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The dynamic nature of knowledge: Insights from a dynamic fieldmodel of children’s novel noun generalization

Larissa K. Samuelson a,*, Anne R. Schutte b, Jessica S. Horst c

a Department of Psychology and Iowa Center for Developmental and Learning Sciences, University of Iowa, E11 Seashore Hall, Iowa City, IA 52242, United Statesb Department of Psychology, University of Nebraska Lincoln, United Statesc Department of Psychology, University of Sussex, United States

a r t i c l e i n f o

Article history:Received 12 March 2008Revised 28 October 2008Accepted 30 October 2008

Keywords:Word learningDevelopmental processesCompetence/performanceComputational modeling

a b s t r a c t

This paper examines the tie between knowledge and behavior in a noun generalizationcontext. An experiment directly comparing noun generalizations of children at the samepoint in development in forced-choice and yes/no tasks reveals task-specific differencesin the way children’s knowledge of nominal categories is brought to bear in a moment.To understand the cognitive system that produced these differences, the real-time decisionprocesses in these tasks were instantiated in a dynamic field model. The model capturesboth qualitative and quantitative differences in performance across tasks and reveals con-straints on the nature of children’s accumulated knowledge. Additional simulations ofdevelopmental change in the yes/no task between 2 and 4 years of age illustrate howchanges in children’s representations translate into developmental changes in behavior.Together, the empirical data and model demonstrate the dynamic nature of knowledgeand are consistent with the perspective that knowledge cannot be separated from thetask-specific processes that create behavior in the moment.

� 2008 Elsevier B.V. All rights reserved.

1. Introduction

There are numerous examples in the cognitive develop-ment literature where children’s abilities appear to shiftacross ages and tasks in seemingly paradoxical ways. Forexample, studies with young infants suggest that 3- and4-month-old children can use knowledge of physical lawsof continuity and solidity to determine where a ball rolleddown a ramp should stop (Spelke, Breinlinger, Macomber,& Jacobson, 1992). Yet, when tested in similar paradigms,2- and 3-year-old children do not seem to have this sameknowledge (Berthier, DeBlois, Poirier, Novak, & Clifton,2000). Similarly, research suggests that 6- to 8-month-old infants can detect the numerical equivalence betweensets of auditory and visual stimuli (Starkey, Spelke, &Gelman, 1990); yet, 3-year-old children fail at a similar

task (Mix, Huttenlocher, & Levine, 1996). Such examplesleave the field in a difficult position: how are we to knowwhen a child possesses some bit of knowledge?

This question comes from a view of cognition that sep-arates knowledge from process. By this view, knowledgeresides in the head of the child, waiting to be accessed bythe appropriate stimuli or task. Thus, developmentalistsdesign tasks to tap into children’s knowledge; if childrenperform competently they are said to have the requisiteknowledge, if children fail they are said to lack the knowl-edge. One problem with this view is that it pits children’scompetence (i.e., knowledge) against their performance(i.e., behavior). Consequently, when children fail at a taskit can always be claimed that they have the knowledge,but that the task did not effectively elicit that knowledge(see Sophian, 1997, and commentaries for discussion). Asecond problem with this view is that it leaves unex-plained what is critical for acting in the world and for theunfolding of developmental process—how knowledge iscreated and how it is brought to bear in a task.

0010-0277/$ - see front matter � 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.cognition.2008.10.017

* Corresponding author. Tel.: +1 319 335 2211; fax: +1 319 335 0191.E-mail address: [email protected] (L.K. Samuelson).

Cognition 110 (2009) 322–345

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Cognition

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An alternative and growing view is that knowledge isnot separate from the processes that create behavior in atask. That is, knowledge is not a unitary thing that can behad, rather, it is distributed in and across many processes(e.g. Barsalou, 1999; Plumert, 2008; Port & VanGelder,1995; Samuelson & Smith, 2000b; Skarda & Freeman,1987; Spencer & Schöner, 2003; Spivey & Dale, 2006;Thelen & Smith, 1994). By this view, one cannot ask aboutknowledge independent of the task that brings that knowl-edge to bear in a moment in time. Rather, the question tobe asked is how the specifics of the task cohere with thechild’s prior history of perceiving, thinking, and acting tocreate behavior in the moment.

Direct support for this view in developmental sciencecomes from work by Esther Thelen, Linda Smith, and theircolleagues showing how infants’ performance in the classicPiagetian A-not-B task is influenced by a host of intrinsicand extrinsic factors (Clearfield, Diedrich, Smith, & Thelen,2006; Diedrich, Highlands, Thelen, & Smith, 2001; Died-rich, Thelen, Smith, & Corbetta, 2000; Smith, Thelen, Titzer,& McLin, 1999; Thelen, Schöner, Scheier, & Smith, 2001;Thelen & Smith, 1997). Although such studies have con-tributed foundational support for the idea that knowledgeis bound to behavior in a particular task, the implicationsof this work for cognition more generally have been calledinto question given that the A-not-B phenomenon is lar-gely grounded in sensorimotor activity (Freeman, 2001;Glenberg, Cowart, & Kaschak, 2001; Markman, 2001;Munakata & McClelland, 2003; but see Spencer & Schöner,2003). An important question, then, is whether this viewhas implications for higher-order cognition.

This question is well illustrated by a current debate inthe word learning literature (see Samuelson & Bloom,2008). In a typical experimental procedure, a young childshown a novel solid, rigid object and told a novel name(e.g., ‘‘this is a dax”) will most likely say that only other ob-jects that share the same shape as the exemplar can becalled by the same name (Imai, Gentner, & Uchida, 1994;Landau, Smith, & Jones, 1988; Samuelson & Smith, 1999).Young children are thus said to show a ‘‘shape bias” whengeneralizing novel names for solid objects. Importantly,however, children do not always generalize novel namesby shape similarity. Rather, attention to shape and otherobject dimensions has been shown to be context, stimulus,and language specific, and thus exquisitely tuned to thelanguage being learned (see Smith & Samuelson, 2006;Yoshida & Smith, 2003). Furthermore, recent studies sug-gest that children who learn to attend to shape whennaming novel objects subsequently show acceleratedvocabulary development (Samuelson, 2002; Smith, Jones,Landau, Gershkoff-Stowe, & Samuelson, 2002) and thatdevelopment of a shape bias is related to the developmentof the early noun vocabulary (Gershkoff-Stowe & Smith,2004; Samuelson & Smith, 1999).

Nevertheless, there has been sharp debate regarding theorigin of the shape bias (Booth & Waxman, 2002; Diesend-ruck & Bloom, 2003; Smith, Jones, Yoshida, & Colunga,2003). At its core, this debate is about the foundational nat-ure of cognition and whether knowledge/competence canbe separated from performance (Colunga & Smith, 2008;Samuelson & Horst, 2008; Smith & Samuelson, 2006).

Booth, Waxman, and Huang (2005), and Bloom and col-leagues (Bloom, 2000; Bloom & Markson, 1998; Diesend-ruck & Bloom, 2003) argue that children’s biasedattention to shape reflects their conceptual understandingthat shape is an important indicator of object kind. Thesearguments stem from a traditional view of cognition thatparses mental activity into discrete and separable pro-cesses of sensing, thinking, and acting. In contrast, Smithand colleagues argue that the shape bias is an attentionalbias that itself is the developmental product of the child’sexposure to a language in which solidity and categoryorganization by shape are highly correlated (Smith, 2000;Smith & Samuelson, 2006). This idea stems from the viewof cognition that sees knowledge as embedded in processand denies a separation between sensing, thinking, andacting.

Critically, progress in this debate has been hampered bythe fact that little attention has been paid to differences inthe tasks and stimuli used to elicit noun generalizationsin studies that purport to support one view over another. Inthis way, then, the word learning literature mirrors the lar-ger developmental and cognitive science literatures both interms of the existing disagreements concerning the natureof the cognitive system and in the need for a greater under-standing of how the specifics of a task elicit knowledge in amoment. In the present paper, we examine these issues viaa case study that probes similarities and differences in chil-dren’s novel noun generalizations for solid and deformablethings and, critically, how these differences depend on thedetails of the tasks that are used to elicit those generaliza-tions. We show how an understanding of the processesthat support behavior in a task yield insights into the nat-ure of developmental changes in knowledge.

Our work is inspired by the view that knowledge is notseparate from the processes that create behavior in a task.Note that this view does not deny a long-term accumula-tion of information based on specific experiences with ob-jects and words. As applied to the development of theshape bias, this view suggests that as children learnindividual name–object pairings, they learn a system ofregularities between linguistic devices, the structure of ob-ject categories, and perceptual properties (see Smith &Samuelson, 2006). This information accumulates over thedevelopment of the early noun vocabulary and is the‘‘knowledge” children bring to the task of generalizing anovel name from a novel object to new instances. Thus,when we refer to ‘‘knowledge” we are referring to thechild’s accumulated history of experiencing naming con-texts paired with objects in particular ways.

The critical question is how these prior experiences arebrought to bear in the moment that a child is asked tomake a novel noun generalization. In the current work,we explore this issue by first experimentally examiningdifferences in the way children’s accumulated knowledgeof nominal categories is brought to bear in specific taskcontexts. We examine the interaction of knowledge withprocess by submitting the same knowledge to a model thatconcretely specifies critical aspects of these processes, andfind that, as in the experiment with children, differentbehaviors emerge across tasks. Systematic manipulationsof the model parameters that specify the input knowledge

L.K. Samuelson et al. / Cognition 110 (2009) 322–345 323


and processes demonstrate that the experimental patternof results only obtains when the inputs are processed inparticular ways. This is further illustrated in simulationsof developmental changes in novel noun generalization.This work thus demonstrates that changes to either the in-put knowledge alone or the processes alone do not capturedifferences in children’s behavior across tasks and develop-ment—it takes a coherent pattern of change in both to yieldthe specific pattern of behavioral change.

1.1. Background: naming deformable things

A bias to attend to shape, although useful for learningnouns such as table, hammer, and key, that name solid ob-jects in shape-based categories (Samuelson & Smith, 1999),may not be appropriate for all nominal categories. In par-ticular, deformable things such as paper, blankets, and tow-els provide an interesting test case for children’s attentionto shape because similarity in material may be as impor-tant to the organization of these nominal categories assimilarity in shape. In fact, studies with adults suggestdeformable things are organized into nominal categoriesbased on similarity of material (Samuelson & Smith,1999, 2000a). Further, material substance is often criticalto what can be done with these things. For example, whileboth blankets and towels are likely to have a rectangularshape, it is their particular material composition that dis-tinguishes one from the other and that influences whatwe do with each. Thus, children may be biased to general-ize novel names for novel deformable things according tomaterial substance.

On the other hand, many deformable things do havecharacteristic shapes (e.g., shirts, pants, and socks) and thusshape is an important factor in the organization of thesenominal categories. Further, while deformable things canbe folded, balled, squished or otherwise manipulated to al-ter their shape, they can be returned to their originalshapes following such manipulations. In addition, analysisof the early noun vocabulary suggests that many of the cat-egories of deformable things that children learn to nameearly are similar to categories of rigid things in that bothare named with count nouns (‘‘a shirt” rather than ‘‘�someshirt”, Samuelson & Smith, 1999). In the early noun vocab-ulary, count noun syntax is associated with categories or-ganized by similarity in shape (Samuelson & Smith,1999). It is therefore also possible that the similarity inthe syntactic frame associated with rigid and deformablethings may direct children’s attention to shape when nam-ing deformables (Samuelson, Horst, Schutte, & Dobbertin,2008; Samuelson & Smith, 2000a).

Thus, there are reasons to expect that compared to rigidthings, children’s naming of deformables would be morevariable and subject to influences of task structure. Thereis some indication of this in the literature. Samuelsonand Smith (2000) found that 3-year-old children general-ized novel names by similarity in shape in a yes/no task.In contrast, Gathercole and colleagues (Gathercole, Cramer,Somerville, & Haar, 1995) found that 4-year-old childrenwere more likely to attend to substance when namingdeformable stimuli in a forced-choice task (see alsoSamuelson et al., 2008). However, direct comparison

between studies is difficult due to differences in the stimuliused and the specifics of the task (i.e. whether a function orproperty of the exemplar was demonstrated prior to nam-ing). Further, the use of children of different ages acrossstudies also means that participants differed in vocabulary,which has been suggested to be a critical determinate toattention to shape in similar tasks (Gathercole & Min,1997; Gershkoff-Stowe & Smith, 2004; Samuelson & Smith,1999).

1.2. Overview of this study

The fact that some factors associated with deformablesmay direct children’s attention to similarities in material,while other factors may direct their attention to similari-ties in shape provides an opportunity to probe whetherand how the specifics of the task influence children’s noungeneralizations. Toward this end, we present an experi-ment that contrasts the performance of children the sameage and with the same productive vocabulary acrossforced-choice and yes/no noun generalization tasks withthe same stimuli. Data from this experiment suggestimportant differences in the specifics of children’s perfor-mance related to the particulars of the two tasks. We pres-ent a dynamic field model to formally specify the real-timeprocesses that turn knowledge of nominal categories into aforced-choice or yes/no response. The model reveals con-straints on the structure of the accumulated knowledgechildren bring to bear in these tasks. We show that thecombination of the hypothesized processes and knowledgeaccurately captures both global qualitative differences inperformance across forced-choice and yes/no tasks as wellas specific quantitative differences.

Next, we quantitatively fit data from 2- to 4-year-oldchildren from a study using the same stimuli in a yes/notask. These fits illustrate how changes in children’s accu-mulated knowledge of nominal categories translate intodevelopmental changes in behavior in this task. Thus, themodel illustrates how an understanding of process pro-vides insights both into what children bring to the taskbased on their prior history and how this accumulatedprior history changes over time. The model also illustratesthe dynamic nature of knowledge and it’s inseparabilityfrom process, and thus, has important implications forour understanding of cognition more generally.

2. Experiment 1

Most of the categories of rigid things that young chil-dren learn to name early provide clear links among solid-ity, category organization, and syntax—solid, rigid thingstend to be in categories organized by similarity in shapeand tend to be named with count nouns (Samuelson &Smith, 1999). Moreover, research suggests that childrenlearn to exploit this regularity in novel noun generalization(Samuelson, 2002; Smith et al., 2002). In contrast, thedeformable things children learn to name early do notpresent as regular a relationship (Gathercole et al., 1995;Samuelson & Smith, 1999, 2000a). Many deformable thingshave specific shapes but those shapes can be changed.

324 L.K. Samuelson et al. / Cognition 110 (2009) 322–345


Adults typically judge deformable things, like nonsolidsubstances, to be in categories well organized by similarityin material substance, but deformable things, like rigid ob-jects, are often named with count nouns (Samuelson &Smith, 2000a). Given the possibility that young childrencould organize deformable things by either shape or mate-rial, the purpose of this experiment was to directly exam-ine the extent to which children’s noun generalizationswith deformable things are influenced by the task. We col-lected novel noun generalizations in forced-choice and yes/no tasks from groups of children that were the same in ageand productive vocabulary. We tested 2.5-year-old chil-dren because previous studies suggest developmentalchanges in the amount of attention to shape in noun gen-eralization between 2 and 3 years of age (Gershkoff-Stowe& Smith, 2004; Landau, Smith, & Jones, 1998; Samuelsonet al., 2008; Smith, Jones, & Landau, 1992), and because pi-lot testing suggested that children this age could effec-tively complete both forced-choice and yes/no versions ofthe task. In both tasks, we highlighted the rigidity or defor-mability of the exemplar object before naming it. This wasdone to ensure children were aware of the relevant differ-ences in the stimuli, and because prior studies with theseand similar stimuli had used this procedure (Gathercole& Min, 1997; Samuelson & Smith, 2000a; Samuelsonet al., 2008).

2.1. Method

2.1.1. ParticipantsThirty-two monolingual, English-speaking children (M =

31 m 13 d, range = 28 m 16 d–32 m 24 d; 18 girls, 14 boys)were recruited from local county birth records. All of thechildren were from middle-class families. Half of the chil-dren participated in a forced-choice task (8 females, 8males) and half in a yes/no task (6 females, 10 males). Chil-dren in the forced-choice and yes/no conditions did not dif-fer in age (M = 31 m 11 d and 31 m 16 d, respectively),t(30) = .36, ns, or total noun vocabulary (M = 284.8 and293.5, respectively), t(30) = .88, ns, as measured by theMacArthur-Bates Communicative Development Inventory:Words and Sentences (MCDI; Fenson et al., 1994)—a vali-dated parental checklist of the 680 words commonlylearned by children up to 30-months of age. Data from anadditional four children who participated in the yes/no con-dition were not analyzed due to experimental error (1), be-cause the child did not finish (1), or due to a potentiallanguage delay (2). Informed consent was obtained fromchildren’s parent or guardian prior to the experimental ses-sion. Children received a small gift for participating.

2.1.2. StimuliNine objects familiar to young children were used on

training trials. The exemplar for these trials was a purpleplastic egg. The test objects were an identical egg, a redwooden block, a plastic flower, a plastic teapot, a smallbasket, a rubber duck, a multi-colored miniature slinky,and a small stuffed dinosaur. All of the objects were similarin size.

Four sets of novel objects were used during the test tri-als (see Fig. 1). Each set consisted of an exemplar and six

test objects. For each set, two of the test objects were thesame shape as the exemplar but were a different colorand were made from a different material, two were madefrom the same material as the exemplar but were a differ-ent shape and color, and two were the same color as theexemplar but different in shape and material. The exem-plars for sets 1 and 2 were made from rigid materials.The exemplars for sets 3 and 4 were made from nonrigid,deformable materials. The exemplar for set 1 was a14.0 cm � 3.8 cm barbell-shaped piece of wood paintedgreen with a bumpy texture. The exemplar for set 2 wasan 8.3 cm in diameter blue clay ball with four clay pegs.The exemplar for set 3 was a 14.0 cm tall � 5.7 cm widepiece of yellow sponge cut into a rounded ‘‘V” shape. Theexemplar for set 4 was an 11.4 cm � 9.5 cm pink poly-gon-shaped plastic bean bag. A white tray divided intotwo equal sections was used to present the stimuli in theforced-choice task.

Each exemplar had two different kinds of propertiesthat could be demonstrated. One kind of property was de-signed to highlight the shape of the rigid exemplars andthe material of the deformable exemplars. These propertiesare referred to as ‘‘related” properties because they werebased on the shape of the rigid exemplars and the materialof the deformable exemplars. The related property for sets1, 2, 3, and 4 were rolling, fitting into a puzzle, squishinginto a cup, and folding, respectively (see Fig. 1). The otherkind of property was not based on the shape, color, ormaterial of the exemplar. Thus, these are referred to as‘‘arbitrary” properties. Because children only saw two arbi-trary properties and because these properties were notbased on any features of the exemplars, the same two arbi-trary properties—having a small design on that glowed inthe dark or a sticker on the back—were used for all foursets. Four novel names—Rel, Hux, Kiv, and Gaz—were used.

2.1.3. Design and procedureThe design was identical for the forced-choice and yes/

no conditions. Each child saw all four sets of stimuli. Eachchild saw a related property demonstrated for one of therigid exemplars and an arbitrary property demonstratedfor the other. Likewise, each child saw a related propertydemonstrated for one of the deformable exemplars andan arbitrary property demonstrated for the other. Whichexemplar had related and which had arbitrary propertieswas counterbalanced across children in each condition.

Children sat across from the experimenter at a large ta-ble. Parents sat next to their child and were asked not todirect their child’s responses in any way. Parents com-pleted the MBCDI during the experimental session.

In the forced-choice condition, the experiment beganwith a series of training trials to familiarize the child withthe task and experimental setting. On the first trainingtrial, the child was introduced to a stuffed animal and told,‘‘Edward is a very picky bear. He only likes things like this”.The experimenter then showed the child the egg exemplar.To familiarize the child with the demonstration procedurethe experimenter then said, ‘‘This is an egg, and you knowwhat? It opens”, and opened and closed the egg. The exper-imenter set the egg by Edward and told the child they weregoing to find more eggs for Edward. The experimenter gave



the child two test objects to explore briefly—a second eggidentical to the named exemplar, and another object thatdiffered from the egg in shape, color, and material. Theexperimenter then retrieved the two test objects, placedthem on the tray, said, ‘‘Remember this is an egg, and itopens (pointing to the exemplar)”. She then asked, ‘‘Canyou get another egg?” while sliding the tray towards thechild. Children were praised if they chose the egg and cor-rected otherwise. The experimenter then gave the child thetest objects for the next trial which proceeded in the samemanner. The experimenter reminded the child that the eggopened on each training trial. The right/left position of theegg on the tray alternated across trials. To ensure that chil-dren understood the task, training trials continued untilthe child made four consecutive correct responses or untilthey had completed eight trials, at which point the exper-

imenter continued with the test trials. All children an-swered at least two training trials correctly.

The test trials proceeded in the same manner as thetraining trials, with the exception that children’s responseswere neither praised nor corrected. For each of the fourstimulus sets, the experimenter introduced the child to anew stuffed animal and a novel object, for example,‘‘Nathan only likes things like this. This is a rel, and youknow what? It rolls”. The experimenter demonstrated theassigned property and placed the exemplar next to the ani-mal. In order to reduce the total number of trials, and be-cause prior studies indicated that children rarelygeneralized novel names to color match test objects (Sam-uelson et al., 2008; Samuelson & Smith, 2000a), childrendid not see the color match stimuli in the forced-choicecondition. Thus, on each trial the child was presented with

Fig. 1. Stimuli used in the experiment.



a shape match and a material match. Within each set, eachshape match was presented once with each material matchfor a total of four trials per set. Before each trial, the exper-imenter reminded the child of the exemplar’s name anddemonstrated property (e.g., ‘‘Remember, this is a rel andit rolls”). After the child completed the four trials for oneset, they were allowed to choose a sticker to take home be-fore the experimenter moved on to the next set. Children’schoices were coded offline from videotape by coders una-ware of the experimental hypotheses. Intercoder reliabili-ties were obtained for 25% of the sessions using exactpercent agreement. Agreement between the two coderswas 94%. All disagreements were resolved by review ofthe videotapes.

As in the force choice condition, the yes/no conditionbegan with training trials. The same training stimuli wereused. On the first training trial, the child was introduced toa stuffed animal and told that the animal only liked eggsand was shown a plastic egg. The experimenter demon-strated that the egg opened and then brought out a seriesof test objects one at a time and, for each, asked, ‘‘Is thisan egg?” As in the forced-choice condition, the experi-menter reminded the child that the egg opened beforeeach test trial. During training, the experimenter praisedthe child for correct responses and corrected incorrect re-sponses. Each child was presented with up to eight ran-domly ordered training trials, which included at leasttwo presentations of the identical egg. To ensure that chil-dren understood the task, we required that children cor-rectly answer four consecutive training trials in order tobe included in the analysis (c.f., Samuelson & Smith,2000a). All children met this criterion.

The test trials proceeded in the same manner as thetraining trials with the exception that the experimenterdid not praise or correct the child during these trials anddifferent stimulus sets were used. The experimenter intro-duced the child to a stuffed animal, told the child the ani-mal only ‘‘wants things like this”, named the exemplar anddemonstrated the property for the child before placing theexemplar by the animal. Then the experimenter presentedeach test object one at a time. Before presenting each testobject, the experimenter reminded the child of the exem-plar’s property. For example, the experimenter would say‘‘Remember, this is a rel and it rolls”, and then present atest object and ask, ‘‘Is this a rel?” After all six test objectsfor a set were presented, the experimenter moved on tothe next set. As in previous studies using this task, we re-quired that children say ‘‘no” to at least one test objectduring the experimental trials in order to be included inthe final analyses (c.f., Samuelson & Smith, 2000a). Allchildren met this criterion. This provided an additionalcheck that children understood the task. The order ofexemplars and test objects was randomly determinedand counterbalanced across children. Children’s yes/no re-sponses were recorded by the experimenter during theexperiment.

2.2. Results

The left panels of Fig. 2 show the proportion of shapechoices in the forced-choice task for deformable (top

panel) and rigid (bottom panel) exemplars. The right pan-els of the figure show the proportion of yes responses toeach of the three test objects in the yes/no task for thedeformable (top panel) and rigid (bottom panel) exem-plars. Analyses revealed no effects of relatedness (i.e.,whether an arbitrary or related property was demon-strated); thus, the figure collapses across this factor. Thedata in the figure indicate that children’s attention toshape when naming deformable exemplars was influ-enced by the task, while attention to shape when namingrigid exemplars remained uniformly high regardless ofthe task. We first examined the patterns of noun general-ization within each task using ANOVAs. We then per-formed a set of analyses comparing data from the twotasks directly.

2.2.1. Forced-choice taskAs can be seen in the left panels of Fig. 2, children were

more likely to generalize names for deformable things bysimilar material than by similar shape, but systematicallygeneralized novel names for rigid things by similar shape.This was confirmed by a rigidity (rigid vs. deform-able) � relatedness (related vs. arbitrary) repeated mea-sures ANOVA in which both factors were within subjects.This analysis revealed a significant main effect of rigidityF(1,15) = 29.25, p < .0001, g2

p ¼ :66, but no other main ef-fects or interactions. t-Tests against chance confirmed thatchildren chose shape-matching test objects at levels signif-icantly below chance when exemplars were deformable,t(15) = �2.145, p < .05, d = .24, but above chance whenexemplars were rigid, t(15) = 5.13, p < .001, d = 1.037.

2.2.2. Yes/no taskAs can be seen in the right panels of Fig. 2, children

were more likely to generalize novel names for bothdeformable and rigid exemplars by shape in the yes/notask. Children’s yes responses were entered into a rigidity(rigid vs. deformable) � relatedness (related vs. arbi-trary) � test object (shape, color, material) repeated mea-sures ANOVA. There were significant main effects ofrigidity, F(1,15) = 6.32, p < .05, g2

p ¼ :30, and test object,F(1,30) = 28.36, p < .0001, g2

p ¼ :65, and a significant rigid-ity � test object interaction, F(1,30) = 7.36, p < .01,g2

p ¼ :33. There were no significant main effects or interac-tions involving relatedness. Thus, the data were collapsedacross relatedness and further analyzed via simple effectstests split by rigidity.

For the deformable exemplars, there was a significanteffect of test object, F(1,30) = 17.12, p < .0001, g2

p ¼ :59.Follow-up Fisher’s PLSD tests revealed that the propor-tion of yes responses to shape-matching test objectswas significantly higher than the proportion of yes re-sponses to material-matching test objects which in turn,was higher than the proportion for color-matching testobjects. For the rigid exemplars, there was also a signifi-cant effect of test object, F(1,30) = 27.53, p < .0001,g2

p ¼ :65. Follow-up Fisher’s PLSD tests revealed that theproportion of yes responses to the shape-matching testobjects was higher than the proportions for the material-and color-matching test objects, which did not differsignificantly.



2.2.3. Comparison across tasksAnalyses of responses in each task suggest that 2.5-

year-old children generalized novel names for rigid thingsby shape in both the forced-choice and yes/no tasks, butonly systematically generalized novel names for deform-able things by material in the forced-choice task. To exam-ine the difference in responding across tasks more directly,we compared the yes/no and forced-choice data after con-verting the yes/no data to proportion of shape choices viathe Luce choice rule (Luce, 1963). Specifically, for individ-ual children the proportion of shape choices for a givenstimulus set was taken to be equal to the proportion ofyes responses to shape-matching test objects divided bythe sum of the proportion of yes responses to shape- andmaterial-matching test objects.1 We collapsed over related-ness in this analysis because the ANOVAs showed no signif-icant effects of this factor. Thus, the proportion of shapechoices for the deformable and rigid sets was taken to be

equal to the average proportion of yes responses to shape-matching test objects divided by the sum of the average pro-portions of yes responses to shape- and material-matchingtest objects. These data are shown in Fig. 3, along with thecorresponding data from the forced-choice task.

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Fig. 2. Data from the experiment. The left panels show the proportion of shape choices for deformable and rigid exemplars following demonstrations ofrelated and arbitrary properties in the forced-choice task. The right panels show the corresponding proportions of yes responses to the shape-, color-, andmaterial-matching test objects in the yes/no task. There were no effects of relatedness so the figure collapses across this factor.

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ProportionShapeChoices

Fig. 3. Comparison of performance in the forced-choice and yes/no tasksof the experiment. Yes/no data were converted to proportion shapechoices via the Luce choice rule.

1 One child in the yes/no task said ‘‘no” to all the deformable test objects.This would result in a proportion shape score of 0 by the Luce choice rule,even though the child did not say ‘‘yes” to any of the material-matching testobjects. Thus, to be conservative, we opted to not include data from thischild in this analysis.



As is clear in the figure, the proportion of shape choicesmade when a rigid exemplar was named did not differacross task. Importantly, however, the proportion of shapechoices made when a deformable exemplar was nameddiffered markedly across tasks. We analyzed this data atthe level of individual children. Table 1 provides the num-bers of individual children in each condition whose pro-portion of shape choices was below chance (<.50), atchance (=.50) or above chance (>.50) for both the deform-able and rigid stimulus sets. As is clear in the table, withdeformable stimuli there were more children whose pro-portion of shape choices was at or below chance in theforced-choice condition than the yes/no condition. In con-trast, with the rigid stimuli the numbers of children whoseproportion shape choices was above chance were almostidentical across tasks. Chi-square tests of homogeneity ofproportions revealed a significant difference across condi-tions with deformable stimuli, v2(2) = 11.23, p < .01,w = .60, but no significant difference with rigid stimuli,v2(2) = 3.80, ns.

2.3. Discussion

These results indicate that children equated for age andproductive vocabulary generalize names for deformablestimuli differently when presented with a forced-choicecompared to a yes/no task. Specifically, data from theforced-choice task suggest that 2.5-year-old children thinkthat rigid things are named by similarity in shape whereasdeformable things are named by similarity in material sub-stance. In contrast, data from the yes/no task suggest chil-dren this age do not distinguish between rigid anddeformable things in naming, and generalize names forboth kinds by shape similarity. In this way, then, data fromthe two tasks lead to different conclusions about what chil-dren know about how deformable things are named. Giventhat the same stimuli were used in the two tasks and thatgroups were equated for age and vocabulary level, thesedata suggest that differences in the processes that bring

children’s accumulated vocabulary knowledge to bear ineach task are critical to determining the specifics of theirperformance.

There are two critical differences between the forced-choice task and the yes/no task that seem likely to influ-ence children’s behavior. First, in the forced-choice task,children see the two test objects at the same time in closeproximity (i.e., on the same tray), whereas in the yes/noversion of the task, children see each test object one at atime. Thus, children can make direct comparisons betweenthe test objects in the forced-choice task, but must makethese comparisons in memory (if at all) in the yes/no ver-sion of the task. Second, the nature of the forced-choicetask is to force the child to pick one object to the exclusionof the other, whereas in the yes/no version of the task, thechild is free to say yes (or no) to all of the test itemsindividually.

These differences have important implications for howchildren’s prior history of perceiving and acting is broughtto bear in a moment in time, that is, for how their accumu-lated knowledge of nominal categories is brought to bearin different novel noun generalization tasks. For example,a relatively small bias to favor similarity in material maybe magnified when children are forced to pick between atest object that matches an exemplar in shape and one thatmatches it in material. Likewise, a relatively weak appreci-ation of the importance of shape for deformable thingsmay be more robust in a yes/no task because judgmentsof the similarity of shape and material test objects aremade independently. To probe these issues in greater de-tail, we implemented these task differences in a dynamicfield model and simulated performance in the forced-choice and yes/no versions of the novel noun generaliza-tion task.

3. Quantitative modeling of performance across tasks

The general goal of these simulations was to examinethe possibility that different patterns of behavior can arisein the forced-choice and yes/no tasks even when the samestimuli are used and the same knowledge is accessed. Ifthis is the case, it suggests that some of the differences ob-served in the previous experiment may arise from the spe-cifics of the real-time processes that combine perceptualinputs with long-term memory of how stimuli are catego-rized to create responses in novel noun generalizationtasks. The specific goal of our modeling efforts was toquantitatively fit the data from the experiment, that is, toproduce the particular amounts of attention to shape andmaterial we found in 2.5-year-olds in a model that cap-tures the processing differences underlying the forced-choice and yes/no tasks. Note that we did not simulatethe demonstrations of related and arbitrary properties be-cause this aspect of the task had little influence on chil-dren’s performance. Likewise, we did not simulateperformance with the color-matching stimuli becausethese stimuli were not included in the forced-choice task.

In what follows, we first present a general overview ofour dynamic field model, including qualitative results fromsingle representative simulations of performance in each

Table 1Numbers of individual children in the forced-choice and yes/no conditionsof Experiment 1 whose proportion of shape choices was below chance(<.50), at chance levels (<.50) or above chance (.<.50) for the deformableand rigid stimulus sets. Results of chi-square tests of homogeneity ofproportions comparing the patterns of responding across the two tasks foreach stimulus set are also provided.

Condition

Forced-choice Yes/no

DeformableProportion shape <.50 6 2

=.50 9 4>.50 1 9

v2(2) = 11.23, p < .01

RigidProportion shape <.50 2 0

=.50 1 4>.50 13 12

v2(2) = 3.80, ns

Note: The total number of children reported for the yes/no task withdeformable stimuli is not equal to 16 because one child said no to all thedeformable test objects.



task. We then discuss the selection of the particular param-eters we used. Finally, we present quantitative results fromour simulations of the data from the experiment, followedby a discussion of the implications of this modeling work.The details of the model, including the model equations,can be found in the Appendix.

3.1. The model

The starting point for the model is work by Spencer andcolleagues modeling the dynamics of responses in forced-choice and discrimination (same/different) tasks (Johnson,Spencer, & Schöner, 2008; Simmering, Spencer, & Schöner,2006; Spencer, Simmering, & Schutte, 2006). Our model, pic-tured in Fig. 4A, is an extension of the Dynamic Field Theory(DFT), a general theory of spatial cognition and visual work-ing memory (see Johnson et al. (2008), Spencer, Simmering,Schutte, & Schöner, 2007). The current work builds on priortheoretical, computational, and empirical work using DFT tocapture real-time and developmental change in tasks rang-ing from spatial memory to change detection to habituationin infancy. Note that by ‘‘real-time” we are referring to thetime scale of processes that generate individual responseswithin a trial. Previous work has mapped the real-timegeneration of peaks in similar dynamic neural field modelsto the generation of neural representations in visual cortexand motor cortex (Bastian, Riehle, Erlhagen, & Schöner,1998; Bastian, Schöner, & Riehle, 2003; Jancke et al., 1999).However, this is the first application of DFT concepts totask-specific behavior in a word learning context (for relatedwork, see Faubel & Schöner, 2008).

The model consists of an input field (top field in panelA) and decision field (bottom field Panel A). The x-axis ofeach field shows a set of neurons arranged by ‘‘similarity”.Neurons that are tuned to respond to stimuli that are sim-ilar overall (i.e., with receptive fields tuned to similar val-ues along particular feature dimensions) would be closeneighbors along this dimension, while neurons that aretuned to respond to stimuli that are dissimilar overallwould be far from one another along this dimension. Theactivation of each neuron is plotted along the y-axis. Timeis shown along the z-axis as the sequence of events in a sin-gle trial unfolds. Note that many models of similarity andobject categorization compute similarity as the distancebetween the high-dimensional representations generatedby, say, the presentation of two objects (e.g., Kruschke,1992; Nosofsky, 1987; Samuelson, 2002). Our use of simi-larity capitalizes on this idea, that is, we assume a systemthat can represent similarity in this way and pass metricinput regarding the distance between two items to thedecision field probed here (for an additional discussion ofthe concept of ‘‘similarity” in dynamic field models, seethe Section 5 and Faubel & Schöner, 2008). Importantly,we assume that the metric similarity input to the modelreflects similarity in the context of a naming task (see dis-cussion of parameters below). Note also that the strengthof inputs captures the salience of each item. Salience canbe affected by multiple factors such as long-term learningabout which features of objects are important for wordlearning, or factors such as whether an item is withingraspable space.

The stimuli were presented to the model via the inputfield. Inputs took the form of Gaussians representing theexemplar (leftmost peak) and two test objects, positionedaccording to their relative similarities (see Section 3.2).The number of test objects presented to the decision fielddiffered according to the task (see below). The exemplarwas present throughout the trial in both tasks, but its acti-vation was lower because it is farther from the child.

The time-dependent processes (i.e., the dynamics) thatdetermine the model’s response occur in the decisionfield. Neurons in this field interact according to a localexcitation/lateral inhibition function, a form of interactioncommon in neural models of cortical function (e.g., Dur-stewitz, Seamans, & Sejnowski, 2000). This means thatneurons close to one another along the similarity dimen-sion excite one another while neurons far apart inhibiteach other. The local excitation/lateral inhibition functionallows the network to form stable peaks of activation thatrepresent behavioral decisions to, for instance, select aparticular input in a forced-choice task. It is also possible,however, that the model will fail to form an activationpeak. Whether this occurs depends on the similarity of in-puts, the strength of neural interactions (i.e., the details ofthe interaction function), and the resting level of the neu-rons in the field. The critical differences between theforced-choice and yes/no versions of the novel noun gen-eralization task emerge from differences in the strengthand time structure of the inputs and from the interactivedynamics of the decision field. These differences are de-scribed below.

3.1.1. Dynamics of the forced-choice taskIn the forced-choice version of the novel noun general-

ization task, the child is presented with two test objects atthe same time and encouraged to pick one on each trial.Thus, children have the opportunity to compare the testobjects directly and have to make a relatively constrainedresponse—select one object over the other. As can be seenin the top field of Fig. 4A, on each trial the model is alsopresented with two test objects at the same time andencouraged to pick one—that is, to form a peak of activa-tion centered at one input or the other. To capture thehighly selective nature of this task, we made the inputsstrong and the decision field competitive (i.e., neuronsinteract strongly). This allows for a detailed ‘‘comparison”between stimuli. Fig. 5 shows the interaction kernels foreach task (see Table 2 for specific parameter values). Ascan bee seen in the figure, the parameters that structuredthe interaction dynamics in the forced-choice task weresuch that the decision field started relatively far fromthreshold (see hi in Table 2) and had strong levels of inhi-bition (see wiFC in Fig. 5) with strong excitatory interaction(weFC in Fig. 5) and strong inputs (j). Consequently, thedecision field reflected the inputs strongly and was highlycompetitive. When the tray was moved forward and theresting level boosted (see hb in Table 2), competition in-creased and the field was forced to make a selection.Importantly, this set of parameters put the field in a regimein which the peak that formed was centered at the locationof one of the two test objects, rather than at an indetermi-nate location or at the location of the exemplar.



Fig. 4. Dynamic field model used to simulate differences in performance in forced-choice and yes/no tasks. Model consists of an input field (top field inPanel A) and decision field (bottom field Panel A). The x-axis of each field represents a set of neurons arranged by ‘‘similarity”. Activation of each neuron isplotted along the y-axis. Time is shown along the z-axis as the sequence of events in a single trial unfolds. Panel A depicts a forced-choice trial. The top twofields in Panel B depict a yes/no trial with similar inputs, the bottom two fields, a yes/no trial with dissimilar inputs. See text for further details.



The course of events as a single forced-choice trial unfoldscan be seen in the bottom field of Fig. 4A. At the start of thetrial (back of figure), all three inputs (pictured in the input

field at the top) are fed into the decision field (lower fieldin panel A). The decision field is given a boost of activationat the point in the trial corresponding to when the tray

Fig. 5. Interaction functions for the decision field when the model performed the forced-choice (solid line) and yes/no (dashed line) tasks. The solid line at 0marks the difference between excitatory interactions and inhibitory interactions. Bars indicate magnitude of parameter values given in Table 2. See text fordetails.

Table 2Parameters used in model simulations. Parameters in the upper half of the table structured the interactive dynamics in the response field for the forced-choiceand yes/no tasks. Parameters in the lower half of the table specified the Gaussian inputs for the deformable and rigid test sets. The three values of eachparameter in this section correspond to the exemplar, shape-matching test object, and material-matching test object, respectively. See text for discussion.

Parameters for interactive dynamics

Forced-choice Yes/no Description

Interaction inhibition (wi) 7.0 1.0 How much neurons inhibit each otherInteraction strength (we) 20 8.68 Amount of interaction between neuronsInitial H level (hi) �15.0 �5.0 Resting level of fieldResponse H level (hr) �2.0 �2.365 Field resting when response requestedInput gain (j) 6.7 1.0 Strength of input to decision field

Input parameters

Deformable (exemplar, shape, material)Input width (rD) 60, 20, 22Input centers (xCD) 21, 41, 56Input strength (AD) 1.0, 1.3163, 1.3623

Rigid (exemplar, shape, material)Input width (rR) (60, 20, 26) (.80)Input centers (xCR) 21, 41, 56Input strength (AR) 1.0, 1.3690, 1.3670



with the test objects is slid towards the child and a requestfor a response is made. In the model, this change increasesboth competition among the neurons and the overall acti-vation in the field, thereby forcing the creation of a single,stable peak centered at one of the test objects. As can beseen in the figure, on this trial the model formed a peakat the location of the material-matching test object; thusit ‘‘picked” this test object.

3.1.2. Dynamics of the yes/no taskIn the yes/no version of the novel noun generalization

task, the child is presented with each test object individu-ally and must make a yes or no response for each. Conse-quently, the judgments children make concerning eachtest object are relatively independent in this task—childrencan say ‘‘yes” or ‘‘no” to each test object. Overall then, thedecisions children make in the yes/no task are less con-strained and are more sensitive to the similarity of an indi-vidual test object and the exemplar. As can be seen in thetop field of Fig. 4B, the model was also presented with onetest object at a time and made an independent judgment ofeach. The formation of a stable peak in the decision fieldrepresented a ‘‘yes” response and the failure to form a sta-ble peak, a ‘‘no” response. To capture the greater relianceon overall similarity in the yes/no task, we made neuronsin the decision field more excitable and less competitive(see weYN in Fig. 5), thereby allowing more blending acrossstimuli with good sensitivity to overlap in the input. In theyes/no task, the decision field started closer to threshold(hi) with weaker inhibition (see wiYN in Fig. 5) and weakerinputs (j). Consequently, inputs (in this case, only one testobject and the exemplar) could blend, and the slight boostin the resting level (hb) at the time a response was re-quested allowed for the formation of a stable peak of acti-vation provided there was enough overlapping activation.

The top two fields of Fig. 4B show a simulation of a trialwhere there is relatively high similarity between theexemplar and the test object, while the bottom fields showa simulation with relatively low similarity. As can be seenin Fig. 4B, when the inputs are close together, the locallyexcitatory interactions among neurons in the decision fieldcause the activation associated with these stimuli to blendand increase over time, ultimately combining to form asingle activation profile. If this activation reaches a criticalthreshold—an activation level above 0—the model forms aself-sustaining peak and responds ‘‘yes” (second field fromtop in Fig. 4B). As can also be seen in the figure, however,when the inputs are farther apart, activation patterns donot blend in the decision field. Thus, no above-thresholdpeak is formed and the model responds ‘‘no” (bottom fieldin Fig. 4B).

3.1.3. Summary of qualitative resultsConsidered together, the simulations in Fig. 4 highlight

that the details of the processes that bring knowledge tobear in a task have a critical influence on the specifics ofthe resulting performance. In particular, note that the exactsame inputs were used in the simulations presented in panelsA and B of Fig. 4. In the forced-choice task, the model pickedthe material-matching test object which was slightlystronger. However, when this same test object was pre-

sented in the yes/no task, the fact that this test objectwas relatively far from the exemplar meant that the modelfailed to generate a self-sustaining peak and responded‘‘no”. In contrast, when the input representing the shape-matching test object was presented in the yes/no task,the shared similarity caused a self-sustaining peak to formand the model responded ‘‘yes”. Thus, given the exact sameinputs in the two tasks, the model generalized the namesdifferently, demonstrating a material bias in the forced-choice task, but a shape bias in the yes/no task. The centralquestion, then, is whether these qualitative insights can beextended to provide a quantitative account of the findingsfrom the experiment.

3.2. Method

3.2.1. Model parametersTable 2 lists the model parameters organized as ‘‘inter-

action” parameters that structured the interactive dynam-ics in the decision field for the forced-choice and yes/notasks, and ‘‘input” parameters that specified the Gaussianinputs for the deformable and rigid stimulus sets. We dis-cuss constraints on parameter selection below.

Parameters for interactive dynamics: Selection of the val-ues for the interaction parameters was constrained by thetheoretical proposals reviewed above regarding the natureof the decision dynamics in the forced-choice and yes/notasks. That is, the parameters that specified the interactivedynamics for each task were selected to implement thehypothesis that the forced-choice task requires childrento be highly selective while performance in the yes/no taskdepends more on the overall similarity between an indi-vidual test object and the exemplar. If our selected param-eters then capture differences in children’s performancebetween tasks, this will support our theoretical proposalabout the critical processes that underlie performance inthe two tasks.

Note that in the forced-choice task, the model was re-quired to choose one of the two test objects by building apeak of activation in the decision field centered on thelocation of one of the two input peaks. In contrast, the par-ticular response made in the yes/no task depends onwhether or not a stable peak of activation forms, not onthe exact location of that peak. Thus, we did not requirethat the parameters for the yes/no task place the field ina regime that constrained peak formation to the locationof an input. We did verify, however, that peaks did notform outside the range of the inputs to ensure that theywere the result of the interaction of the inputs, not spuri-ous peaks created by noise.

As can be seen in Table 2, five parameters that deter-mined the competitive nature of the interactions were var-ied across tasks. Conceptually, these parameters specifyhow children’s attention is modulated by the specifics ofthe task (see Section 2.3 for further details).

Input parameters: Selection of the input parameter val-ues was constrained by the goal of presenting the same ri-gid and deformable inputs in the two tasks and by thenecessity of finding reasonable parameters given what isknown about children’s attention to shape and materialin novel noun generalization tasks. In addition, we wanted



to be able to manipulate the inputs to examine possibleconstrains on the interface between children’s knowledgeand task performance (see Section 2.3). The inputs thatrepresented the exemplar, shape-matching, and material-matching test objects for the deformable and rigid setswere represented by two sets of three Gaussians. EachGaussian was specified by three parameters: (1) input cen-ter (x), (2) input width (r), and (3) input strength (A). Thefinal parameter values are given in Table 2. In the table, thevalues given for each parameter are for the exemplar,shape-matching test object, and material-matching testobject, respectively. Differences in relative position,strength, and width of the inputs within and across inputsets can be taken to capture overall similarity, strength,and precision of the representational states, respectively,that were created when children viewed the stimuli inthe context of a novel noun generalization task.

As can be seen in the table, the input width values fortest objects for both the deformable (rD) and rigid (rR) setswere not as broad as the exemplar in either set. This is be-cause the test objects were always presented closer to thechildren than the exemplar and were the focus of chil-dren’s attention. The fact that the shape-matching test ob-ject was a bit narrower than the material-matching testobject in each set fits with data suggesting children makedistinctions in noun generalization based on shape similar-ity before they make similar distinctions based on materialsimilarity (Gathercole & Whitfield, 2001; Landau et al.,1988; Samuelson & Smith, 1999). Note that for the rigidstimuli, the input width values were scaled by .80. This fitswith the fact that rigid things generally have more precisefeatural characteristics than deformable things.

The same input center values were used for the both thedeformable (xCD) and rigid (xCR) sets. In both sets, theshape-matching test object was more similar to the exem-plar (i.e., their centers were closer) than the material-matching test object. For the deformable set, the greatersimilarity of the shape-matching test object to the exem-plar fits with the fact that deformable things have charac-teristic shapes that they return to following perturbations.Similarly, for the rigid set, the greater similarity of theshape-matching test object fits the fact that rigid thingsmaintain their shape over transformations. The greatersimilarity of shape-matching test objects to the exemplarin both sets also fits with data suggesting that childrenhave learned an association between the importance ofshape similarity and naming tasks such as the ones weare modeling (Landau et al., 1988; Samuelson, 2002; Smith& Samuelson, 2006; Smith et al., 2002).

The input strengths were slightly different for the twokinds of stimuli. Specifically, for the deformable sets, thematerial-matching test object had a slightly higherstrength than the shape-matching one. This reflects theimportance of material for what can be done with deform-able things, especially in a task in which a demonstration isused to highlight the material composition of some of thestimuli. The two test objects were more similar in strengthfor the rigid set, though the shape-matching test objectwas slightly stronger to reflect the importance of shapefor what can be done with rigid things. It is also importantto emphasize that the particular strength values in Table 2

were multiplied by the input gain (j) for each task. Thus,the small differences in the strength of the material- andshape-matching test objects within a set were amplifiedin the forced-choice task relative to the yes/no task dueto the greater input gain.

Fig. 6 depicts the inputs for the deformable and rigidsets that result from the final parameters. This figure high-lights the similarity of the inputs across sets. Nevertheless,we will see that these small differences had a substantialimpact on the model’s performance in the context of theinteractive dynamics of the decision field.

3.2.2. Simulation detailsSimulations were conducted in MATLAB (Mathworks

Inc.) on a PowerMac G5 with dual 2.7 GHz processors(the MATLAB code is available from the first author on re-quest). The dynamic field equation was integrated usingthe Euler method. Each run of the model in each task sim-ulated a single trial. A network with 101 neurons was usedfor all simulations. Trials began with the field at the levelspecified by hi. The inputs were then presented for 610time steps. Following this, the resting level was boostedto the level specified by hb. The response was determinedafter an additional 500 time steps. The response in theforced-choice task was found by taking the location ofthe maximum activation in the decision field at the endof the simulation and determining which of the two inputsit was closest to. Individual simulations verified that thepeaks that formed were at the exact location of one ofthe test objects. For the yes/no task, the response was ta-ken as a ‘‘yes” if the field formed a stable peak and a‘‘no” otherwise (responses were checked to ensure thatpeaks always formed within the range of the inputs). Weconducted 200 repetitions of individual trials from eachtask with each stimulus set (deformable and rigid), andverified that the model converged on similar values across10 sets of 800 simulations (200 repetitions � 2 tasks � 2stimulus sets).

3.3. Results and discussion

We calculated the mean number of times the model se-lected the material- or shape-matching test object in theforced-choice task as well as the mean number of ‘‘yes”and ‘‘no” responses in the yes/no task for the deformableand rigid stimulus sets. The data from the model simula-tions along with the corresponding data from the experi-ment are presented in Fig. 7. As is clear in the figure, themodel fit the experimental data extremely well. To quan-tify the fit, we calculated the root mean squared error(RMS) across the two stimulus sets and two tasks. This va-lue was .02 for the pictured simulation. We also examinedthe average RMS for the 10 sets of 800 simulations we con-ducted. The average was .04 with a standard deviation of.014 and a range of .02–.06. Thus, the model’s performanceshown in Fig. 7 was quite robust.

Like the 2.5-year-old children in the experiment, themodel generalized novel names for deformable things bymaterial in the forced-choice task but by shape in theyes/no task, and generalized novel names for rigid thingsby shape in both tasks. The excellent fit of the model to



the data even though we used the same stimulus setsacross tasks thus confirms the importance of the taskdynamics in shaping children’s behavior when generaliz-ing novel nouns. These simulation results support the ideathat the way children are asked to generalize novel namescan create different patterns of performance even whenthe same accumulated vocabulary knowledge is accessed.

The robust fit of the dynamic field model to the datamay lead some to question whether the model is actuallytoo general and whether it could ‘‘model anything”. Theanswer is no. The dynamic field equations capture strongtheoretical assumptions, for example, that input is local-ized, that the interaction functions are homogeneous andsymmetrical, and that inputs can be superimposed. Thus,simulation of any arbitrary input–output mapping is pre-cluded by the internal structure of the DFT. Put differently,the DFT implements a form of nonlinear decision makingwhere only the right convergence of inputs and interactiondynamics will put the field into a state that creates a stablepeak. Thus, there are real constraints on processing in thismodel ensuring that it cannot capture just any input–out-put mapping.

Another critical question, however, is whether the de-tails of the quantitative simulations are meaningful inthe context of the extant literature. To evaluate this issue,we conducted a set of follow-up analyses of the model’sperformance. We first asked whether the ordering of theinputs on the similarity dimension was critical to the re-sults. Recall that the shape-matching test object was closerto the exemplar for both the rigid and deformable input

sets. This configuration implies that the shape-matchingtest object is more similar to the material-matching onein the representational state created when children viewthese stimuli in these tasks. To test the necessity of thissimilarity relationship for the obtained results, we set upinputs in which the material-matching test object wasmore similar to the exemplar than the shape-matching testobject in the deformable stimulus set. Even though this setof inputs was otherwise quite similar to the final set, wewere not able to capture the full pattern of results seenin Fig. 7 with inputs structured this way.

More specifically, we were only able to adequately cap-ture data from one task at a time with the deformable in-puts structured in this way. In order to capture children’syeses to the deformable shape-matching test object inthe yes/no task, the shape-matching test object must over-lap somewhat with the exemplar. However, this configura-tion causes the material-matching test object to be so closeto the exemplar that the model chooses it more than thechildren did in the forced-choice task. This is the criticaltrade-off seen in children’s performance in these tasks—they are sensitive enough to importance of shape fordeformable things that they do generalize novel namesfor deformable things by shape in the yes/no task. How-ever, when forced to choose between shape- and mate-rial-matching test objects, they generalize novel namesby material similarity more often. This trade-off is realizedin the parameters for the deformable set—the shape-matching test object is necessarily closer to the exemplar,resulting in ‘‘yes” responses in the yes/no task, but the

Fig. 6. Model inputs for the deformable and rigid sets that result from the final input parameters. Relative overall similarity is represented along the x-axis,activation along the y-axis. Solid lines represent deformable inputs, dashed lines represent rigid inputs. Each set of inputs includes an exemplar (leftmostpeaks), a shape-matching test object (center peaks), and a material-matching test object (rightmost peaks).



material-matching test object is stronger, resulting in itsgreater selection in the forced-choice task.

There is another element of children’s responses, how-ever, that the model is also able to capture—the fact thatchildren’s responding is variable. In particular, childrendo not always pick the material-matching test object withthe deformable stimuli in the forced-choice task, and donot always say ‘‘yes” to the shape-matching test object inthe yes/no task. Our use of noisy inputs (see Appendix) iscritical to this result. This noise model implies that the rep-resentational states created when children view thesestimuli in these tasks are somewhat variable, although,importantly, this noise is coherent across individual inputs.This means that in the highly-selective forced-choice task,for instance, the (typically) weaker test object may be cho-sen if noise boosts it’s activation above the level of the(typically) stronger input. At the same time, noisy inputsmean that sometimes test objects that are relatively closeto the exemplar are weakened such that they cannot sup-port the formation of a stable peak and a ‘‘yes” response.Thus, the fit seen in Fig. 7 only emerges when the right

set of inputs are given to a model with just the right inter-active dynamics. This fact serves to further validate the rel-ative positioning of the test objects and exemplar shown inFig. 6, and highlights the importance of the interaction be-tween the specific inputs and the task dynamics in creatingbehavior.

One final issue with respect to the modeling work pre-sented thus far is the relation between the different inter-action functions used to model the two tasks and theparticipants in our experimental task. In particular, do dif-ferences in the interactive dynamics used to capture per-formance in the two tasks correspond best to differentsets of processes in two different children, or can they beseen as task-related differences that emerge on-line in anindividual child engaged in a specific task? A close exami-nation of the five interaction parameters that changedacross the two tasks suggests the latter. In particular, theseparameters may be best viewed as arising from a real-timeattentional modulation of the neural circuits responsiblefor decision making in these two tasks. For example, thelarge value of the input gain parameter, j, in the forced-

0.0

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1.0

ProportionShape Choices

Forced Choice

Model

Children

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ProportionYes

Responses

Shape Material

Yes/No

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0.1

0.2

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0.9

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ProportionShape

Choices

Forced Choice

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ProportionYes

Responses

Shape Material

Yes/No

Deformable

Rigid

Fig. 7. Mean proportion of times the model (white bars) selected the shape-matching test object in the forced-choice task as well as the mean proportion ofyes responses to the shape and material-matching test objects in the yes/no task for the deformable and rigid stimulus sets. The corresponding data fromchildren in the experiment are also presented (black bars).



choice task can be thought of as an attentional boost re-lated to the amount of stimulation provided by havingmultiple inputs simultaneously present. Prior work hasdemonstrated such changes can occur via attentional sys-tems in real-time in individual participants (Desimone &Duncan, 1995).

The task differences in the initial resting level, hi, andthe resting level boost during the response, hb, can beviewed in a similar way. The parameter, h, is a constantadded equally to all locations in the field. Thus, rather thanspecifying where a peak should form, this parameter mod-ulates the possibility that a peak will form by moving thedecision field closer to the peak-formation threshold. Con-ceptually, the shift in h during the trial reflects the boost inchildren’s attention to the test objects as the tray is slidforward in the forced-choice task or the children are askedto give a response in the yes/no task. Note that from thisperspective, the smaller boost in the yes/no task corre-sponds to the fact that the stimuli are never moved withinreach of the child.

The between-task differences in the final two parame-ters, interaction inhibition, wi, and interaction strength,we, are captured in Fig. 5. As can be seen in the figure,the interaction functions for the two tasks are actually verysimilar, but the function for the forced-choice task hasbeen lowered and stretched. The lowering is due to thehigher inhibition value used in the forced-choice task.The stretching of the forced-choice function is due to thegreater interaction strength used in this task, which cre-ates a greater degree of interactivity overall. Importantly,both of these changes can be produced in a more neu-rally-realistic dynamic field model with separate excit-atory and inhibitory layers by changing the resting levels(h) of both layers (Schutte & Spencer, in press; Spenceret al., 2007). Because these changes can be created throughthe modulation of global resting levels, they can also bethought of as arising via an attentional modulation of theneural populations involved in decision making in thesetasks.

4. Quantitative modeling of developmental changes

Our dynamic field model captures important differencesin the processes that underlie performance in forced-choiceand yes/no novel noun generalization tasks. The excellentfit of the model to the data from 2.5-year-old children inthese tasks confirms that the interaction of the input andtask dynamics can result in different patterns of noun gen-eralization when the same knowledge representations areprocessed in two different tasks. Thus, the experimentaland simulation results thus far support the perspective thatknowledge cannot be separated from the processes thatbring it to bear in a task, and helps explain why what chil-dren appear to know can look different from task to task. Inthis section, we extend the modeling work further byexploring another important finding in the literature onchildren’s novel noun generalization—developmentalchanges in noun generalization from 2 to 4 years of age.We focus on one recent set of experiments that demon-strate changes in noun generalization in a yes/no task.

Samuelson et al. (2008) examined novel noun general-ization in 2-, 3-, and 4-year-old children using the same ri-gid and deformable stimuli used in Experiment 1. The dataare shown in Fig. 8 (black bars) along with the data from2.5-year-old children in the current paper. As is clear inthe figure, these data suggest differences in the proportionof ‘‘yes” responses across rigid and deformable stimulussets, shape- and material-matching test objects, and age.Our modeling work thus far has captured differences inthe amount of shape responding for rigid and deformablesets in the yes/no task, as well as differences in the propor-tion of yes responses to shape- and material-matching testobjects. Our question, then, was whether the DF modelcould capture developmental differences in responding inthe yes/no task as well.

Three developmental effects stand out in Fig. 8. First,the proportion of yes responses to test objects that matchrigid exemplars in shape increases from 2 to 3 years ofage and remains high (see A in Fig. 8). Second, the propor-tion of yes responses to test objects that match both rigidand deformable exemplars in material drops over this per-iod of development (see Bs in Fig. 8). Finally, 3-year-oldchildren demonstrate a higher rate of yes responses to testobjects that match deformable exemplars in shape (C inFig. 8; see also Samuelson & Smith, 2000a), compared to2- and 4-year-old children (see Samuelson et al. (2008)for statistical analysis and replication of the high shaperesponding in 3-year-old children).

To capture these developmental differences in themodel, we instantiated two hypotheses about changesover development in how children actively representstimuli in a naming context captured by the input array:(1) that the association between shape and naming in-creases over development and (2) that stimulus represen-tations become less noisy (i.e., more stable) overdevelopment. The first hypothesis fits with a number ofstudies in the literature on early word learning that sug-gest children’s attention to shape when naming novel ob-jects becomes stronger over development (Gershkoff-Stowe & Smith, 2004; Landau et al., 1988; Samuelson &Smith, 1999; Smith et al., 1992). The second hypothesisfits with recent arguments concerning the nature ofdevelopmental change and work using similar DF models(Schöner & Dineva, 2007). For example, Schutte andSpencer (in press) captured the pattern of developmentalchange in young children’s spatial memory via changes inthe specifics of the local excitation/lateral inhibition func-tion in a DF model of spatial cognition. These changes inneural interaction resulted in more stable representationsof items in working memory, that is, reduced noise inhow children actively represented stimuli as hypothe-sized here. The critical question is whether the complexpattern of results would emerge when these two devel-opmental changes to children’s representations interactwith the real-time decision processes captured in themodel.

4.1. Methods

The model was identical to that used previously exceptwhere noted below. That is, we used the same interactive



dynamics parameters for the yes/no task and the same in-put parameters for the rigid and deformable stimuli. Tosimulate development (2-, 3-, and 4-year-old children),we scaled the noise strength, q, and varied the strengthof the shape inputs relative to the values used previouslyfor our simulations of the data from 2.5-year-old children.Specifically, noise strength (q) decreased systematicallyover development, while the strength of the shape inputsincreased over development. The differences in noise andshape strength relative to the prior simulations are de-picted in Fig. 9.

Simulations were conducted in MATLAB (MathworksInc.) on a PowerMac G5 with dual 1.8 GHz processors.Otherwise, the simulations were identical in detail to theprevious set. Each run of the model simulated a single trialwith a given stimulus set. We conducted 200 repetitionswith each stimulus set (deformable and rigid) at eachdevelopmental level, and verified that the model con-verged on similar values across 10 sets of 400 simulations(200 repetitions � 2 stimulus sets) at each developmentallevel.

4.2. Results and discussion

We calculated the mean number of times the modelmade ‘‘yes” and ‘‘no” responses for the deformable and ri-gid stimulus sets at each developmental level. Data fromthe model simulations are presented in Fig. 8 (white bars).As is clear in the figure, the model fit the data very well. Toquantify the fit, we calculated the root mean squared erroracross the two stimulus sets and three developmental lev-els. This value was .04 for the pictured simulation. We alsoexamined the average RMS for the 10 sets of 400 simula-tions we conducted at each age level. The average was.05 with a standard deviation of .014 and a range of .03–.08. Thus, the model’s performance shown in Fig. 8 wasquite robust.

These simulations, then, suggest that changes in youngchildren’s attention to shape and material from 2 to 4 yearsof age are related to changes in the strength of the link be-tween naming tasks and attention to shape, and the preci-sion of the representational states created when childrenview the stimuli in these tasks. Both of these developmen-

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Fig. 8. Mean proportion of yes responses by 2-, 2.5-, 3-, and 4-year-old children (black bars), and the DF model (white bars) to shape- and material-matching test objects in the yes/no task for deformable and rigid stimulus sets. Thirty-two month-old data are from the current paper. Two-, 3- and 4-year-old data are from Samuelson et al. (2008).



tal hypotheses have support in the literature. Nevertheless,an important question is whether both of these changes arenecessary to create the observed pattern in the data. Toexamine this issue, we attempted to capture the patternof results seen in Fig. 8 in two additional sets of simulationsthat included changes to either noise strength or shape in-put strength separately. In the simulations that manipu-lated noise strength only, the best parameter values were.05, .045, and .038 for the 2-, 3-, and 4-year-old simulations,respectively. These values resulted in a average RMS of .05for the best single run at each developmental level, but anoverall average RMS of .078 (SD = .039, range .02–.14)across 10 sets of 400 simulations at each developmental le-vel. A two sample t-test revealed that the RMS values forthe noise-only simulations were significantly poorer thanthose for the main simulations reported above, t(58) =�3.65, p < .001. This poor performance is due to the factthat reducing noise in the model serves to reduce the num-ber of ‘‘yes” responses overall, which is not the develop-mental pattern children show between 2 and 4 years ofage. Four-year-old children do show an overall reductionin yes responses compared to 3-year-old children. How-ever, between 2 and 3 years of age, the number of yes re-sponses increases for shape-matching test objects whiledecreasing for material-matching test objects (compare Aand B in Fig. 8). Thus, while changing noise strength aloneresults in relatively low RMS values, there is no consistentset of changes to this parameter alone that can simulta-neously capture children’s responding to the shape- andmaterial-matching test objects.

A similar pattern emerged in the simulations that manip-ulated shape input strength only. The best parameter valuesfor this set of simulations were 1.00000001, 1.00036, and.9995 for the 2-, 3-, and 4-year-old simulations, respectively.Because the difference in 2.5- and 3-year-old children’s

responding was captured in the main simulations with achange in the noise strength parameter alone, we used themain simulations for 2.5-year-olds in this follow-up. Thesevalues resulted in a average RMS of .08 for the best singlerun at each developmental level, and an overall averageRMS of .088 (SD = .026, range .04–.13) across 10 sets of 400simulations at each developmental level. A two samplet-test revealed that the RMS values for the shape-multiplier-only simulations were significantly poorer than those for themain simulations reported above, t(58) = �6.87, p < .001.This poor performance is due to the fact that increasing thestrength of the shape input does not influence respondingto the material-matching stimuli which contrasts with re-sults shown in Fig. 8. Thus, while changing shape strengthalone results in relatively low RMS values, it does not cap-ture the full pattern of results. In particular, there are no con-sistent set of changes to the shape input strength alone thatcan capture both the increase the number of yeses to test ob-jects that match exemplars in shape and the decrease in thenumber of yeses to test objects that match exemplars inmaterial that children show over development.

Overall, then, these simulations suggest that our dy-namic field model can capture important developmentaldifferences in children’s noun generalization from 2 to 4years of age with relatively modest and conceptuallyappealing changes to two parameters. These parameters re-flect the strength of attention to shape in naming tasks andthe amount of noise in the representations children formwhen viewing the stimuli in a naming context. Thus, thesechanges correspond to prior hypotheses concerning thenature of developmental change in novel noun generaliza-tion (Jones & Smith, 1993; Samuelson, 2002; Smith, 2001;Smith & Samuelson, 2006; Smith et al., 2002) and the stabil-ity of children’s representations (Schöner & Dineva, 2007). To-gether with the prior simulations of performance differences

Fig. 9. Change in noise strength (q) and shape strength parameters across simulated developmental levels relative to simulations of 2.5-year-old children.



in forced-choice and yes/no tasks, the DFT provides novelinsights into how knowledge is brought to bear in a mo-ment and how that knowledge changes over development.

5. General discussion

The goal of this paper was to examine the processesthat bring young children’s knowledge of nominal catego-ries to bear as they generalize novel nouns. As in priorstudies, we found that children robustly generalize novelnames for rigid objects by similarity in shape, and that thisbias appears in both forced-choice and yes/no novel noungeneralization tasks (Booth et al., 2005; Landau et al.,1988). Nevertheless, we found that children generalizednames for deformable things by material in a forced-choicetask, but not in the yes/no task, even though the children’sage and vocabulary size were equated across tasks, and allchildren saw the same stimuli and demonstrations high-lighting the material of deformable exemplars. This task-dependent performance when generalizing names fordeformable things fits both with prior studies of noun gen-eralization (Gathercole & Min, 1997; Samuelson et al.,2007; Samuelson & Smith, 2000a), and adult judgmentsof the similarity structure of categories of deformablethings (Samuelson & Smith, 1999, 2000a). The currentwork makes a contribution by showing how the interactionof represented knowledge and task processes can result inconsistent performance across tasks in some cases (rigidstimuli) and variable performance in others (deformablestimuli).

A dynamic field model that captured critical differencesin the decision processes in the forced-choice and yes/notasks provided a demonstration that processing differencescan yield behavioral differences between tasks even whenthe same vocabulary knowledge is accessed. This modelalso provided an excellent quantitative fit to the experi-mental data from both the rigid and deformable stimulussets. Further, the model was able to capture developmentalchanges in children’s performance in the yes/no task. Inthis way, then, the model provides a window onto boththe real-time processes that can produce different patternsof responses in different task contexts, and what changesdevelopmentally to produce different performance at dif-ferent ages (see also Plumert, 2008).

5.1. Real-time processes

The DF model presented here is the first processed-based model of the real-time noun generalization behav-iors that form the basis of current theories of early wordlearning. As such, one key contribution of our DF modelof children’s naming behaviors comes from the real-timespecification of the processes that bring children’s knowl-edge of nominal categories to bear in different noun gen-eralization tasks. Studies of the early noun vocabularyhave documented a clear and systematic association be-tween nominal categories of rigid things and the impor-tance of shape for category organization (Samuelson,2000; Samuelson & Smith, 1999; Samuelson et al., 2008).

These studies also suggest a more complex relationshipbetween nominal categories of deformable things andthe importance of shape and/or material for categoryorganization. We contend that the more complex relation-ship between category organization and naming fordeformable things allows signatures of real-time pro-cesses to be seen in children’s noun generalizations—chil-dren generalize names for deformable things by shape inyes/no tasks, but by material in forced-choice tasks (seealso Gathercole & Min, 1997; Samuelson et al., 2007;Samuelson & Smith, 2000a). Our DF model suggests thatthe key processing difference reflected in these behavioraldata is grounded in the competitive nature of the forced-choice task that allows for direct comparison of the testobjects and asks the child to pick one object relative tothe yes/no task that does not. In the DF model, decisionsin the forced-choice task are based on which input peakwins the competition and suppresses other competitorsto enter a self-sustaining state. In contrast, decisions inthe yes/no task are based on the similarity of each individ-ual test object input to the exemplar; if the input is similarenough it will blend with the exemplar’s input in the deci-sion field and will create a self-sustaining peak (a ‘‘yes”response). The excellent fit of the simulations presentedhere to children’s data support our proposal regardingthe differing processes at work in the two tasks. In addi-tion, the simulations support the proposals that attentionto material is slightly stronger for categories of deform-able things, resulting in generalization by material in theforced-choice task, but that things that match in shapeare more similar overall, resulting in generalization byshape in the yes/no task.

This modeling work suggests that further exploration ofthese real-time processes could help clarify some of thediscrepancies in the literature on early noun learning. Forexample, Gershkoff-Stowe and Smith (2004) found that itwas not until children had 50 nouns in their productivevocabulary that they began to demonstrate a shape biaswith rigid stimuli. In contrast, Booth et al. (2005) foundthat 18-month-olds with an average of 19 count nouns intheir productive vocabulary generalized novel names fornovel rigid objects by shape. The work presented here sug-gests that these differences may reflect the importance ofreal-time comparison processes in determining how chil-dren’s accumulated knowledge of nominal categories man-ifest in the particulars of young children’s noungeneralizations. Gershkoff-Stowe and Smith (2004) useda five-item forced-choice task. In contrast, Booth et al.(2005) used a three-item forced-choice task that includedmultiple named exemplars and vignettes describing theexemplars as artifacts. More test objects means that chil-dren have more items to attend to and more comparisonsto make when generalizing a novel name. In the DFT, thepresentation of multiple choice items increases competi-tion among the choices. This would reduce the influenceof the small differences in the strength of inputs to themodel that were critical to capturing the current data,and would thus lead to more chance responding by themodel (for evidence that the number of choices influencesbehavior in the DFT see Spencer et al. (2006)). Thissuggests then, that children may be able to demonstrate



a reliable shape bias based on weaker underlyingrepresentations of the stimuli in a three-item forced-choice task compared to a five-item forced-choice task.Likewise, the supports Booth et al. (2005) added to theirtask (e.g., presenting multiple exemplars and a contrastitem, and naming exemplars multiple times in vignettes)may have also helped younger children make decisionsbased on weaker underlying knowledge.

Thus, this modeling work serves as a reminder thatwhen children acquire 50 nouns, it is not the case that aswitch flips in their head turning on a shape bias. Rather,the behavior we call the shape bias is the emergent prod-uct of children’s accumulating knowledge of how thingsare named and the real-time processes of the task (Sam-uelson & Smith, 2000b). As children acquire more andmore words, they learn more and more about the regular-ities inherent in the language they are learning. For chil-dren learning English, one of these regularities is thatmany count nouns refer to solid things in categories orga-nized by similarity in shape (Gathercole & Min, 1997;Samuelson & Smith, 1999). This accumulating knowledgecan serve as the basis of novel noun generalizations andsubsequent word learning as captured by the AttentionalLearning Account proposed by Smith and colleagues to ex-plain the development and realization of the shape bias(Smith, 2000; Smith & Samuelson, 2006; Yoshida & Smith,2003). What the current work adds to this is a demonstra-tion of the importance of the real-time processes in mak-ing that connection between the child’s prior wordlearning history and the here-and-now of a novel wordin a novel situation with novel stimuli. In this sense, ourmodel highlights that differences in the specific resultsof individual studies are not problems, but rather, impor-tant windows onto the underlying real-time processesthat have received relatively little attention in work onearly word learning.

Another key contribution of the model in this context isthat it is, to our knowledge, the first real-time processmodel of the comparison processes in word learning tasks(for other process models of comparison see, e.g. Gold-stone, 1994; Larkey & Love, 2003). Based on studies in in-fant categorization, early word learning, and thedevelopment of analogical reasoning, a number of authorshave argued recently for the importance of comparison incognitive processing and early word learning (Gentner &Medina, 1998; Gentner & Namy, 2006; Namy & Gentner,2004; Oakes & Madole, 2003; Sandhofer, 2001). However,the nature of the comparison process in this literaturehas been underspecified. The model presented here takesa first step towards greater specification by detailing thenature of the comparison process—interaction of a set ofneurons according to a local excitation/lateral inhibitionfunction—as well as the result—a stable peak of activationat a particular location on an ordered dimension. Further,the modeling work presented here explicitly ties behaviorin novel noun generalization tasks to a more generaltheory of decision processes and a theoretical frame-work—the DFT—that is grounded in neural principles (seeSimmering, Schutte, & Spencer, 2008; Spencer, Dineva, &Schöner, in press; Spencer et al., 2007). Thus, our compar-ison process is neurally plausible.

These contributions notwithstanding, it will be impor-tant in the future development of this model to incorporatea more rigorous representation of similarity. The modelpresented here used a very basic notion of similarity—asingle dimension where distance along that dimensioncaptures overall similarity—akin to the use of distancemetrics in other models (e.g., Kruschke, 1992; Nosofsky,1987; Samuelson, 2002). Although the similarity structureof our inputs was well grounded in the literature, a morecomplete model should include separate dimensions forparticular feature dimensions such as shape, material, size,color, and so on. Adding a more complex representation ofdifferent object properties would enable fine-grained dis-tinctions between the relative importance of features suchas rounded corners and straight edges for rigid vs. nonrigidor nonsolid things. Further, such a representation wouldallow for easier manipulation of the relative importanceof such features with changes in the nominal categoriesin the productive vocabulary.

Towards this end, Faubel and Schöner (2008) haveused coupled, multi-dimensional dynamic fields in anautonomous robot that quickly learned to name 30 ob-jects (see also Johnson et al., 2008). Importantly, this worksuggests that the similarity structure of nominal catego-ries—that is, the fact that things called ‘‘banana” are moresimilar to each other and to things called ‘‘squash” thanthey are to things called ‘‘stapler”—is emergent from thesystem’s prior history of naming, and correlations be-tween particular names and activation of relevant featuredimensions in a given task context. Incorporating a morecomplex representation of similarity in our model willalso require, however, corresponding advances in ourunderstanding of how children represent similarity. Thishas been limited in the past by procedural constraintssuch as the small number of trials an individual childcan perform in a single experimental session. We are cur-rently working on a new method for eliciting similarityjudgments in children that will overcome some of theselimitations.

5.2. Toward developmental process

The fact that we were able to use the same model tocapture differences in children’s naming of deformableand rigid things from 2 to 4 years of age suggests thatunderstanding processes at the level of individual trialscan aid in understanding developmental change. Thedevelopmental simulations presented here point to twocritical changes in knowledge representations over thisage range: (1) an increase in the strength of the associationbetween naming tasks and shape similarity and (2) areduction in the amount of noise in the representationalstates created when young children view stimuli in thesetasks. These relatively simple developmental changes arewell supported in the literature. The critical insight fromthe model is that the complex pattern of responding wesee across this age range emerges when these two simple,quantitative and systematic developmental changes arecombined and brought to bear in a moment.

Further understanding of the complexities of perfor-mance in these tasks and over development will come



from future work that ‘‘closes the loop” between real-timeperformance and development. We need to understandhow individual behaviors on the real-time scale accumu-late to create the differences in performance seen in chil-dren of different ages and vocabulary levels. According tothe Attentional Learning Account proposed by Smith andcolleagues (Smith, 2001; Smith & Samuelson, 2006),biases such as the shape bias are learned products of thechild’s experiences with language. Thus, the very earlyword learning experiences of the child influence futureword learning via accumulation of regularities over multi-ple individual exposures to words and categories. Impor-tantly, the DFT provides a process by which individualexperiences can build upon each other to influence thedynamics of future real-time behavior and thereby createbiases. Specifically, in their work on spatial cognition,Spencer and colleagues (Spencer et al., 2007) have useddecision fields, similar to the ones used here, coupled tolong-term memory fields (see also Faubel & Schöner,2008). In these models, self-sustaining working memorypeaks generated over the course of individual trials leaveactivation traces in long-term memory that can feed backand influence working memory (implementing a form ofHebbian learning; for discussion, see Spencer et al., inpress). This system, then, provides a concrete process bywhich statistics of past decisions can accumulate overmultiple individual trials and, in turn, can be brought tobear on current behavior.

These neurally grounded models have been used tocapture changes on the intermediate timescale of biasesthat accumulate over the course of an experiment as wellas differences in children’s spatial memory abilities from6 months to 6 years of age (see Spencer et al. (2007) fora review). For example, Hund and Spencer (2003) foundthat if adult participants are asked to recall three loca-tions but one location is responded to more often thanthe others, memory responses come to be biased towardsthe more frequently responded to-location. Similarly,Divena and colleagues (Dineva, 2005) have found that in-fants’ trial-by-trial responses in the classic Piagetian A-not-B task impact their subsequent performance. In fact,infants who early on in the task spontaneously reach towhat will be the correct location later, are less likely tomake search errors on the critical test trials. In the DFmodel used to capture this finding, it is the individualdecisions made on each trial that are the critical influenceon long-term memory and thus subsequent behavior. Wehave found a similar behavioral result in recent work on24-month-old children’s generalizations of names fornonsolid substances. As reported in Samuelson and Horst(2007), these young children become less likely to gener-alize a novel name for a novel solid rigid object by shapeif, over the course of the experimental session, they havepreviously seen many nonsolid substances and solidthings broken into pieces. A critical question will bewhether this trial-by-trial effect, like those found in pre-vious reports that tap spatial and sensorimotor systems,is necessarily based on the naming decisions childrenmake over the course of the experiment. Answering thisquestion will have clear implications for the nature of

the process by which vocabulary statistics accumulateto create biases. More generally, incorporating a coupledlong-term memory system into the current model willprovide a means to further explore how the developmentof word learning biases might arise from individual nam-ing experiences.

5.3. Conclusions

The goal of the current work was to examine an issue atthe core of modern developmental science and cognitivepsychology: is it useful to think of knowledge and processas separate or must we move towards a view in whichknowledge is understood in conjunction with, and relativeto, the processes that bring it to bear in a moment in a task.Our work is clearly inspired by this second perspectivewhich acknowledges that our only window onto knowl-edge is via the behaviors we study and thus necessarilythrough the pane of the processes that create those behav-iors. This is clearly illustrated in the data from our firstexperiment in which the influence of real-time processon ‘‘knowledge” is seen in the differing generalizations ofchildren equal in age and vocabulary knowledge whendoing different tasks. It is also clearly seen in the modelingwork presented here which demonstrates the dynamicinteraction of represented knowledge and decision pro-cesses in creating the patterns of children’s behavior seenin specific tasks and over development. And because weused an authentic process model that generated individualresponses on individual trials just as children do (ratherthan mapping simulated activation levels onto responseprobabilities) the DF model presented here demonstratesthe critical nature of real-time processes in children’s indi-vidual naming behaviors.

In this respect, this work follows the lead of pioneerssuch as Gibson (1969) and Thelen and Smith (1994) inexamining how far the real-time processes of the systemcan take us in understanding behavior and behavioraldevelopment. Note, however, that this is not to say thatthe underlying knowledge must be as limited as the repre-sentations used in the current work. Rather, the point isthat far less may be required from underlying knowledgethan might have been expected because the dynamic inter-action of that knowledge in a task in real-time is so criticalin shaping behavior. Additionally, the developmental sim-ulations presented here suggest the importance of under-standing these real-time behaviors when considering thenature of developmental change. Thus, the model pointsto important generalizations that can be made about therole of comparison, stimulus similarity, noise, and acquiredknowledge in directing children’s behavior at a given pointin development. However, this work also makes clear thenecessity of future work examining individual differencesfor a full understanding of knowledge, behavior, and pro-cess in word learning and cognitive development moregenerally.

Future expansion of the model within the more generalDF framework offers the additional possibility of bridgingthe gap between the real-time performance seen in ourexperiment, and captured in our task simulations, and



the long-term changes captured in our developmental sim-ulations. In particular, because this model is inspired by aline of theoretical, computational, and empirical workexamining a range of behaviors from spatial memory, tochange detection, habituation, discrimination and spatiallanguage, it ties children’s noun generalization behaviorsto this larger picture of cognitive process. In this way, thecurrent model provides a means to generalize insightsabout cognition gained in relatively simple sensorimotorexamples (like the A-not-B task) to tasks that tap higher-level cognition, categories, and linguistic systems. Towardsthis end, the current data and model demonstrate theimportance of considering behavior in a task, and supporta view of knowledge as created in the moment from theinteraction of the child’s history and real-time, task-spe-cific dynamics.

Acknowledgements

Preparation of this manuscript was supported byNICHD Grant No. 5 R01 HD045713 to the first author. Por-tions of the data were presented at the 2006 meeting of theCognitive Science Society. The authors wish to thank JohnSpencer, Jodie Plumert, and Linda Smith for thoughtful dis-cussions of this work and helpful comments on earlier ver-sions of the manuscript. We also thank Ryan Brink, BrandiDobbertin, and the members of the Language and CategoryDevelopment Lab for assistance with data collection. Final-ly we thank the parents and children who participated inthe studies, without whom this work would not be possi-ble. Jessica Horst is now at the Department of Psychology,University of Sussex, UK.

Appendix

The Dynamic Field Theory is in a class of bi-stable neu-ral networks where ‘‘on” and ‘‘off” states coexist (Amari &Arbib, 1977; Erlhagen & Schöner, 2002; Thelen et al., 2001).Thus, these networks can capture stable decisions—the‘‘on” state—as well as cases where stable decisions arenot reached—the ‘‘off” state. The continuous evolution ofactivation in the decision fields shown in Fig. 4 is specifiedby a differential equation that determines a rate of change,du(x,t)/dt, for every activation level, u(x,t), at every fieldlocation, x, and any moment in time, t. The basic stabiliza-tion mechanism of the field is modeled by an inverse rela-tionship between the rate of change and the current levelof activation, u(x,t). This means that at high levels of activa-tion, negative rates of change drive activation down, whileat low levels, positive rates of change drive activation up.The activation level that emerges is a function of the bal-ance of different inputs and interactions in the field. Forexample, when a negative resting level, h < 0, coexists witha source of excitatory input, S > 0, then the resulting stablestate of the activation dynamics:

sduðx; tÞ=dt ¼ �uðx; tÞ þ hþ Sðx; tÞ

is u(x,t) = h + S(x,t), the level at which positive and negativerates of change balance so that du/dt = 0. Note that s, a

parameter that fixes the time scale of the activation field,was set to 75.2

When the rate of change of activation at a field site, x,depends not only on the activation level, u(x,t), and currentinputs, S(x,t), but also on the activation levels, u(x0,t), atother field sites, x0, then activation dynamics are interac-tive. Locally excitatory/laterally inhibitory interactionsare described by an interaction function, w(x � x0), suchthat

wðx� x0Þ ¼ weffiffiffiffiffiffiffi2pp exp �ðx� x0Þ2

2r2w

!" #�wi

In the reported simulations, this interaction rw was alwaysset to 12.0. Only sufficiently activated sites, x0, contributeto the interaction. This is expressed by passing activationthrough a sigmoidal function:

f ðuðx0; tÞÞ ¼ 1=ð1þ expð�buðx0; tÞÞÞ

Such threshold functions are necessarily nonlinear and arethe basis for bi-stability. For the simulations reported hereb was set to 5.0. This creates a relatively sharp thresholdfunction and thus allows for the strong nonlinearitiesneeded to create stable activation peaks (i.e., stabledecisions).

Thus, the full model took the form:

sduðx;tÞ=dt¼�uðx;tÞþhþjSðx;tÞþZ

dx0wðx�x0Þf ðuðx0;tÞÞ

where j was a general gain factor that modulated thestrength of the input, S(x,t).

Inputs to the model took the form of Gaussians repre-sented by the following equation:

Sðx; tÞ ¼ A exp �ðx� xCÞ2

2r2

" #

where A is the amplitude or strength of the input, xc is thecentral position of the input along the similarity dimen-sion, and r determines the precision of the input. The spe-cific inputs to the model varied depending on the task andthe stimulus set. For the forced-choice task, the exemplarand both the shape-matching and material-matching testobjects were all presented at once. Thus, the input equa-tion for this task was:

SFCðx; tÞ ¼ SExemplarðx; tÞ þ SShapeðx; tÞ þ SMaterialðx; tÞ

In the yes/no task, each test object was presented individ-ually with the exemplar. Thus, for one trial of this task theequation was:

SYN 1ðx; tÞ ¼ SExemplarðx; tÞ þ SShapeðx; tÞ

2 We assume that one time step is roughly equivalent to 4 ms, thusmaking the time between stimulus onset and response request about 2.5 s,and thus giving the model 2 s to respond (see Section 3.2.2). One advantageof process-based models such as this one is the ability to make predictionsabout reaction time. Unfortunately, however, standard procedures for thesetasks are not controlled enough to obtain reaction time measurements inthe young children studied here. We are currently pursuing the develop-ment of procedures that would overcome this limitation.



and for the other it was:SYN 2ðx; tÞ ¼ SExemplarðx; tÞ þ SMaterialðx; tÞThe stimuli for the deformable and rigid sets varied in thestrength, precision, and location of the test objects (theexemplar was always in the same location). Details ofthese stimulus sets are discussed below.

Noise was added to the model using fluctuating ampli-tudes for all inputs. This introduces a form of spatially cor-related noise that is consistent with neural principles(Dineva, 2005; Schutte, Spencer, & Schöner, 2003). Thus,the generic equation for the inputs including noise was:

Sðx; tÞ ¼ ðAþ qnðtÞÞ exp �ðx� xCÞ2

2r2

" #

The noise strength, q, was set to .05 for all simulations. nwas a normally distributed random number. Different ran-dom numbers were selected at each time step and for eachcomponent of the input (e.g., shape-matching test objectvs. material-matching test object) independently.

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