P SY CH OL OG I C AL S CIE N CE

Research Article

Using Speakers’ Referential
Intentions to Model Early
Cross-Situational Word Learning
Michael C. Frank, Noah D. Goodman, and Joshua B. Tenenbaum
Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology

ABSTRACT—Word learning is a ‘‘chicken and egg’’ prob-

lem. If a child could understand speakers’ utterances, itwould be easy to learn the meanings of individual words,
and once a child knows what many words mean, it is easy
to infer speakers’ intended meanings. To the beginninglearner, however, both individual word meanings andspeakers’ intentions are unknown. We describe a computational model of word learning that solves these twoinference problems in parallel, rather than relying exclusively on either the inferred meanings of utterances orcross-situational word-meaning associations. We tested
our model using annotated corpus data and found that it
inferred pairings between words and object concepts withhigher precision than comparison models. Moreover, as
the result of making probabilistic inferences about speakers’ intentions, our model explains a variety of behavioral
phenomena described in the word-learning literature.
These phenomena include mutual exclusivity, one-trial
learning, cross-situational learning, the role of words inobject individuation, and the use of inferred intentions to
disambiguate reference.
When children learn their first words, they face a challenging
joint-inference problem: They are both trying to infer whatmeaning a speaker is attempting to communicate at the moment
a sentence is uttered and trying to learn the more stable mappings between words and referents that constitute the lexicon of
their language. With either of these pieces of information, theirtask becomes considerably easier. Knowing the meanings ofsome words, a child can often figure out what a speaker is talking
Address correspondence to Michael C. Frank, Department of Brain
and Cognitive Sciences, Massachusetts Institute of Technology, 77
Massachusetts Ave., Room 46-3037D, Cambridge, MA 02139, e-mail:mcfrank@mit.edu.

578

about, and inferring the meaning of a speaker’s utterance allows
a child to work backward and learn basic-level object nameswith relative ease. However, for a learner without either of thesepieces of information, word learning is a hard computational
problem. Quine (1960) suggested an apt metaphor: A wordlearner is climbing the inside of a chimney, ‘‘supporting himself
against each side by pressure against the others’’ (p. 93).
Many accounts of word learning focus primarily on one aspectof this problem. Social theories suggest that learners rely on arich understanding of the goals and intentions of speakers andassume that—at least in the case of object nouns—once thechild understands what is being talked about, the mappings
between words and referents are relatively easy to learn (St.
Augustine, 397/1963; Baldwin, 1993; Bloom, 2002; Tomasello,2003). These theories must assume some mechanism for making
mappings, but this mechanism is often taken to be deterministic,
and its details are rarely specified. In contrast, cross-situational
accounts of word learning take advantage of the fact that words
often refer to the immediate environment of the speaker, whichallows learners to build a lexicon based on consistent associations between words and their referents (Locke, 1690/1964;
Siskind, 1996; Smith, 2000; Yu & Smith, 2007).
Computational models of word learning have primarily followed the second, cross-situational strategy. Models using
connectionist (Plunkett, Sinha, Mller, & Strandsby, 1992),
deductive (Siskind, 1996), competition-based (Regier, 2005),
and probabilistic (Yu & Ballard, 2007) methods have had significant success in accounting for many phenomena in wordlearning. However, speakers often talk about objects that are notvisible and about actions that are not in progress at the momentof speech (Gleitman, 1990), adding noise to the correlations
between words and objects. Thus, cross-situational and associative theories often appeal to external social cues, such as eye
gaze (Smith, 2000; Yu & Ballard, 2007), but these are used as
markers of salience (the ‘‘warm glow’’ of attention), rather than

Copyright r 2009 Association for Psychological Science

Volume 20—Number 5Michael C. Frank, Noah D. Goodman, and Joshua B. Tenenbaum

as evidence about internal states of the speaker, as in social
theories.
More generally, cross-situational models address only one
part of the learner’s task. Such models are able to learn words,
but they do not use the words that speakers utter to infer the
speakers’ intended meanings. By focusing only on the long-term
mappings between items in the lexicon and referents in theworld, purely cross-situational models treat the complex andvariable communicative intentions of speakers as noise to beaveraged out via repeated observations or minimized via the useof attentional cues, rather than as an important aspect of communication to be used in the learning task.
In this article, we present a model that captures both aspectsof the word-learning task: It simultaneously infers what speakers
are attempting to communicate and learns a lexicon. We firstpresent the structure of the model and show that it obtains
competitive results in learning from corpus data. We then show
how the probabilistic structure of the model allows it to predictexperimental results such as mutual exclusivity, one-trial wordlearning, and rapid cross-situational learning, as well as how its
explicit representation of intention allows it to predict results on
object individuation and the use of intentional cues.

two assumptions. The first is that what speakers intend to say is afunction of the physical world around them. The second is thatthe words speakers utter are a function of what the speakers
intend to say and how those intentions can be translated into thelanguage they are speaking. With these assumptions and an
observed corpus of situations—utterances and their physicalcontext—our model can work backward using Bayesian inference to find the most likely lexicon.
Though a speaker’s intentions could, in principle, be very
complex, we limit ourselves here to the task of learning names
for objects. Thus, we represent the physical context of an utterance as the set of objects present during the utterance, thespeaker’s referential intention as the object or objects he or she
intends to refer to, and the lexicon as a set of mappings between
words and objects. We also assume that objects are identified as
instances of basic-level object categories, putting aside thechallenge of identifying the particular aspect of an object being
named (Xu & Tenenbaum, 2007).
Formally, our model defines a probability distribution overunobserved lexicons L and the observed corpus C of situations.
Our goal is to infer the lexicon with the highest posterior probability. We find this posterior probability using Bayes’ rule:PðLjCÞ / PðCjLÞPðLÞ:DESIGN OF THE MODEL

Our model (which we refer to as the intentional model) consistsof a set of variables representing the word-learning task and a setof probabilistic dependencies linking these variables in accordance with our assumptions about the task (see Fig. 1). The
variables represent the lexicon of the language being learned,
the referential intentions of the speaker, the words uttered by the
speaker, and the learner’s physical context at the time of theutterance. We define the relationships among these variables via

Objects

LexiconL

Referential
Intention

Words

O

s2C

I

W

Situations

S

Fig. 1. Illustration of the dependence relations in our model. O, I, and W
represent the objects present in the context, the objects that the speakerintends to refer to, and the words that the speaker utters, respectively.
These variables are related within each situation s. The words that the
speaker utters are additionally determined by the lexicon of the speaker’s
language, L, which does not change from situation to situation (and hencelies outside the representation of the set of situations).

Volume 20—Number 5

Bayes’ rule factors the posterior probability of a lexicon given the
corpus into two terms, the likelihood of the corpus given thelexicon and the prior probability distribution over lexicons. We
chose a prior probability distribution that favored parsimony,making lexicons exponentially less probable as they included
more word-object pairings: P(L) / ea|L|. The choice of a simple
prior puts most of the work of the model in the likelihood term,
P(C|L); hence, the likelihood term captures the learner’s assumptions about the structure of the learning task.
The likelihood term can be written as a product over situationsof the probability of the components of the corpus (the words W,
objects O, and speaker’s intentions I for each situation s), given
the lexicon:YPðCjLÞ ¼
PðWs ; Os ; Is jLÞ:ð1ÞWe can now use our assumptions about the structure of thetask to factor Equation 1. First, W and O are conditionally independent given I (as shown in Fig. 1). Thus, we can rewrite theright-hand side as a product of P(Ws|Is,L), the probability of thewords given the speaker’s referential intentions and the lexicon,
and P(Is|Os), the probability of the speaker’s intentions given thephysical context. Second, because we cannot directly observe
the speaker’s referential intention, we sum over all possible
values of Is under the constraint that Is  Os (i.e., that therelevant subset of possible intentions consists of those that referto a subset of the objects in the physical context). Because
speakers often refer to objects outside the physical context, Is

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Probabilistic and Referential Word Learning

can be empty (Gleitman, 1990). We rewrite Equation 1 as
Y XPðWs jIs ; LÞ  PðIs jOs Þ:PðCjLÞ ¼
s2C Is Os

For simplicity (and because we have no information about Is
other than the words that are uttered), we set P(Is|Os) / 1 so thatall possible intentions are equally likely.
To complete our definition of the model, we define the term
P(Ws|Is,L) by assuming that the words fw1 . . . wn g in Ws are
generated independently (ignoring any syntax), and that there are
two possible causes for uttering a word. A word is uttered either
referentially—in order to refer to an object in the speaker’s intention set—or nonreferentially. The probability of a word being
uttered if it is used referentially (PR) is the probability that it will
be chosen from the lexicon to refer to any of the intended referents.
The probability of a word being uttered if it is used nonreferentially(PNR) is the probability that it will be picked from the lexicon at
random, independently of the speaker’s referential intention.
Verbs, adjectives, and function words are generated nonreferentially, as are object nouns for which the relevant object is not
currently present. The parameter g is the probability that a word isused referentially in any given context. Thus, we havePðWs jIs ; LÞ
"
#
X 1
Y
PR ðwjo; LÞ þ ð1  gÞ  PNR ðwjLÞ :
g
¼
jI j
w2Ws
o2Is sThe probability of a word being used referentially for an object, PR(w|o,L), is the probability that the word is chosen uniformly from the set of words linked to that object in the lexicon. If
there are, for example, two words linked to an object in thelexicon, each word has a probability of .5 of being used to refer tothat object; if a word is not linked to an object, its referential
probability for that object is 0. The nonreferential probability ofa word being used is the probability of its being picked from thefull set of words observed in the corpus. This choice is made withprobability proportional to 1 if the word is not in the lexicon andwith probability proportional to k otherwise. Thus, when k is lessthan 1, words that are in the lexicon are less likely to be uttered
nonreferentially than words that are not in the lexicon.
In the simulations reported here, we employed stochastic
search methods using simulated tempering (Marinari & Parisi,
1992) to find the lexicon with the maximum a posteriori probability given an observed corpus. In our on-line supporting information (see p. 585), we provide code for all models discussed
here (Word-Learning Model Code) and implementational details
regarding the search methods and simulations (Technical Appendix).
CORPUS EVALUATION

MethodWe coded two video files (me06 and di03, each approximately 10
min long) from the Rollins section of the Child Language Data

580

Exchange System (CHILDES; MacWhinney, 2000). In thesevideos, two preverbal infants and their mothers played with a setof toys. Each line of the transcripts was annotated with a list of
all midsize objects judged to be visible to the infant.1
For comparison, we implemented several other models ofcross-situational word learning using co-occurrence frequency,
conditional probability, and point-wise mutual information. We
also implemented IBM Machine Translation Model I (Brown,
Pietra, Pietra, & Mercer, 1994), the statistical machine-translation model used by Yu and Ballard (2007). We used thetranslation model to compute association probabilities both for
objects given words (as in Yu & Ballard) and for words given
objects.
We evaluated all models both on the accuracy of the lexicons
they learned and on their inferences regarding the speakers’
intent. Each of the comparison models produced a single summary statistic linking words and objects (e.g., association
probability). We chose the threshold value for this statistic thatmaximized the F score—the harmonic mean of precision (proportion of pairings that were correct) and recall (proportion of
total correct pairings that were found)—of the resulting lexicon.
We then used each model to make guesses about the speaker’s
intended referents for each utterance. For our model, we chosethe intention with the highest posterior probability given
the best lexicon; for the comparison models, we assumed that theintended referents were those objects for which the matchingwords in the best lexicon had been uttered. We computed scores
relative to a gold-standard lexicon and a gold-standard set ofintents, both created by a human coder. The gold-standard
lexicon incorporated all standard word-object pairings (for alamb toy, ‘‘lamb’’), plurals (‘‘lambs’’), and baby talk (‘‘lambie’’);the gold-standard set of intents contained the human coder’sbest judgment of which objects in the visual context were beingreferred to in each utterance.

Results
Our intentional model substantially outperformed the comparison models with respect to the lexicons the model learned(Table 1) and the intentions it inferred (Table 2). This advantage
was robust across systematic variation of the model’s three freeparameters (a, the degree to which the model favors small lexicons; g, the probability of using words referentially; and k, theparameter controlling how likely words in the lexicon were to be
used nonreferentially, compared with words outside the lexicon).
In addition, the advantage remained when k and g were set totheir maximum a posteriori values (the joint empirical Bayes
estimate; see Carlin & Louis, 1996), reducing the number of freeparameters to one—the same number as in the baseline models.
Table 3 shows the best lexicon learned by the intentional model.
1

These videos are the same ones used by Yu and Ballard (2007); the annotations are our own.

Volume 20—Number 5Michael C. Frank, Noah D. Goodman, and Joshua B. Tenenbaum

TABLE 1
Precision, Recall, and F Score of the Best Lexicon Found by Each
Model When Run on the Annotated Data From the Child
Language Data Exchange System
Model
Association frequency
Conditional probability (object|word)
Conditional probability (word|object)
Mutual information
Translation model (object|word)
Translation model (word|object)
Intentional model
Intentional model (one parameter)

Precision

RecallF score

.06
.07
.07
.06
.07
.15
.67
.57

.26
.21
.32
.47
.32
.38
.47
.38

.10
.10
.11
.11
.12
.22
.55
.46

TABLE 2
Precision, Recall, and F Score for the Referential Intentions
Found by Each Model, Using the Lexicons Scored in Table 1
Model
Association frequency
Conditional probability (object|word)
Conditional probability (word|object)
Mutual information
Translation model (object|word)
Translation model (word|object)
Intentional model
Intentional model (one parameter)

Precision

RecallF score

.27
.59
.32
.36
.57
.40
.83
.77

.81
.36
.79
.37
.41
.57
.45
.36

.40
.45
.46
.37
.48
.47
.58
.50

Note. The highest values obtained are highlighted in boldface.
Note. The highest values obtained are highlighted in boldface (differences
between values may not be apparent because of rounding).

Both the simple statistical models and the translation model
found a large number of spurious lexical items; the best lexicons
found by these models were considerably larger than the bestlexicon found by our model.2 The high precision of the lexicon
found by our model was likely due to two factors. First, thedistinction between referential and nonreferential words allowed our model to exclude from the lexicon words that wereused without a consistent referent. Second, the ability of themodel to infer an empty intention allowed it to discount utterances that did not contain references to any object in the immediate context.
PREDICTION OF EXPERIMENTAL RESULTS

As a consequence of its structure, our model exhibits a gradedpreference for certain kinds of lexicons and utterance interpretations. First, the model prefers sparse lexicons because thesimplicity prior biases the model against adding word-object
mappings that do not increase the likelihood of the data. Second,
the model tends to prefer one-to-one lexicons if they are consistent with the observed data, because having multiple words
that can refer to an object reduces the probability of any single
word being used consistently to refer to that object. Finally, themodel prefers that people have intentions to talk about the objects that are present, because words that are generated referentially from an intention to talk about an object have higher
likelihood than words that are generated nonreferentially at
random from the entire vocabulary of the language. These threepreferences allow the model to predict a number of empiricalresults in early word learning.
2
The performance we report for the translation model is considerably lower
than that reported by Yu and Ballard (2007). Several factors may have contributed to this difference. The speech transcripts used in our study were taken
directly from CHILDES, whereas those in Yu and Ballard’s study may havediffered because the utterance boundaries in their transcripts were identified
via the application of speech-recognition software to the original videos (C. Yu,
personal communication, June 25, 2007). Also, our coding of the corpus andtheirs may have included slightly different sets of objects for each situation.
Finally, our gold-standard lexicon likely differed from theirs as well.

Volume 20—Number 5

Cross-Situational Word Learning
Recent work has provided strong evidence that both adults andchildren are able to learn cross-situational associations between
words and objects even in the absence of individually unambiguous trials (Smith & Yu, 2008; Vouloumanos, 2008; Yu &Smith, 2007). Our model and all of the comparison models
successfully found all the correct word-object pairings withperfect precision and recall when presented with the stimulus
TABLE 3
The Best Lexicon Found by the Intentional
Model
Word

Objectbear
bigbirdbird
birdiebookbottlebunniesbunnyrabbit
handhat
hiphopkittycat
lamb
laugh
meow
mhmm
mirrormoocow
oink
on
pig
put
ring
sheep

bear
bird
duck
duck
book
bear
bunny
bunny
hand
hat
mirror
kitty
lamb
cow
baby
hand
mirror
cow
pig
ring
pig
ring
ring
sheep

Note. Entries judged to be correct according to the gold
standard are shown in boldface.

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Probabilistic and Referential Word Learningmaterials used in Yu and Smith’s artificial-language experiments. Given that the statistics in these experiments sharply
favor the correct lexicon, the success of human learners does nothelp to differentiate among the models we compared.

Mutual Exclusivity
In classic demonstrations of mutual exclusivity, a child is presented with two objects, one familiar and one novel. The experimenter asks, ‘‘Can you hand me the [novel name]?’’ and thechild hands over the novel object, indicating that he or she hascorrectly inferred that the novel name refers to it (Golinkoff,
Hirsh-Pasek, Bailey, & Wenger, 1992; Markman & Wachtel,
1988). Markman and her colleagues (Markman, 1989; Markman& Wachtel, 1988; Markman, Wasow, & Hansen, 2003) havesuggested that children possess a principle of mutual exclusivity
that leads them to prefer lexicons with only one label for eachaobject. Other researchers have suggested alternate explanations, including more limited principles that are learned withexperience (Golinkoff, Mervis, & Hirsh-Pasek, 1994; Mervis &Bertrand, 1994) and more general pragmatic principles (Clark,
1988, 2002).
Without building in an explicit assumption of mutual exclusivity, our model shows a soft preference for one-to-one mappings. We tested our model in the classic mutual-exclusivity
paradigm (Markman & Wachtel, 1988) and found that it correctly inferred that the novel word mapped to the novel object.
We scored four possible lexicons on our original CHILDES
corpus extended with a mutual-exclusivity scenario (the word‘‘dax’’ is uttered in the presence of a bird toy and a novel object, adax). Each panel of Figure 2 shows the relative posterior probability of one lexicon under the model along with its relative
prior probability and the relative likelihood it assigns to both theoriginal corpus data and the new mutual-exclusivity situation.

b
bird

"dax"

bird

"dax"

dax

dax
1.00

Relative Probability

Relative Probability

1.00
.75
.50
.25
.00

.75
.50
.25
.00

Prior

CorpusExpt.

Posterior

c

Prior

CorpusExpt.

Posterior

d
bird

"dax"

bird

"dax"

dax

dax
1.00

Relative Probability

Relative Probability

1.00
.75
.50
.25
.00

.75
.50
.25
.00

Prior

CorpusExpt.

Posterior

Prior

CorpusExpt.

PosteriorFig. 2. Our model’s relative probabilities for a learner’s possible lexical hypotheses in a mutual-exclusivity experiment. If theexperimenter utters the novel word ‘‘dax’’ in the presence of a novel object (a dax) and a known object (a bird), the learner can
decide the word refers to (a) neither object, (b) the dax, (c) the bird, or (d) both objects. Each panel shows the prior probability,
the likelihood of the original corpus data, the likelihood of the experimental situation, and the posterior (total) probability for one
hypothesis. A parameter set less extreme than the one in the corpus simulations was used so that absolute rather than log
probabilities could be plotted, but this change did not affect the ordering of hypotheses. All probabilities were normalized acrossthe four possible hypotheses.

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Volume 20—Number 5Michael C. Frank, Noah D. Goodman, and Joshua B. Tenenbaum

Lexicons in which ‘‘dax’’ was mapped to the familiar object, bird
(Figs. 2c and 2d), were unlikely with respect to the original
corpus because each sentence in which ‘‘bird’’ was uttered became less likely as a result of the unrealized possibility ofhearing ‘‘dax.’’ The lexicon in which no new words were learned(Fig. 2a) had a higher prior probability because it involved no
growth in the size of the lexicon, but had a low likelihood in theexperimental context (because under this hypothesis, the word‘‘dax’’ was not in the lexicon and hence must have been uttered
nonreferentially, rather than being uttered because of an intention to refer to the dax). Overall, our model preferred thecorrect lexicon (Fig. 2b).
This result is not unique to our model: The basic finding of
mutual exclusivity is captured by many of the baseline models
we tested. In the example just discussed, the conditional probability of the word ‘‘dax’’ given the presence of the bird is quite
low, whereas the probability of the word ‘‘bird’’ given the presence of the bird is still very high. Combined with the demonstration that adults and infants are able to use some sort ofstatistical information in cross-situational learning tasks (Smith& Yu, 2008; Yu & Smith, 2007), the success of our model andothers suggests that it is not necessary to posit domain-specificprinciples to account for findings of mutual exclusivity.
One-Trial Learning
Another classic result in the literature on word learning is theability of children to learn a new word from only one or a small
number of incidental exposures (Carey, 1978; Markson &Bloom, 1997). Our model and the comparison models predictthat there are some situations that—in conjunction with thelearner’s previous experiences—can provide sufficient evidence for a word’s referent to be inferred after a single exposure;in fact, the mutual-exclusivity experiment just described provides one such situation. We next turn to a set of experimental
results that, to the best of our knowledge, cannot be captured by
the comparison models.
Object Individuation
Even before their first birthday, infants are able to use thepresence of words as an aid in individuating objects (Xu, 2002).
In one experiment by Xu, infants saw first a duck and then aball emerge from and then retreat behind a screen. Infants in the
two-word condition heard, ‘‘look, a duck’’ and then ‘‘look, aball’’; infants in the one-word condition heard, ‘‘look, a toy’’
twice. At test, the screen dropped, revealing either one or two
objects. Infants in the one-word condition looked longer when
two objects were revealed than when one object was revealed(indicating that they expected only one object), whereas infantsin the two-word condition looked slightly longer when one object
was revealed than when two objects were revealed (indicatingthat they expected two objects and were surprised that one had
disappeared).

Volume 20—Number 5

Why would hearing two different labels allow infants to makethe inference that two different objects were behind the screen?
Perhaps the infants’ assumptions about how words are normallyused allowed them to infer what state of the world (one object ortwo) would be most likely to make a speaker utter the labels they
heard. Because our model prefers lexicons with more one-to-one
mappings and lexicons that interpret the corpus as having morereferential words, the best interpretation of Xu’s (2002) twoword condition in our model is that each word refers to a different
object and that both words are being used referentially. Under
this interpretation, there must be two different objects behindthe screen, so that each of the two words can be used referentially to refer to one of the objects. Likewise, in the one-wordcondition, the most likely interpretation is that the one wordrefers to one object and that the word is being used referentiallyfor that object; thus, there is likely only one object behind thescreen.
To simulate Xu’s (2002) paradigm formally in our model, we
created sets of situations corresponding to the two experimental
conditions. For each set, we created two construals: one in which
there were two objects (though they were seen one at a time) and
one in which there was only one object. To simulate the infant’s
uncertainty about the meanings of the word or words in the experiment, we evaluated each construal for all possible lexicons.
In order to link the probability of a particular state of the world
under our model to the looking time of infants in Xu’s study, weused surprisal (negative log probability), a measure that has
previously been used successfully to link model probabilities tohuman reaction time data (Levy, 2007). We compared the surprisal of the model for the two construals of each experimental
condition (e.g., two words, one object vs. two words, two objects).
This comparison can be interpreted as measuring, for a learnerwith no knowledge of what the words mean, how much more orless surprising it would be to find one object as opposed to twobehind the screen. We found a crossover interaction, with surprisal being higher when the number of words did not match thenumber of objects. This result mirrors those Xu (2002) obtained(see Fig. 3). Thus, our model was able to use its assumptions
about how words work to make inferences about the states of theworld that caused a speaker to produce particular utterances.

Intention Reading
Baldwin (1993) conducted an experiment in which 19-monthold toddlers were shown two opaque containers, each containing
a different novel toy. The experimenter opened one container,
named the toy inside without showing the child the contents ofthe container, gave the child the toy from the second container toplay with, and finally gave the child the first (labeled) object.
Despite the greater temporal contiguity between the label andthe second toy, the children showed evidence of learning that thelabel corresponded to the first toy. Baldwin interpreted theseresults as evidence that the children used the experimenter’s583

Probabilistic and Referential Word Learningab8

Surprisal

Looking Time (s)One Object
Two Objects

1.0

10

6
4

0.5

2
0

Two Words

One Word

Xu (2002), Experiment 1

0.0

Two Words

One Word

Intentional-Model Predictions

Fig. 3. Looking-time results reflecting infants’ use of labels to individuate objects and simulation resultsfrom the intentional model proposed here. The graphs present (a) mean looking time in Xu’s (2002)
Experiment 1 as a function of experimental condition and (b) surprisal (negative log probability) calculated from the model in the same four conditions.

referential intention as their preferred guide to the meaning of
the novel label. Our model, built around inferring the speaker’s
intended referents, can capture this interpretation directly. To
illustrate this point, we constructed a situation with two novel
objects and a single novel word. Whereas we previously treatedthe speaker’s intention as a hidden variable, to model Baldwin’stask, we gave the model additional information that the speakerintended to refer to the first novel object. The model then highly
preferred the correct pairing.
This result should not be surprising, as we directly incorporated the referential intention of the speaker into our simulation.
But a model that does not incorporate a representation of referential intent will be unable to predict Baldwin’s (1993) results.
Under a salience view, in order for the correct mapping to occur,
the object that is out of sight would have to be more perceptuallysalient than the unlabeled object. Thus, models that rely directlyon perceptual salience do not capture these results.
GENERAL DISCUSSION

We have presented a model that unifies cross-situational statistical approaches and intentional approaches to word learning.
The model performs well in learning words from a natural corpus
and also predicts a variety of behavioral phenomena reported in
the word-learning literature. Previous evaluations of wordlearning models have focused on either their behavioral coverage (Regier, 2005) or their performance in learning words from
corpus data (Yu & Ballard, 2007), but, to our knowledge, ourstudy is the first systematic attempt to evaluate models on bothcriteria.
Our model operates at the ‘‘computational theory’’ level of
explanation (Marr, 1982). It describes explicitly the structure ofa learner’s assumptions in terms of relationships between observed and unobserved variables. Thus, in defining our model,
we have made no claims about the nature of the mechanisms thatmight instantiate these relationships in the human brain. This584

kind of ideal-observer analysis is only one part of a full accountof early word learning, and many other computational models
can provide insights into different aspects of this process (Colunga & Smith, 2005; Gold & Scassellati, 2007; Li, Zhao, &MacWhinney, 2007; Regier, 2005).
The success of our model supports the hypothesis that specialized principles may not be necessary to explain many of thesmart inferences that young children are able to make inlearning words. Instead, in some cases, a representation of
speakers’ intentions may suffice. Our model is only a first step,
but we hope that this work will inspire future modelers to use
intentional inference to unite the rich variety of information
available to young word learners.
Acknowledgments—The authors gratefully acknowledge Roberta Golinkoff, Kathy Hirsch-Pasek, Fei Xu, and Chen Yu forvaluable discussions. The first author was supported by a Javits
Fellowship. The second and third authors were supported by
grants from the Air Force Office of Scientific Research, theOffice of Naval Research, and the James S. McDonnell Foundation Causal Learning Collaborative Initiative.
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(RECEIVED 12/3/07; REVISION ACCEPTED 9/30/08)

SUPPORTING INFORMATION

Additional Supporting Information may be found in theon-line version of this article:
Technical Appendix
Word-Learning Model Code
Please note: Wiley-Blackwell is not responsible for thecontent or functionality of any supporting materials suppliedby the authors. Any queries (other than missing material)
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