a configural theory of attention and associative learning...a configural theory of attention and...
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A configural theory of attention and associative learning
David N. George & John M. Pearce
# Psychonomic Society, Inc. 2012
Abstract A formal account of the relationship betweenattention and associative learning is presented within theframework of a configural theory of discrimination learning.The account is based on a connectionist network in whichthe entire pattern of stimulation presented on a trial activatesa configural unit that then enters into an association with thetrial outcome. Attention is assumed to have two roles withinthis network. First, the salience of the stimuli at the input tothe network can be increased if they are relevant to theoccurrence of reinforcement and decreased if they are irrel-evant. Second, the associability of configural units canincrease on trials when the outcome is surprising and de-crease when the outcome is not surprising.
Keywords Associative learning . Attention . Classicalconditioning
The theory in the present article differs in a fundamentalway from the other theories considered in this special issue.When a pattern of stimulation is repeatedly paired with agiven outcome, then, according to the other theories, eachelement of the pattern has the capacity to enter into an
association with the outcome. In contrast, the present theoryassumes that each conditioning trial will provide the oppor-tunity for only a single association to form. The associationwill be between a representation of the pattern in its entiretyand a representation of the outcome with which it is paired.This configural account of conditioning has been presentedformally on a number of occasions (Pearce, 1987, 1994,2002; Pearce, Esber, George, & Haselgrove, 2008), andPearce (2002) described its application to a range of phe-nomena including blocking, overshadowing, conditionedinhibition, the solution of simple and complex discrimina-tions, and so forth. A shortcoming of the original formula-tion of configural theory is that it failed to account forchanges in attention that take place during the course ofconditioning. We assume that a change in attention to astimulus is reflected by its conditionability. If the condition-ability of a stimulus is high, it is assumed to be paid moreattention than when its conditionability is low. The overallpurpose of the present article is to present a formal modifi-cation of configural theory that allows it to explain howsuch changes in conditionability take place.
There is, in fact, a growing body of evidence to suggestthat the attention paid to a stimulus is influenced accordingto two different sets of principles (see Pearce & Mackintosh,2010). An early experimental design that has been said toshow the influence one kind of attention on conditioningwas conducted by Mackintosh and Little (1969). Twogroups of pigeons initially received two discriminations ofthe form AW+BW–, AX+BX– (see Table 1). Each com-pound consisted of coloured lines. A and B belonged to onedimension—say, orientation—which was relevant, and Wand X to the other dimension—say, color—which was irrel-evant. Once the initial discriminations had been mastered,subjects were transferred to a set of new discriminationsinvolving novel values from the two dimensions. Animals
D. N. George (*)Department of Psychology, University of Hull,Hull HU6 7RX, UKe-mail: [email protected]
D. N. GeorgeSchool of Psychology, University of New South Wales,Sydney, New South Wales, Australia
J. M. PearceSchool of Psychology, Cardiff University,Cardiff CF10 3AT, UKe-mail: [email protected]
Learn Behav (2012) 40:241–254DOI 10.3758/s13420-012-0078-2
receiving an intradimensional shift (IDS), in which thesignificance of the two dimensions remained the same forboth stages, acquired the second set of discriminations morereadily than those receiving an extradimensional shift(EDS), in which the significance of the dimensions wasreversed for the second stage. The generally accepted ex-planation for the foregoing outcome has been that the initialtraining resulted in pigeons paying more attention to therelevant than to the irrelevant stimuli, and that this effectgeneralized to the new values from the two dimensions forthe test discrimination (see, e.g., Mackintosh, 1975;Sutherland & Mackintosh, 1971).
An experiment by Hall and Pearce (1979) revealed evi-dence of a rather different attentional process. Rats firstreceived Pavlovian conditioning in which a conditionedstimulus (CS) was paired with a small shock before it waspaired with a larger shock in Stage 2 of the experiment. Onthe basis of the principles that have just been put forward, itwould be expected that the initial training would result inconsiderable attention being paid to the CS, which wouldthen facilitate learning when the CS was paired with thelarger unconditioned stimulus (US). In fact, conditioning inStage 2 progressed slowly, which prompted Pearce and Hall(1980) to propose a new theory of attention. Animals wereassumed to pay attention to stimuli whose significance wasuncertain, such as a CS at the outset of conditioning, as thiswould promote rapid learning when it was needed. In con-trast, once conditioning with a CS had reached asymptote,attention to it was assumed to decline, as there was nothingmore to be learned about the stimulus, and hence no need toattend to it.
The two kinds of attention that have just been describedcan be viewed as serving rather different purposes. The firstallows animals to detect stimuli that signal events of signif-icance in their environment, and presumably will guideanimals efficiently towards reward and away from punish-ment. This kind of attention could be said to alter theeffective salience of a stimulus, and thereby influence thechances of it being detected in the future. By enhancing thesalience of relevant stimuli, and lowering that of irrelevantstimuli, this kind of attention would also make it easier tosolve discriminations when irrelevant stimuli are involved.To take account of this type of change in attention, we shall
introduce a parameter, α, the value of which will reflect theeffective salience of a stimulus.
The second kind of attention allows the mechanisms ofassociative learning to concentrate on stimuli whose signif-icance remains uncertain, and about which further learningis necessary. This kind of attention might be said to alter theconditionability of a stimulus. However, rather than alter theconditionability of individual stimuli, we propose that thistype of attention influences the conditionability of individ-ual units in a connectionist network that represent the entirepattern of stimulation on the current trial. We shall introducea second parameter, σ, to refer to the conditionability of aconfigural unit. In keeping with the proposals of Pearce andHall (1980), σ is assumed to increase on trials in which theoutcome is surprising and decrease on trials in which theoutcome is expected.
Given these different functions of attention, and giventhat there is good evidence for each of them (see Pearce &Mackintosh, 2010, for a review), it should not be surprisingto discover that we are not the first to propose that theyshould both be incorporated into a single theory (e.g., LePelley, 2004). Indeed, Pearce, George, and Redhead (1998)presented an outline of how a configural theory of associa-tive learning might accommodate the two kinds of attentionthat have just been described, but it was presented informal-ly. In the present article, therefore, we start by providing anintroduction to the configural theory of Pearce (1994). Wethen show how this theory can be adapted formally to permitmore attention to be paid to relevant than to irrelevantstimuli and, at the same time, to take account of the princi-ples advocated by Pearce and Hall (1980). Finally, weexplore how well the modified theory can account for thebasic phenomena of conditioning, particularly those thatmight be said to reveal an influence of attention on associa-tive learning.
A configural network for discrimination learning
Figure 1 shows a simple configural connectionist networkthat can solve an AX+BX– discrimination (ignore thedashed and dotted lines for the moment). In this discrimi-nation, compound AX signals food, and BX signals theabsence of food. Stimuli A and B are relevant by virtue ofbeing uniquely associated with the presence and absence offood, respectively, and X is irrelevant by virtue of beinguninformative about the trial outcome. To the left of thenetwork is a column of receptor units that are activatedwhenever stimuli A, B, or X are presented. Once a receptorunit is activated, it will excite an input unit to the network. Ifthe compound AX is presented to the network, the inputunits for A and X will be connected to a configural unit inthe next layer. Since AX is paired with food, an excitatory
Table 1 Design of an IDS–EDS experiment with A, B, C, and Dbelonging to one dimension and W, X, Y, and Z belonging to anotherdimension
Group Stage 1 Stage 2
IDS AW + BW– AX + BX– CY + DY– CZ + DZ–
EDS AW + BW– AX + BX– CY + CZ– DY + DZ–
242 Learn Behav (2012) 40:241–254
link will develop between the configural unit and an outputunit on the right-hand side of the network. If B and X arepresented together and followed by nothing, then a newconfigural unit representing this combination will beconnected to the relevant input units, and it will enter intoa negative or inhibitory association with the output unit.Once these connections are fully formed, presenting AX tothe network will excite strongly the AX configural unit,which will strongly excite the output unit. In addition, thepresence of X will activate the BX unit, but the absence of Bwill mean that this activation is incomplete. Even so, themodest activation of the BX configural unit will excite tosome extent the inhibitory link to the output unit and weak-en slightly the response excited by AX. If A should bepresented by itself, it will activate only the AX unit, albeitincompletely, and lead to a relatively strong conditionedresponse (CR). Presenting B alone will activate only theBX unit and have an inhibitory effect on the output unit,while presenting X alone will excite each of the configuralunits incompletely and result in a modest excitatoryresponse.
According to Pearce (1994), the formal principles behindthese proposals are as follows. The level of activation of areceptor unit is determined by the intensity of the stimulus thatexcites it. The level of activation of an input is determined bythe signal it receives from the receptor unit and by the numberof other input units concurrently activated. Equation 1 showshow the level of activation of input unit i, ui, is determinedwhenmore than one stimulus is present (where i ranges from 1to the number of input units activated).X
u2i ¼ 1 ð1Þ
One consequence of Eq. 1 is that the effective salience ofa stimulus will be greater when it is presented alone than
when it is accompanied by another stimulus. It is partly forthis reason that the theory of Pearce (1994) is able to explainthe phenomenon of external inhibition (Pavlov, 1927). Forease of discussion, we shall assume that whenever a stimu-lus is presented, it activates its receptor unit to the maximumlevel of 1. If this level of activity is transferred to the inputunits, it follows from Eq. 1 that the value of ui for anyactivated input unit will be given by Eq. 2, where n is thenumber of activated input units.
ui ¼ 1ffiffiffin
p ð2Þ
Presenting a pattern of stimulation to the network for thefirst time will result in the recruitment of a single configuralunit. The unit will become connected to all of the input unitsexcited by the pattern, and the configural unit will fire at itsmaximum level of 1. If the same pattern should be presentedagain, the same array of input units will be activated, and theconfigural unit will again be activated to its maximum level.If a different pattern is presented to the network, only afraction of the units connected to the original configural unitwill be excited, and it will be only partially activated.Whenever a pattern of stimulation should fail to excite anyexisting configural unit to the maximum value, the patterncan be regarded as novel, and a new configural unit will berecruited.
The strength of the connection between input unit i andthe configural unit j, wi,j, is the same as the level of activa-tion of the input unit, ui. Equation 3a shows how theactivation of configural unit j, aj, will be affected whenany pattern of stimulation, familiar or novel, is presentedto the network (where i ranges from 1 to the number of inputunits).
aj ¼X
wi;jui ð3aÞ
Pearce (1994) proposed that Eq. 3a should be replacedwith Eq. 3b, in order to allow predictions from the networkto be consistent with predictions from an earlier formulationof the theory (Pearce, 1987).
aj ¼X
wi;jui� �2
ð3bÞ
Adopting Eq. 3b rather than 3a has at least two conse-quences. First, presenting a pattern to the network willactivate the configural unit for a different pattern to asmaller extent according to Eq. 3b than to 3a. Thus, themodification has the effect of sharpening the generalizationgradient from one pattern to another. Second, Pearce (1994)has shown that the right-hand side of Eq. 3b is formallyequivalent to the expression Nc
2/(Nx × Ny), where Nc is thenumber of common elements shared by patterns X and Y,and Nx and Ny are the number of elements unique to each of
AX
BX
A
X
B
A
X
B US CR
ConfiguralUnits
ReceptorUnits
InputUnits
OutputUnit
Excitatory Link
Inhibitory Link
Feedback Link for
Feedback Link for
Fig. 1 Connectionist network for a configural theory of associativelearning, showing the connections involved in the solution of an AX +BX– discrimination. The feedback links permit changes in the con-ditionability of configural units (dotted lines) and changes in therelative effectiveness of input units (dashed lines)
Learn Behav (2012) 40:241–254 243
the patterns. This expression has been used on more thanone occasion to compute the similarity between two patterns(e.g., Atkinson & Estes, 1963). Thus, the extent to whichone pattern of stimulation will excite the configural unit foranother pattern can be said, according to Eq. 3b, to bedetermined by the similarity between them. Kinder andLachnit (2003; see also Pearce et al., 2008) have suggestedthat the exponent 2 in Eq. 3b may not be fixed, but may varyaccording to the nature of the experimental stimuli. For allof the simulations reported here, the exponent of Eq. 3b wasset at 2.
Although only one configural unit will be activated max-imally on any trial, other units might be activated to a lesserextent as the result of previous training with patterns similarto the one currently presented. The previous trials may haveresulted in these configural units entering into associations,of strength E, with the output unit. Pearce (1994) proposedthat the overall activation of the output unit to pattern K, Vk,is then given by Eq. 4 (where j ranges from 1 to the numberof configural units).
Vk ¼X
ajEj ð4Þ
The only configural unit whose associative strength maychange on a particular trial is the one representing thecurrent pattern of stimulation, which will be the only onethat is fully activated. The change in associative strength ofthis unit is given by Eq. 5. In this equation, λ is theasymptote of conditioning, which is normally set at 1, andβ is a learning rate parameter with a value set between 0 and1 that is determined by the properties of the reinforcer.
ΔEk ¼ b l� Vkð Þ ð5Þ
A computer simulation based on the foregoing equationsrevealed that the AX+BX– discrimination will be solvedwhen the associative strength of the configural unit for AXis 1.066 and that for BX is –.266. For the simulation, thevalue of λ was set at the maximum permissible value of 1,and β was set at .2. The simulation also revealed that, whenpresented alone, the stimuli A, B, and X would activate theoutput unit to .53, –.133, and .4, respectively. The negativeassociative strength of B will then allow it to manifest all ofthe properties of a conditioned inhibitor (Rescorla, 1969).
Changes in salience (α) of relevant and irrelevant stimuli
The configural network is thus capable of solving discrim-inations involving both relevant and irrelevant stimuli. Asthe network has been presented, however, it has not beenpossible to distinguish between those stimuli that are rele-vant, which should receive attention, and those that areirrelevant, which should be ignored. In order to achieve this
goal, we propose that the network shown in Fig. 1 containsfeedback links that transfer a signal from the configurallayer to the input layer. These links are represented by thedashed lines. The purpose of the links is to enable inputunits for stimuli that in the past have been relevant to a trialoutcome to be activated to a greater extent by their respec-tive receptor units, than those that have been irrelevant. Inthe case of an AX+BX– discrimination, a reduction in thesensitivity of the input unit for X will reduce the extent towhich, say, compound AX will excite the configural unit forBX, and thus reduce generalization between the two com-pounds. The discrimination will therefore be easier to solvethan when there are no changes to the sensitivity of the inputunits. Indeed, it was for this reason that we suggested thatchanges in salience take place at the input layer.
In order to increase the sensitivity of an input unit, con-figural units that correctly predict the trial outcome feedback a signal that increases the sensitivity of the input unitsto which they are connected. On the other hand, configuralunits that incorrectly predict the trial outcome feed back asignal that reduces the sensitivity of their input units. Moreformally, on any trial, a signal is returned from each config-ural unit to all of the input units to which it is connected.The magnitude of the feedback from configural unit j toinput unit i, fj,i, is the product of the associative strength ofthe configural unit and its net input activation, and is givenby Eq. 6.
fj;i ¼ Ej
Xwi;jui� � ð6Þ
As well as a magnitude, the feedback signal also has asign. This is determined by the concordance between theassociative strength of the configural unit and the occur-rence, or not, of a US on that trial. If the value of Ej ispositive, feedback is positive when the US occurs, butnegative if it does not occur. Conversely, if Ej is negative,feedback is negative when the US occurs, but positive if itdoes not. In this way, positive feedback indicates that theconfigural unit is contributing to the prediction of the correctoutcome for that trial, whereas negative feedback indicatesthat it is predicting the incorrect outcome.
The net feedback to each input unit is obtained by firstcalculating the sum of the signed feedback signals from eachconfigural unit to that input unit. In order that the feedbackreflect the extent to which each input unit contributes to theprediction of the trial outcome, this sum is then multipliedby the activation of the input unit. The net feedback to inputunit i, Fi, is given by Eq. 7 (where j ranges from 1 to thenumber of configural units).
Fi ¼ uiX
fj;i ð7Þ
Once the feedback to each input unit has been calculated,the effectiveness of the input units is updated. If a single
244 Learn Behav (2012) 40:241–254
input is active, its effectiveness, α, is updated according toEq. 8a, where θ is a rate parameter (set to 0.1 for all of thesimulations reported here). A single cue that predicts thecorrect outcome will gain in effectiveness, whereas a cuethat predicts the incorrect outcome will lose effectiveness.
Δai ¼ θFi ð8aÞWhen two or more input units are active, the change in
the effectiveness of any one of these will be dependent notonly on the net feedback to that input unit, but also on thefeedback to other input units. This is achieved by subtract-
ing the arithmetic mean of the feedback to all input units, F,from the feedback to each unit, as is shown in Eq. 8b.Hence, it should always be the case that the effectivenessof a unit that is the best predictor of a trial outcome willincrease, the effectiveness of the worst predictor shoulddecrease, and when all stimuli contribute equally to theprediction of the outcome, there should be no changes inthe effectiveness of any of them.
Δai ¼ θ Fi � F� � ð8bÞ
To understand the influence of an input unit’s effective-ness on the network, we must first consider a modificationto Eq. 2 first described by Pearce (1994). This modification,given in Eq. 9, was made in order to accommodate stimuliof different intensities, by allowing the activation of receptorunits to have any real value rather than being confined tojust 0 or 1. The activation of a particular input unit, ui, is afunction of the activation of its receptor unit, Pi, and that ofall other receptor units. Despite the difference betweenEqs. 2 and 9, the latter still ensures that the combined levelof activation of all the input units on any trial is in keepingwith the relationship expressed in Eq. 1.
ui ¼ PiffiffiffiffiffiffiffiffiffiffiffiPP2
p ð9Þ
The effectiveness, α, of an input unit affects activity in theinput layer in much the same way as activity in its receptorunits does. That is, an increase in the effectiveness of an inputunit will have the same effect as an increase in the activation ofits receptor unit, and a decrease in the unit’s effectiveness willhave the same effect as a decrease in the activation of itsreceptor unit. This is implemented in the manner shown inEq. 10, by simply multiplying the activation of each receptorunit by the effectiveness of the corresponding input unit.When the activation of each receptor unit in a given patternis the same, and the effectiveness of the corresponding inputunits are equal, this equation reduces to Eq. 2.
ui ¼ PiaiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPPað Þ2
q ð10Þ
Changes in conditionability (σ) of configural units
For the network to take account of the proposals of Pearceand Hall (1980), a further layer of feedback links has beenincluded (see the dotted lines in Fig. 1). Because we wantedto capture the idea of Pearce and Hall that the surprisingnessof the US on one trial influences the conditionability on thenext trial of the stimuli with which it was paired, these linksinfluence the ease with which associations between config-ural units and output units can develop. In short, on everytrial that a configural unit is fully activated, its associabilityfor the subsequent trial is determined by the degree to whichthe presented outcome is surprising.
Whereas Pearce and Hall (1980) proposed that the asso-ciability of individual stimuli was determined by the surpris-ingness of the events that followed them, we are proposingthat the associability of entire patterns of stimulation isdetermined in this manner. More formally, the links transmita signal of magnitude (λ – Vk), which is determined byevents on the current trial, to the configural unit that ismaximally activated. This signal then determines the associ-ability of the configural unit for the next occasion on whichit is maximally activated. Equation 11 shows how the valueof σ on trial n is determined by the events on trial n – 1 (seePearce, Kaye, & Hall, 1982). Equation 12 shows how σinfluences the acquisition of associative strength to config-ural unit K.
σn ¼ g ln�1 � VKn�1
�� ��þ 1� gð Þσn�1 ð11Þ
ΔEk ¼ σb l� Vkð Þ ð12ÞHence, if the outcome on a trial with pattern K should be
unexpected—that is, the discrepancy (λ – Vk) is large—theconditionability of configural unit K will be high for thesubsequent trial, but if the outcome is expected—that is,(λ – Vk) is small—the conditionability of this unit will below. The parameter γ determines the extents to which σ isinfluenced by the discrepancy (λ – Vk) on trial n – 1 and towhich it is influenced by all previous trials. When γ is large,σ is primarily determined by the discrepancy on trial n – 1.
Application of the network
In order to derive predictions from the network, a series ofcomputer simulations was conducted. For these simulations,the values of λ and β in Eq. 5 were set at 1 and .1,respectively, and the values of the parameters θ and γ wereset at .1. Unless stated otherwise, the intensity of a stimulusat the receptor units was 1, and its initial values of α and σwere both .6. The values of both α and σ were constrainedwithin the range .05–1.0.
Learn Behav (2012) 40:241–254 245
Conditioning with a single CS
Acquisition The first simulation was conducted in order todetermine the predicted course of acquisition when a singleCS, A, is paired with a US of moderate intensity (λ 0 .2).This training will result in the recruitment of a single con-figural unit. Panel A in the top row of Fig. 2 shows thepredicted level of activity in the output unit, which willdetermine the strength of the CR, as training progresses.Panel B shows the predicted growth of the associativestrength of the configural unit for A. Because only a singleconfigural unit is involved in this training, the graphs inpanels A and B are identical. Panels C and D show,respectively, the predicted changes in the values of αand σ with continued training. As desired, the value ofα increases as the A becomes a better predictor of the US, andσ decreases as the outcome of a trial becomes more accuratelypredicted.
Hall and Pearce, (1979) effect The next simulation exam-ined the predicted effect of pairing a CS with a large US,after it has been employed for the training just considered(Hall & Pearce, 1979). The magnitude of λ for this newstage of training was 1. Panel A in Row 2 of Fig. 2 showsthat conditioning progresses slowly with A when it is firstpaired with the large US. This effect is a consequence of theinitially low value of σ for the configural unit for A.Experience of the large US after A will, however, restorethe value of σ and enable responding to attain a normalasymptote, as the figure shows. The results for a control CS,B, which was paired only with the strong US, are alsoshown. The novelty of this stimulus at the outset of thesimulation put it at an initial disadvantage in terms of itsassociative strength, but at an advantage through the highassociability, σ, of its configural unit. The rapid condition-ing with B then permits it to elicit stronger responding thanA after a few trials. Thus, the modified theory is able to
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Fig. 2 Predicted changes in (A)the strength of response to apattern of stimulation; (B) theassociative strength of theconfigural unit activated by thepattern; (C) the effectivesalience, α, of the cues creatingthe pattern; and (D) theassociability, σ, of theconfigural unit activated by thepattern. In Row 1 (top row), thepattern was a single stimulus,A, paired with a weak US. InRow 2, the pattern was the samestimulus, or a novel stimulus, B,paired with a large US. In Row3, the pattern was a light pairedwith a tone–food sequence oneither a continuous (Group C)or a partial (Group P)reinforcement schedule. In Row4, the pattern was the light fromRow 3 paired directly with food
246 Learn Behav (2012) 40:241–254
predict the finding of Hall and Pearce (1979) that pairing atone with a weak shock results in latent inhibition when it ispaired with a strong shock. Panel C of Row 2 shows that thevalue of α is predicted initially to be greater for CS A thanfor CS B for this stage of the experiment. This difference,however, is not predicted to have an impact on the course ofacquisition in the present design. If only a single stimulus ispresented, it follows from Eq. 10 that no matter what itssalience, as determined by either α or P, it will excite itsinput unit to its maximum value of 1. Changes in the rate ofconditioning with this stimulus will then be determinedsolely by the value of σ. When two or more stimuli arepresented together, changes in α will be effective by influ-encing the degree of generalization among compounds towhich the stimulus belongs, and not by directly influencingthe rate of association formation.
The latent inhibition effect just described is rather unusualbecause the preexposed stimulus was paired initially with aUS. More conventional demonstrations of latent inhibitioninvolve repeatedly presenting a stimulus by itself before it ispaired with a US for the test phase (e.g., Lubow & Moore,1959). The theory that we are proposing predicts that latentinhibition will also be seen in these circumstances. When astimulus is repeatedly paired with nothing, it follows fromEq. 11 that the value of σ for the configural unit itactivates fully will decline, and thus disrupt subsequentconditioning with that stimulus. It is worth noting thatthis treatment will not affect the value of α for theinput unit activated by the preexposed stimulus. For areduction in the value of this parameter to take place,the stimulus must be presented in a context where it isa less accurate predictor of the trial outcome than thestimuli that accompany it. In the case of conventionallatent inhibition training, it can normally be assumedthat all of the stimuli on a preexposure trial signal thesame outcome—nothing.
By acknowledging that preexposure takes place in anexperimental context, the theory makes the additional pre-diction that latent inhibition will be context specific.Presenting stimulus A in context X will result in a configuralunit, AX, being connected to both stimuli. If this combina-tion of stimuli is not followed by a US, the value of σ for theconfigural unit representing AX will decline. Should A thenbe presented in a different context, Y, a new configural unit,AY, will be deployed. As the initial value of σ for the AYunit will be relatively high, conditioning with A in thiscontext will progress more rapidly than in context X. Avariety of experiments have confirmed this prediction(e.g., Hall & Channell, 1985). The latent inhibition effectdemonstrated by Hall and Pearce (1979) is also predicted tobe context specific; support for this prediction can be foundin Swartzentruber and Bouton (1986).
Influence of partial reinforcement The Pearce and Hall(1980) theory predicts that more attention will be paid to astimulus that is paired with a reinforcer on a continuousrather than an intermittent schedule. To test this prediction,Kaye and Pearce (1984) presented a continuous group ofrats with the sequence light–tone–food. A partial groupreceived the same training, but this training was intermixedrandomly among trials with the light by itself. Subsequentlythe light was paired with food, and it was anticipated thatappetitive conditioning would progress more rapidly inGroup Partial than in Group Continuous. Serial conditioningwas used in Stage 1 for two reasons. The first was to reducethe level of magazine activity during the light to such a lowlevel that a difference between the groups could be detectedin Stage 2. The second was to ensure that the light wasfollowed by a stimulus of sufficient motivational signif-icance to ensure that the value of σ was greater in thepartial group than in the continuous group. These stepswere effective, as conditioning in Stage 2 progressed morereadily with the partial than with the continuous group (seealso Swan & Pearce, 1988; Wilson, Boumphrey, & Pearce,1992).
The lower two rows of Fig. 2 show the outcome of asimulation conducted to determine the predictions made bythe present theory concerning the experiment of Kaye andPearce (1984). The predicted effect of serial conditioning forboth groups is shown in Row 3 of Fig. 2. Panel B depicts thegrowth of the association between the configural unit for thelight and the reinforcing properties of the tone. Panel A hasbeen omitted from the row, as it is hard to predict how thestrength of the light–tone association will influence behav-ior. In the study of Kaye and Pearce, the conditioned re-sponse of magazine activity was weak in both groups duringserial conditioning with the light. Panel C of Row 3 showsthat the value of α is predicted to grow in both groups, butmore rapidly for the continuous group. In keeping withtheoretical predictions, the value of σ is predicted to besustained at a higher value in the partial than in the contin-uous group. The outcome of the simulation concerning thesecond stage of the experiment is presented in the bottomrow of Fig. 2, from which it is apparent that conditioning ispredicted to be more effective with the partial than with thecontinuous group. The transient increase in the value of σ inboth groups (see panel D) can be attributed to the fact thatthe delivery of the US immediately after the CS will initiallybe surprising.
Compound conditioning
Overshadowing The next two simulations were conductedto explore the effect of using two stimuli presented simul-taneously, AB, to signal a US. For the first of these simu-lations, the intensities of A and B were both .6, and for the
Learn Behav (2012) 40:241–254 247
second, A was set at the maximum value of 1 and B at .5.Once again, only a single configural unit will be recruited,which will be activated fully whenever AB is presented tothe input layer. Panels A and B of the upper row of Fig. 3show the familiar predicted pattern of a negatively acceler-ated growth in the strength of the response to the compound,and in the associative strength of the AB configural unitwhen A and B are of equal salience. The equivalent resultsfor the simulation when A and B were of different saliencescan be seen in the next row. Panel C in both rows shows thepredicted effect of compound conditioning on α. The valueof this parameter is predicted to be maintained at its startingvalue for each stimulus when they are of equal saliences, butwhen they are of different saliences, α for the more salientstimulus is predicted to approach 1, while for the less salientstimulus it is predicted to approach 0. Panel D in both rowsindicates that this training is predicted to result in σ increas-ing for a few trials and then declining to a low value for theconfigural units for the compound stimuli in both condi-tions. In order to determine the predicted effects of com-pound conditioning on the strength of the response elicitedby individual stimuli, test trials were conducted at the end ofthe simulation. The associative strengths of both compo-nents of a compound were predicted to be .46 when theirsaliences were both .6. When the salience of Awas 1 and ofB was .5, the predicted response strengths were .86 for Aand .21 for B. Thus, reciprocal overshadowing is predicted
for stimuli of equal salience. When they are of differentsaliences, the strong stimulus considerably overshadowsthe weak stimulus, but the weak stimulus has little impacton the strong one. These predictions are in keeping withreported findings (e.g., Mackintosh, 1976).
Blocking In order to investigate the predictions that thetheory makes concerning blocking, we examined the effectsof pairing compound AB with a US (λ 0 1) after extendedtraining in which A by itself had been paired with the sameUS. Panel A of the third row of Fig. 3 shows the predictedstrength of the CR during the conditioning trials with AB.Responding is initially predicted to be weaker during ABthan the asymptotic strength that would be expected for A.Such an outcome is a consequence of the generalizationdecrement that will result from presenting A in compoundwith B. Panel B shows that the associative strength of theconfigural unit for A is predicted to be sustained at a highlevel throughout conditioning with AB, while the associa-tive strength of the configural unit for AB is predicted to berelatively weak. Panel C shows the effect of this training onα for the two stimuli. Its value remains consistently high forA but is reduced to a low level for B. As for σ, its value isconsistently low for the configural unit for A throughout theAB trials, which is understandable, but it is maintained at amoderate level to the unit for AB. The last result was notexpected, but it is not hard to understand. As α for B
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Fig. 3 Panels A–D have thesame significance as in Fig. 2.In Row 1 (top row), the patternwas a compound, AB, of twoequally salient stimuli pairedwith a US. In Row 2, the patternwas a compound, AB, of twostimuli paired with a US, withA being more salient than B. InRow 3, the pattern was acompound, AB, of two equallysalient stimuli paired with a USafter A had been paired with thesame US
248 Learn Behav (2012) 40:241–254
declines rapidly during compound conditioning, the salienceof this stimulus will eventually be so low that when AB ispresented it will activate maximally the configural unit forA, rather than AB. As it is only possible for the value of σfor the maximally activated configural unit to change on anytrial, from this point on there will be no further loss in thevalue of σ for the AB configural unit. A test trial with B byitself revealed that it is predicted to elicit a very weakresponse of strength .02. If the pretraining with A had beenomitted, the simulation above of overshadowing with twostimuli of equal strength indicates that the predicted strengthof response to B would be substantially greater than for theblocking group, with a value of .46.
Asymmetries in generalization
As it was originally formulated, the configural theory ofPearce (1994) predicted that a number of straightforwardmanipulations will have symmetrical effects. For example, afeature-positive discrimination of the form AX + X– ispredicted to be acquired as readily as a feature-negativediscrimination, X + AX–. Similarly, training with A+ andthen testing with AX is predicted to result in the same loss inthe strength of responding as training with AX+ and testingwith A. In fact, demonstrations of the feature-positive effecthave shown that a feature-positive discrimination is ac-quired more readily than a feature-negative discrimination(e.g., Reberg & LeClerc, 1977), while Brandon, Vogel, andWagner (2000) have shown that the decrement in respond-ing brought about by the transition from AX+ to A is greaterthan that from A+ to AX. Both of these results can beexplained with the modification to configural theory that iscurrently being proposed.
Feature-positive effect Panel A of Fig. 4 shows the pre-dicted courses of acquisition of a feature-negative, A +AB–, and a feature-positive, CD + C–, discrimination.
Panel B shows the acquisition of associative strength pre-dicted for the four configurations created by the two dis-criminations. Panel C shows the predicted changes in α paidto these stimuli as training progresses. Throughout training,α to A, B, and D is predicted to increase gradually, whereasit gradually declines to C. Such an outcome is understand-able, as the first three stimuli all provide information aboutthe outcome of a trial, whereas this is not the case for C. Asthe theory predicts that the value of σ for the reinforcedconfigurations will be the same throughout training, thepredictions concerning this parameter have been combinedin panel D, and likewise for the nonreinforced configura-tions. The panel shows that, at least initially, σ for thereinforced configurations is greater than for the nonrein-forced configurations. This outcome is predicted becauseat the outset of training the discrepancy that determines thevalue of σ is greater on reinforced than on nonreinforcedtrials. With continued training, the value of σ declines to alow level for all four configurations.
Inspection of Panel A shows that the feature-negativediscrimination is predicted to be acquired marginally moreslowly than the feature-positive discrimination. The expla-nation for this difference resides in the loss of attention to C.This reduction in the effective salience of C will reducegeneralization between the reinforced and nonreinforcedtrials and facilitate the acquisition of the feature-positivediscrimination. The absence of a similar loss of attentionto the common element of the feature-negative discrimina-tion, A, means that generalization between A and AB willbe considerable throughout training and render this discrim-ination harder to solve than its feature-positive counterpart.Support for this analysis can be found in an experiment byHaselgrove, Esber, Pearce, and Jones (2010) in which ratsreceived two feature-positive discriminations, AX + X– andBY + Y–, prior to an AY + AX– BY– test discrimination.The AY + AX– discrimination was acquired more slowlythan the AY + BY– discrimination, which implies that the
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considered in panel A; (C) the effective salience, α, of the four stimulifrom the discriminations considered in panel A; and (D) the associ-ability, σ, of the configural units considered in panel B
Learn Behav (2012) 40:241–254 249
salience of the previously relevant stimuli, A and B, wasgreater than that of the previously irrelevant stimuli.
Generalization between compounds and elements We havealready seen that conditioning with a compound, AB, withtwo stimuli whose salience is .6 will result in AB eliciting aCR of asymptotic magnitude, while either A or B alone willelicit a response of almost half this magnitude, .46. A furthersimulation was conducted to explore the predicted effect ofthe converse of this procedure. That is, of training with C byitself and testing with CD, where D is novel. If both stimuliare of equal salience (.6) and if training with C has reachedasymptote, then the strength of the response to CD is pre-dicted to be .70. The reason for this asymmetry in the effectof adding and removing a stimulus is based on the differentchanges in α that will take place during the initialtraining. The training with AB will result in each stim-ulus retaining its initial α value of .6, whereas thetraining with C alone will allow α on this occasion toreach 1. In the case of AB, removing from a compoundone component that is equally as salient as the othercomponent will result in a generalization decrement ofapproximately 50 %. On the other hand, adding a novelstimulus with an α value of .6 to a CS with an α valueof 1 will result in a generalization decrement of consid-erably less than 50 %.
Asymmetries in acquisition during compound conditioning
We close this discussion of compound conditioning with aresult by Rescorla (2000) that, at first glance, appears tocontradict our theoretical proposals. Animals received train-ing of the form A + C + X + XB– XD– before conditioningwith AB+. Rescorla found that responding during subse-quent test trials was stronger with BC than with AD, whichled him to conclude that compound conditioning with ABresulted in an asymmetry in the rates of acquisition ofassociative strength by A and B, with the rate being fasterfor B than for A. According to the theory of Pearce (1994),
such an asymmetry should not have been found. The AB+trials are predicted to result in the growth of a single asso-ciation between a representation of the compound in itsentirety and the reinforcer, so that any apparent growth inthe associative strength of A will be matched by a similargrowth for B (see Rescorla, 2000, p. 436). Once it is ac-knowledge that the conditioning trials might influence thevalues of α for A and B, the present version of the theorymakes a different prediction. The value of α is predicted tobe close to 1.0 for all five stimuli by the end of the initialtraining, but slightly lower to X than to the other stimuli.The AB+ trials are then predicted to maintain this value forA but to result in α falling for B, because the AB configuralunit will be paired with a different outcome than will theother configural unit activated by B, XB. The loss ofsalience by B will then permit more generalization ofexcitation, and less generalization of inhibition, to BCthan to AD, and thus result in the outcome recorded byRescorla (2000).
Evidence for enhanced attention to relevant stimuli
A growing body of evidence supports the proposal bySutherland and Mackintosh (1971) that cues that are rele-vant to the solution of a discrimination are paid more atten-tion than those that are irrelevant. The purpose of thissection is to determine whether our modified version ofconfigural theory is compatible with this evidence.
AX + BX– discrimination
We introduced Pearce’s (1994) configural theory by dem-onstrating its application to an AX + BX– discrimination.The predictions from the present revision of configuraltheory concerning this discrimination can be seen inFig. 5. The predicted changes in the strength of the responseto the two compounds are shown in panel A, and thepredicted changes in the associative strengths of the
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discriminations considered in panel A; (C) the effective salience, α, ofthe three stimuli from the discriminations considered in panel A; and(D) the associability, σ, of the configural units considered in panel B
250 Learn Behav (2012) 40:241–254
compounds can be seen in panel B. Panel C shows that thediscrimination will result in a decline in the value of α for X,while the value of this parameter will increase for both Aand B. In support of these predictions, Dopson, Esber, andPearce (2010) and Pearce, Esber, George, and Haselgrove(2008) have shown that after an AX + BX– discrimination,the associability of A is greater than that of X, whileDopson, Williams, Esber, and Pearce (2010) have shownthat the associability of B is greater than that of X. To ourknowledge, the latter report was the first to demonstrate thatanimals pay considerable attention to a cue that signals theabsence of food.
IDS–EDS effect
We return now to the IDS–EDS experiment that was intro-duced at the outset of this article (see Table 1). During Stage2 of this type of experiment, subjects are given discrimina-tions with stimuli belonging to two dimensions. For the IDSgroup, the dimension that is relevant in Stage 2 was alsorelevant for a discrimination with different values for thetwo dimensions in Stage 1. In contrast, for the EDS group,the dimension that is relevant in Stage 2 was irrelevant inStage 1. In order to derive predictions from the modelconcerning this type of design, a mechanism is required thatpermits greater generalization among stimuli that belong tothe same dimension, but not among those belonging todifferent dimensions. It is not sufficient to assume that allof the stimuli from the same dimension share a commonelement. Although this would permit generalization amongthese stimuli, it would also mean that during Stage 1 of anIDS–EDS experiment, the common element for the relevant
dimension would be irrelevant. The consequent loss ofattention to this cue would then prevent a beneficial effectof the Stage 1 training from being observed in Stage 2, andthe group trained with an IDS would perform similarly tothe group trained with an EDS.
To circumvent the foregoing problem, we propose thatstimuli can excite unique and common receptor units. Aunique receptor unit will be excited by a specific stimulus,whereas a common receptor unit will be excited by two ormore stimuli, even if they are presented individually. If it isassumed that two similar stimuli excite a fair number of thesame common units, whereas only a few such units areexcited by two very different stimuli, it follows that gener-alization will be stronger between similar than betweendifferent stimuli. It also follows that an increase in attentionto one stimulus will generalize to similar stimuli. With theseprinciples in mind, a computer simulation was conducted forthe IDS–EDS design outlined in Table 1. For the purposesof simplifying the simulation, each stimulus was assumed toexcite one unique receptor unit and three common receptorunits, each of which would be excited by just one of thethree remaining stimuli belonging to the same dimension.
Panel A in the top row of Fig. 6 shows the predictedchanges in the strength of responding to the reinforced andnonreinforced compounds for Stage 1 of training, and panelB shows the predicted changes in the associative strengthsof the configural units based on the four compounds. PanelC shows how α changes for the relevant and irrelevant inputunits during the initial discrimination training. As expected,the irrelevant units are predicted to lose attention, and therelevant units to gain attention. Panel D shows the changesin the value of σ that are predicted for the configural unitsduring the first stage of the experiment.
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Learn Behav (2012) 40:241–254 251
The two panels in the lower row of Fig. 6 show thepredicted changes in the strength of responding duringStage 2 for the reinforced and nonreinforced compoundsfor the group trained with the IDS discrimination (left-handpanel) and the group trained with the EDS discrimination(right-hand panel). The former group is predicted to acquirethe discrimination more readily than the latter. George andPearce (1999) have demonstrated successfully an IDS–EDSeffect using a biconditional discrimination. Although thedesign of their experiment was substantially more compli-cated than the design of the study just considered, computersimulations again confirmed that the present theory is ableto correctly predict this result.
Configural discriminations
Many of the discriminations that have been studied can besolved by focusing on the significance of individual stimuli.For instance, a feature-positive discrimination, AB + B–,can be solved once it is appreciated that A signals theoutcome and that B is of no significance. This type ofdiscrimination can be referred to as an elemental discrimi-nation. Other discriminations cannot be solved in this way.Instead, the solution depends on the organism grasping thesignificance of combinations of stimuli. For instance, apositive patterning discrimination, A– B– AB+, can be
solved by learning that A and B separately signal the ab-sence of the outcome, but together they signal the occur-rence of the outcome. This type of problem is referred to as aconfigural discrimination. We now turn to the predictionsour theory makes concerning configural discriminations.In fact, the distinction between elemental and configuraldiscriminations is largely irrelevant for the theory, as allassociations are assumed to be based on configuralrepresentations.
The upper row of Fig. 7 shows the predictions made bythe theory for the changes in associative strength for thereinforced and nonreinforced trials of a positive patterningdiscrimination. The discrimination is predicted in panel A toprogress quite normally. For this, and all of the remainingsimulations, unless stated otherwise individual stimuli wereassumed to excite unique, but not common, receptor units.We should add that the addition of common receptor units tothe simulations does not qualitatively affect the predictionsthat are made.
The second row of Fig. 7 shows the predicted outcome ofa negative patterning discrimination, A + B + AB–. Thecourse of acquisition of the discrimination, which is shownin the left-hand panel, is predicted to be slower than that forthe positive patterning task. This predicted pattern of resultsis consistent with experimental findings (e.g., Bellingham,Gillette-Bellingham, & Kehoe, 1985). A comparison of thepredicted changes in α for the two discriminations reveals
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252 Learn Behav (2012) 40:241–254
that it is predicted to decline to a low level for A and Bduring positive patterning and to increase to a high level forthese stimuli during negative patterning. To our knowledge,this prediction has not been tested.
Pearce and Redhead (1993) found that adding a thirdstimulus to each of the trials of a negative patterning dis-crimination, to create an AC + BC + ABC– discrimination,resulted in slower acquisition than with an A + B + AB–discrimination. The results of a simulation for an AC + BC +ABC– discrimination are shown in the bottom row of Fig. 7.A comparison of the results shown in panel A of the bottomtwo rows indicates that the theory predicts that the acquisi-tion of an A + B + AB– discrimination is hindered by thepresence of a common cue on every trial. A further predic-tion from the simulation of the AC + BC + ABC– discrim-ination is that C by itself will elicit an abnormally strongresponse of 2.25λ by the end of training. In support of thisprediction, Williams, Mehta, and Dumont (2004; see alsoWilliams et al., 2002) have demonstrated that an AC + BC +ABC– discrimination resulted in C acquiring greater thanasymptotic associative strength.
The theory thus appears to cope reasonably well withfindings from a variety of configural discriminations (seealso George & Pearce, 1999). We should, however, drawattention to one finding that poses a challenge to the theory.The simulation of the AC + BC + ABC– discrimination alsorevealed that despite C having considerable associativestrength, the value of α for this stimulus is predicted ulti-mately to be low. In contrast to the prediction, Dopson,Esber, and Pearce (2011) discovered that this trainingresulted in the salience of C being particularly high. It wouldbe premature to advocate a radical revision of our proposalson the basis of a single result, but this finding indicates aneed to investigate further the circumstances that influencechanges in attention during the course of configural discrim-inations. If a comprehensive empirical picture can be drawnof how attention is influenced by such discriminations, wesuspect that it will provide a particularly demanding test bedfor the evaluation of all theories of associative learning, notjust the one proposed here.
Concluding comments
In closing this presentation of a configural theory of atten-tion and associative learning, we shall comment briefly onits application to the renewal effect. In an experiment byBouton and Peck (1989), rats received conditioning withstimulus X in context A and then extinction with X incontext B. Rats were then returned to context A, where Xelicited substantially stronger responding than for a controlgroup that had received all three stages in Context A. Therenewal of responding in the final stage can be readily
explained by the present theory, if it is assumed that duringconditioning and extinction the context in which X is pre-sented contributes to the configural representation thatenters into an association with the reinforcer. During Stage1, animals might learn that the configuration AX signalsfood, and during Stage 2 they might learn that BX signalsthe absence of food. On being returned to context A forStage 3, the occurrence of X would then activate the AXconfigural unit and lead to a recovery of responding.Computer simulations have confirmed this analysis, but theyhave also revealed that a generalization decrement isexpected when X is presented for the first time in contextB. Although there was no hint of such a decrement in thestudy by Bouton and Peck (1989), it has been observed inother demonstrations of the renewal effect (e.g., Thomas,Larsen, & Ayres, 2003). In view of these conflicting find-ings, it may well be worth pursuing further our explanationfor the renewal effect.
There is now a strong body of evidence showing that twoattentional processes, which we have represented with theparameters α and σ, influence the acquisition of conditionedresponding in a variety of contexts. By incorporating theseprocesses into a configural theory of learning, it is possibleto explain a wide range of experimental findings. As wehave seen, however, the theory has its limitations, and thereremains the challenge of exploring how they might beovercome.
Author note A MATLAB simulator of the connectionist networkdescribed here can be downloaded from http://psy.hull.ac.uk/Resources/Immediacy/georgepearce.zip. This simulator is compati-ble with MATLAB R2009b and later. This work was supportedby a Royal Society University Research Fellowship to D.N.G. andby a grant from the U.K. Biotechnology and Biological SciencesResearch Council to J.M.P.
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