 1995

• The complexity C of the probe is always 1

• The duration of the prime D is varied (50..200 ms).

Rejected models:

• Limited-capacity models (predicts concave curve);

• Strength of activation models (circular argument);

• Linear preactivation of the processors (predicts linear facilitation);

• Random-walk model with an increasing boundary (predicts concave curve);

«A n op tim al i nf or m at ion -re tri ev al sys te m sh ou ld be b ia sed to fe tc h freq uen tly an d re ce nt ly en co un te re d ite m s. » -P in ke r, 19 97 «L 'am or ça ge ,c 'es ts up er so n

.» -J ean C. Ri en , 1 99 9

PrimingRecognitionRecency effect Det ectionof diagnostic informationConsiste ncyof mappingPriming Recognition RecencyeffectDetection of diagnostic inf ormationConsistency of mappingPrimi ngRecognitionRecencyeffect Detect ion of diagnostic informationConsistency of mappingPrimingRecognition Recen cy effect Detection of diagnostic informat ionConsistency of mappingPriming Rec ognition RecencyeffectDetection of diag

T h e ub iqu it ou s p re se n ce o f p rimi n g

• "Different" responses suggest a serial self-terminating search for the first difference.

• "Same" responses are convex and faster than

"Different", rejecting any serial model (Sternberg,`98).

• With no prime (neutral), there is no effect of the duration D.

• With prime, responses are convex and faster than neutral or invalid (not shown) conditions.

320 340 360 380 400 420 440 460 480

1 2 3 4

Complexity

Reaction times

"Same"

"Different"

345 365 385 405 425 445 465 485 505 525

50 100 150 200

Duration

Reaction times

Primed Neutral

The simpler the object is, the easier the decision is.

The longer the prime is seen, easier the decision is.

A & B commonalities:

«H ow ca n a m ass ive ly pa ra lle l c om pu te r kno w wh ich p rog ra m to se le ct at a gi ve n m om en t, if t he pr og ra m s ar e no t o rd er ed b y pr io rit y?» -H as br ou cq , pe rs . c om .

1 234 Complexity 2 1

4 3

Duration 1 234 Complexity

2 1 4 3

Duration 0 1 2 3 4 5

RT

0 1 2 3 4 5

RT

1 2 3 4

Comlexity 0 1 2 3 4 5

RT

1 2 3 4

Comlexity Hypothesis: Duration effect and Complexity effect are but two aspects of the same phenomena: Priming.

Priming results from a preactivation of relevant processors so that performance are better than baseline,

but also from a rapid decay of that preactivation so that the concerned processors return to baseline performance.

Are there other tasks with such a "signature" in the results? Yes.

33 ms 33 ms 33 ms Shiu & Pashler, 1997

50 100 150 200 250 300 0.2

0.4 0.6 0.8 1

50

60

70

80

90

100

1 2 3 4

340 360 380 400 420 440 460 480

t

t

t

t

∆θ

Figure 1: RT distributions when the number of racers ρvaries Figure 2: Predicted RT Figure 3: Random walk representation

Vulgarization of the model

• The model can be seen as a Random-Walk model (Ratcliff, 1977; see Figure 3).

• The drift rate is given by an angle θ. Any increase in noise (i.e. complexity or shorter duration) decreases the drift rate by a constant value ∆θ.

• The average time tto cross the boundary is thus given by the cotangent ! This curve for θvalues between 90 and 30 degrees turns out to be an EXCELLENT approximation to both the model (Figure 2) and the empirical data (A2 and B2).

I would like to thank C. Lefebvre and S. Hlie for their comments.

20 30 40 50

Valid Neutral Invalid Cue validity

P(errors)

One Four Eight

Identification task; easier when fewer mask, suggesting that noise is partly responsible for the curve.

Cousineau & Shiffrin, in prep.

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* 4

* 50 ms 50 ms

50 ms Number of features

Perceiving well-learned features and well-learned configuration is easier, suggesting that preactivation can be internalized.

× *

The Same-Different task (Bamber, 1969, Nickerson, 1967) is one of the simplest tasks used to study the recognition of visual patterns.Yet, the response times (RTs) obtained are among the most enigmatic in cognitive psychology (Sternberg, 1998). RTs to respond «different»seem to comply with a serial, self-terminating comparison model (because RTs are linearly longer for more complex objects and linearly shorter for dissimilar objects). However, RTs for «same»responses are shorter than any «different»responses. This rules out serial exhaustive processing when the two objects are identical. We present a model of priming that accounts simultaneously for both «same»and «different»responses. This approach shows that priming tasks and Same-Different judgment tasks are identical. Further, the results from a detection task (Townsend and his colleagues, 1984, 1981) are identical toBamber’sdata. This suggests that priming, or decay of it, also explain these results. Finally, since priming was modeled with the use of a variable threshold, the various points along aROC curve can correspond to various levels of priming. This approach thus synthesizes a large body of classic results in cognitive psychology.

"Different"

"Same"