Learning the Form of Causal Relationships Using Hierarchical Bayesian Models

The mutual exclusivity bias has been posited as a fundamental learning bias (Markman & Wachtel, 1988; Merriman & Bowman, 1989). However, there is mounting evidence that bilinguals do not exhibit mutual exclusivity (Merriman & Kutlesic, 1993; Byers-Heinlein & Werker, 2009;Healey & Skarabela, 2009; Houston-Price, Caloghiris & Raviglione, 2010). It is hypothesised that the amount of variation in the input of bilinguals either lacks enough evidence for a mutual exclusivity bias to emerge, or renders it ineffective. Previously, I showed that a Bayesian model of cross-situational learning (Frank et al., 2009) could not account for differences found between the mutual exclusivity behaviour of monolingual and bilingual children. A reasonable step towards capturing this behaviour would be to add a higher level of abstraction to the model. This would allow the model to alter the strength of its own mutual exclusivity bias in accordance with the amount of variance it encountered.

The research described here implements a hierarchical Bayesian model of causal structure (Lucas & Griffiths,2010;Lucas, 2010). Although it does not address mutual exclusivity directly, it is very relevant. Adult's and children's inferences about causal relationships were affected by their previous experience. A hierarchical Bayesian model that could adjust its assumptions about causal structure was shown to match the performance of adults.
When we learn about causal relationships, we learn to associate a cause with an effect. When there are multiple possible causes, we also need to consider the functional form of the relationships. For example, imagine that two switches are connected to a light. There are a number of possibilities that could cause the light to turn on. Perhaps only one switch needs to be activated (OR), perhaps both are needed (AND). The switches may always work the same (deterministic) or vary some proportion of the time (stochastic or `noisy').

Lucas & Griffiths (2010) show that a hierarchical Bayesian model can match the behaviour of adults in a learning task where they had to make inferences about causal relationships. Previous models of causal structure learning either assume particular functional forms of causal relationships, making them inflexible, or make no assumptions, rendering them incapable of capturing effects of context (see Griffiths & Tenenbaum, 2005, Lucas & Griffiths, 2010). The hierarchical model infers the functional form of the causal relationship as well as the exact relationship between variables.

Although not couched in terms of cross-situational learning, the task is compatible with one. Participants were shown wooden blocks, identical except for a one-letter label (A, B and C in the figure above). The task was to learn which were `blickets'. To help them, there was a `blicket meter' - a device that activated when in the presence of a blicket. Participants were shown several training rounds where one or two blocks were placed on the blicket meter and observed the meter activating or not. After training, they saw another set of blocks (D, E and F) go through a series of blicket tests. They were asked to indicate how confident they were that each block was a blicket.



The experiments had different training conditions. In one, the training data was consistent with the blicket meter's response having a disjunctive relationship (OR) with its causes. That is, it activated when any of the blocks placed on meter were blickets. In another condition, the blicket meter responded consistently with a conjunctive relationship (AND). That is, two blickets were required to activate the blicket meter. The test block was set up to be consistent with either training condition.

Participants' responses in the test block were affected by their experience during training. They saw block D fail to activate the meter 3 alone 3 times, block E fail once and blocks D and F together activate the meter twice. If you assume a disjunctive relationship, then D failing 3 times should be evidence against D being a blicket, while E failing once is less evidence. Indeed, participants in this condition rated D as being less likely to be a blicket than E. Assuming a conjunctive relationship, however, D failing to activate the meter is not informative, whereas seeing D and F activate the meter together is evidence for D being a blicket. Participants given conjunctive training rated D as being more likley to be a blicket. The model matched the participants responses closely.

Lucas & Griffiths argue that this shows that people can make inferences appropriate to causal relationships with more than one kind of functional form (e.g. conjunctive, disjunctive) and that their inferences can be affected by evidence `transferred' from a previous experience. In other words, participants' assumptions about causal relationships can be modified by experience, and this can lead to qualitatively different behaviour.

Lucas (2010) also shows that the model accounts for children's behaviour, too. However, children's responses were more affected by the likelihood than the adults, while adults tended to assume an OR function. This suggests that children are more flexible learners.

However, I'm unsure whether hierarchical Bayesian modelling can be applied to language. Causal forms and causal relationships have a definite hierarchy. But what about F1 and F0? English uses formants to make distinctions at the lexical level and pitch to make distinctions at the pragmatic or phrasal level. Tonal languages, however, use pitch at the lexical level, and some have morphological markers of phrasal boundaries (see Black, 2000).

I suggest that Bayesian models will always have built-in assumptions about the structure of the phenomenon. In studying language evolution, we should be focussing on how this structure emerges in the first place. I propose a different kind of hierarchical model that does not specify a structure in advance. Rather, the role of each level of the hierarchy should be determined by the data. This should be based on the most salient cues that divide the variance in the data in the most functional way.

One possible solution could be general hierarchical dynamic expectation maximisation models. But more on this in the future.

Lucas, C. G., & Griffiths, T. (2010). Learning the Form of Causal Relationships Using Hierarchical Bayesian Models Cognitive Science, 34 (1) pdf

Lucas, C. G. (2010). Developmental differences in learning the form of causal relationships Proceedings of the Cognitive Science Society pdf

Mutual Exclusivity biases in cross-situational learning: A comparison between monolingual and bilingual corpora

This report focuses on models of cross-situational learning and how current models compare when exposed to real monolingual and bilingual input. Several model types were evaluated against two transcribed videos of parent-child interaction, one being monolingual and the other being bilingual. Children have been shown to demonstrate a Mutual Exclusivity (ME) bias (Markman and Wachtel, 1988) during word learning. Frank et al. (2009) showed that their model also exhibited Mutual Exclusivity (ME) behaviour after learning from a monolingual corpus of contexts. The current study takes the same model but with bilingual input and asks whether the same behaviour is exhibited.

Method

Frank et al. (2009) provide a transcribed video of monolingual parent-child interaction coded for use in cross-situational learning. An equivalent bilingual corpus was looked for. The main criterion was a roughly equal number of utterances in both languages. The CHILDES database has suitable resources. A recording from a study by Yip and Matthews was selected (see CHILDES, 2010). The child in question was a native bilingual from birth. Her mother was a native Hong-Kong Cantonese speaker and her father was a native speaker of British English. She was 2;11 in the chosen recording. There are 967 utterances, 48% of which are Cantonese and 52% are English. The objects visible in the video were added to the transcription, along with the mapping between words and objects and the referential intentions of the speakers. The coding scheme was adopted from Frank et al. (2009). The code for the models was supplied by Frank et al. (from Frank,2010).

Results

The performance of different models were analysed in two ways. Firstly, the best estimated lexicon (word-object mappings) of each lexicon was evaluated against a gold-standard lexicon in terms of precision, recall and the resulting F-score.Secondly, the models were asked to guess the intended referent of each utterance-object context.Tables 1 and 2 show the lexicon results for the monolingual and bilingual corpora respectively. Frank et al.’s model returns the highest F-scores in both cases.This is largely due to an advantage in precision, likely stemming from the modeling of non-referential words. Frank et al.’s model returned a word-object mapping for the bilingual corpus with a precision of 0.31 and a recall of 0.27, giving an F-score of 0.29. This is lower than the score for the same model on the monolingual corpus. This could be due to the referential uncertainty (independent from amount of synonymy) in the bilingual corpus being higher.The results for the referential intentions, shown in Tables 3 and 4, have different trends. For the monolingual case, the precision of Frank et al.’s model allows it to outperform the other models. However, it performs relatively poorly in the bilingual case, with the Conditional Probability model performing best. However,all models perform with little precision and recall, suggesting that the task is harder. With more data, results might be different.




Mutual Exclusivity

After the model had processed the corpus, it was presented with a mutual exclusivity task and the relative likelihood of several interpretations were measured.In the task, the model was presented with a context with a new object (e.g. a dax) and a familiar object (a bird for the monolingual model and an orange for the bilingual model) and a new word (e.g. ”dax”). The probabilities were calculated for the model linking the new word with neither object (i.e. it considers the word non-referential), linking it with the new word, linking it with the old word or linking it with both. Figure 1 shows the results of the task with the results for a ’monolingual’ model for comparison.

The monolingual results are re-calculated for this study, so differ slightly from those reported in Frank et al. (2009).The results for the monolingual and bilingual models have the same trend - both rank the possible situations in the same order of likelihood. The most likely situation is the new word being linked to the new object, honouring mutual exclusivity. The second most likely situation is that the word refers to neither object.Intuitively, one would expect a bilingual to be more likely to consider that the new word was another word for the familiar object. Indeed, the bilingual model does consider this possibility relatively more likely than the monolingual model. However, the model still considers neither mapping to be more likely than an extra synonym. This may mean that, given an additional cue (e.g. pragmatic), the bilingual would be more ready to accept a synonymous interpretation. This is an empirical question.

The Prior Probability

The prior probability is simply the number of mappings in the hypothesised lexicon, modulated by a fixed parameter (alpha). This represents a preference for smaller lexicons. This means that a hypothesis which results in the lexicon with fewest mappings will receive the highest prior probability. With the default parameter (alpha = 7), the Mutually Exclusive preference (for DAX-dax) beats the preferences for the original mapping (map neither word to the unfamiliar object),both mappings and the mapping of the unfamiliar object with the familiar name.However, this ranking depends on the lexicon size bias (alpha) parameter. With a low alpha, the most likely mapping is the ME mapping. With a higher alpha, the most likely mapping is the original mapping (see Figure 2).

The same trend also exists between the preference for the ME mapping and both mappings, although the preference for both mappings does not overtake the preference for the ME mapping (see Figure 3).
The explanation is as follows: The original mapping receives a high prior probability because it doesn’t increase the size of the lexicon. However, the likelihood of experiencing a non-referential word is low, leading to a total probability that favours the ME mapping over the original. Assuming a larger lexicon (decreasing alpha), the relative increase in lexicon size is smaller, tipping the balance between the original and ME mapping preferences.Interestingly, the likelihood of choosing both mappings overtakes the original mapping when alpha is less than 1 (see figure 4).
That is, the likelihood of assuming both mappings increases when the prior is set to less than the number of word-object mappings in the lexicon. Such a setting makes sense for a bilingual (who have up to twice as many mappings as bilinguals) because it represents the number of concepts. Put another way, by compensating for the additional synonymy in bilingual input, the likelihood of assuming both mappings increases.The dependence of the ME experiment results on alpha is acknowledged by Frank et al.:

“Note that there is some parameter dependence in our models fit to the mutual exclusivity situation. Depending on the size of the corpus,it might be the case that the prior disadvantage of adding a word to the lexicon would not be outweighed by the increase in corpus likelihood caused by learning a new word. This fact makes a developmental prediction: in early development, when very few words are known,inferences about mutual exclusivity should be weaker.”
Supporting Information for Frank et al. (2009), p. 13.

This prediction is borne out in some studies (Merriman and Bowman, 1989; Frankand Poulin-Dubois, 2002; Merriman et al., 1993). However, Markman and Wachtel (1988) found that the ME constraint weakens over time, with older children showing less of a bias, while Deak et al. (2001) find no change.The issue here is the size of the lexicon. Bilingual children may know more words than monolinguals, but it may be more accurate to judge the lexicon size by the size of one language’s lexicon.The model does not provide a mechanism for modulating the lexicon size prior parameter during learning. Currently the prior is modulated by the alpha parameter and the number of mappings, meaning that adding new mappings is dis-preferred. Bilinguals will have a higher number of mappings, altering their prior probabilities. However, this does not lead to qualitative differences in the mutual exclusivity experiment.The motivation for modulating the prior by the number of mappings is mainly to simplify the model.

“We chose a prior probability distribution that favored parsimony,making lexicons exponentially less probable as they included more word-object pairings ... The choice of a simple prior puts most of the work of the model in the likelihood term ... hence, the likelihood term captures the learners assumptions about the structure of the learning task.”
Frank et al., 2009, p. 579

That is, the decision is driven by the statistical, computational approach to the formal problem rather than being psychologically motivated. Therefore, the interpretation is that mutual exclusivity behaviour stems from the child’s unwillingness to learn new signal-meaning mappings. This seems a little circular - children prefer not to extend mappings from familiar words to unfamiliar objects because they prefer not to extend mappings. It also seems to go against children’s obvious ability and motivation for learning new words and meanings. Several solutions which would make the prior more sensitive to the input involve incorporating the number of concepts, the number of words or the amount of synonymy (proportional to the number of words in the lexicon divided by the number of concepts). However, the nature of the model now changes - we are using it to test specific hypotheses about mutual exclusivity, judged against empirical data,rather than seeing if mutual exclusivity ’falls out’ of more basic assumptions.

Concept-based Prior

The mapping-based prior was biased towards a monolingual mode. The model was altered so that the prior was negatively related to the number of objects in the lexicon. This represents the number of concepts for which the child knows words. The model was run on the bilingual corpus and returned a lexicon with a precision of 0.05, a recall of 0.41 and a resulting F-score of 0.09. The model was also run on the monolingual corpus again, returning a precision of 0.05, a recall of0.79 and an F-score of 0.09. For both monolingual and bilingual corpora, the recall of this model is better than for a mapping-based prior, but the precision is much worse. That is, the model overestimates the number of word-concept mappings. In fact, the models accumulated many hundreds of word-concept mappings for tens of objects (Monolingual: 551 mappings for 22 objects and 419 words; Bilingual:641 mappings for 55 objects and 598 words). The models have failed to acquire a useful vocabulary.However, running the Mutual Exclusivity experiment again, the relative ranking of the preferences has changed. Although the ME mapping is still favoured, the next preferred interpretation is to make both mappings (rather than neither, see Figure 5). However, this difference is exhibited with both monolingual and bilingual input data. By neutralising the difference in the prior, the corpus likelihood now plays a bigger role, leading to a difference in the preferences.




How ’Monolingual’ is the Monolingual corpus?

Although the monolingual corpus is taken from a carer speaking one language, the lexicon the model learns contains synonymy. In fact, for the 15 objects it learned words for, 8 had more than one associated word. For half of these 8 objects, all synonyms were appropriate (e.g. ’bird’ and ’birdie’ to describe the object ’duck’),but half were not appropriate. In other words, the model accommodates synonymy.The original Mutual Exclusivity experiment in Frank et al. was done with the object ’bird’, which had one associated word. The ME experiment was applied for all words that the model learned from the monolingual corpus. There were no significant differences between the posterior probabilities for any of the situations (DAX-dax, Both etc.) for synonymous mappings versus non-synonymous mappings. This holds for both the original and the concept-based prior.

Conclusion

Frank et al.’s model can be used to model word learning in bilinguals. There are some quantitative differences in the ME behaviour of models run on monolingual and bilingual corpora. However, no qualitative differences were found. Even when the prior bias for minimising the number of mappings was neutralised, both models still preferred to map the new object with the new word.

Next Steps
The results are inconclusive, but may reflect the limited data. I suggest that synthetic corpora would make the dynamics more clear. Very simple cross-situational learning corpora could be created with varying amount of ’bilingualism’.

References

Frank MC, Goodman ND, & Tenenbaum JB (2009). Using speakers' referential intentions to model early cross-situational word learning. Psychological science : a journal of the American Psychological Society / APS, 20 (5), 578-85 PMID: 19389131

Byers-Heinlein K, & Werker JF (2009). Monolingual, bilingual, trilingual: infants' language experience influences the development of a word-learning heuristic. Developmental science, 12 (5), 815-23 PMID: 19702772

Deák GO, Yen L, & Pettit J (2001). By any other name: when will preschoolers produce several labels for a referent? Journal of child language, 28 (3), 787-804 PMID: 11797548

Frank, I., & Poulin-Dubois, D. (2002). Young monolingual and bilingual children's responses to violation of the Mutual Exclusivity Principle International Journal of Bilingualism, 6 (2), 125-146 DOI: 10.1177/13670069020060020201

Markman EM, & Wachtel GF (1988). Children's use of mutual exclusivity to constrain the meanings of words. Cognitive psychology, 20 (2), 121-57 PMID: 3365937

Merriman WE, & Bowman LL (1989). The mutual exclusivity bias in children's word learning. Monographs of the Society for Research in Child Development, 54 (3-4), 1-132 PMID: 2608077

Merriman WE, Marazita J, & Jarvis LH (1993). Four-year-olds' disambiguation of action and object word reference. Journal of experimental child psychology, 56 (3), 412-30 PMID: 8301246

Healey, E. and Scarabela, B. (2009). Are children willing to accept two labels for one object? Proceedings of the Child Language Seminar. University of Reading.

How many words for Red? Part 3

This week I've been writing about a bin-packing approach to the bilingual lexicon (here and here). Here's why:

The mutual exclusivity bias is a default approach infants have to learning words which assumes that every object has a single, unique name. However, some studies show that bilingual infants do not follow this bias. The question I'm researching is why assume different things about the world if you're hearing two languages instead of one? Certainly, bilingual children hear more synonyms, but monolinguals also hear many words for the same objects.

The literature has not produced clear-cut results (see my posts here and here), so I've been using a simple model to try and organise my ideas. The model is based on the Categorisation game, where a population of agents try to agree on words for colours. That is, a speaker is presented with a scene of several colours and refers to one of them. A listener must decide which colour the speaker is talking about. Agents begin with no categories and no words, but then divide the colour spectrum into categories and associate words with them, based on verbal interactions. The algorithm is reproduced here.

The algorithm makes some assumptions about mutual exclusivity. The first (what I call Heuristic A) is that, when you see two objects within the same category (e.g. two shades of red), you should divide that category so that there is only one object in each, then assign to each a new unique name. That is, assume that different objects have different names. The second (Heuristic B) is that, when you communicate successfully, delete all other names associated with the category.

These two heuristics limit bilingualism and introduce a mutual exclusivity bias. I ran the categorisation game model without these heuristics to see what would happen. Below are the results of two runs - one with Heuristic A (Black), and one without (Red) (10 runs each, 25 agents, a maximum of 100 perceptual categories, 20,000 rounds). Measures include the number of perceptual categories (both rise and plateau at the same rate), communicative success rate (both similar), the average number of names an agent has, the bin packing depth (bpDepth), bin packing wastage (bpE) and the amount of lexical overlap (overlap function from Baronchelli, Gong, Puglisi and Loreto, 2010).

Removing this heuristic has some interesting consequences for the model. Firstly, the average communicative success is unaffected by removing heuristic A. The number of perceptual categories also increases to the maximum in the same timescale. However, removing the heuristic leads to agents which are more memory-efficient in terms of the number of labels they know, and the efficiency of those names to describe the meaning space. That is, the bin packing metric suggests fewer synonyms and a more efficient coverage of the meaning space. In fact, agents without heuristic A were near optimal in their bin packing.

I suggest that removing heuristic A (each different object has a different name) changes the demands on memory in such a way to favour agents that have several complete descriptions of the meaning space. Dropping heuristic A also reduces the number of lexical items that are stored.

Children exposed to two languages have extra demands on lexical memory. The above analysis suggests that it's a good idea for these children to drop heuristic A in order to save storage space. That is, if you're bilingual, you shouldn't assume that every object has a different name. Indeed, this predicts some of the findings in the experimental literature (i.e. that bilinguals do not apply mutual exclusivity).

However, part of the problem is that this model is a model of emergent structure in labelling perception, it's not a model of acquisition. The method of splitting a perceptual space into categories is also possibly not realistic.

I've just come back from a talk by Kenny Smith, who's been running experiments into Mutual Exclusivity. He trained participants to associate novel words with novel objects, with some participants getting more synonymy than others (objects may have two associated words). After this, participants did a mutual exclusivity task - they were shown two objects, one from the training set and one new object and were asked which one was associated with a novel word. The degree that the participants adhered to mutual exclusivity was proportional to the amount of synonymy they had experienced.

Therefore, it seems that deciding to drop the mutual exclusivity bias may occur on-line. It remains to be seen whether the same results are obtained for children.

Summary: Grassman and Tomasello (2010)

Grassman and Tomasello recently published a study in reaction to Jaswal & Hansen (2006). Jaswal & Hansen found that children ignore pragmatic cues (pointing and looking at objects) in favour of honouring mutual exclusivity. In the first experiment, 24 children (3-4 y.o) were presented with a novel and a familiar item (see my post on diagrams). They were split into two conditions where the experimenter pointed at the familiar object and either asked 'Can you hand me the X?', where X was a novel noun, or made a neutral request ('Can you give it to me?').

All children in the latter 'pragmatic baseline' condition selected the familiar object the experimenter was pointing or looking at, while almost all children selected the novel object when presented with a novel noun. In a second experiment, a similar setup was used, but where the experimenter shifted their gaze towards one object instead of pointing and used an arbitrary label which could refer to any of the objects (e.g. 'Can you give me the one I got yesterday?') instead of the neutral . Here, children presented with a novel label chose the familiar item significantly less often than those in the pragmatic baseline.

The children were aware of the pragmatic cues: Children in both conditions monitored the experimenter's cue equally often. Furthermore, Jaswal & Hansen report that some children, when asked for a novel noun and presented with a pragmatic cue (looking at the familiar object), checked under the table on the side suggested by the pragmatic cue then selected the novel object anyway.

However, Grassman & Tomasello (2010) question Jaswal and Hansen's conclusions, pointing out that gestural cues are ontogenetically and phylogenetically primary to conventional, linguistic cues.

Furthermore, they argue that Jaswal & Hansen's pragmatic cues were non-ostensive. That is, the experimenter's gaze did not follow the pointing or, in the looking condition, there was no gaze alternation. Thus, there was no cue that the pointing/looking was a communicative act intended for the child. Furthermore, they used 'small' pointing, which is associated with redundant information rather than instead of 'big' pointing which is associated with primary information.

Grassmann & Tomasello extend Jaswal & Hansen's experiments with direct linguistic cues ('Give me the X', where X was a novel noun) instead of indirect ('Give it to me'). Two and four year olds showed no preference for linguistic over non-ostensive cues. However, without pragmatic cues, children chose the the novel object, while with ostensive cues (pointing with whole arm, gaze alternation) children chose the familiar object (see my post on diagrams). These directly oppose Jaswal and Hansen's results.

In a second experiment, children were presented with a familiar and novel object and requested a the familiar object verbally while pragmatically cuing the novel item. Children chose the novel object, following the pragmatic cue.

In a third experiment, the experimenter presented two familiar objects while verbally requesting one and pragmatically cuing another. Here, there were no preferences for following the pragmatic or lexical cue. 2 year olds exhibited mixed responses across trials, while 4 year olds were consistent, but with half following the pragmatic cue and half following the lexical cue.

Grassmann & Tomasello place this data in the context of the child's conflict resolution and lexical entries. Children try to integrate cues from different domains into one coherent communicative intention. It is suggested that it may be harder to modify lexical entries for familiar words without a clear reason than to link novel words to familiar objects.

Jaswal VK, & Hansen MB (2006). Learning words: children disregard some pragmatic information that conflicts with mutual exclusivity. Developmental science, 9 (2), 158-65 PMID: 16472316

Grassmann, S., & Tomasello, M. (2010). Young children follow pointing over words in interpreting acts of reference Developmental Science, 13 (1), 252-263 DOI: 10.1111/j.1467-7687.2009.00871.x

Mutual Exlcusivity Diagrams

Lately, I've been reading about experiments on Mutual Exclusivity. I've found it useful to draw up some diagrams to illustrate each. I've posted some of them below. Each diagram represents entities in the Singal, Concept and Environment domains. Circles represent entities (signals, concepts or actual objects). Lines between circles represent a link between them. For instance the word "Dog" would be linked with a concept "Dog" which could be linked to an actual instantiation of a dog in the environment (as long as the observer had learnt these). Dotted circles indicate a novel entity which the observer has not seen before. Dashed lines indicate links trained by the experimenter.

Au & Glusman (1990):
Byers-Heinlein & Werker (2009):

Jaswal & Hansen (2006):


Grassman & Tomasello (2010) - a reaction to Jaswal & Hansen above:

Healey & Scarabela (2009):


Au TK, & Glusman M (1990). The principle of mutual exclusivity in word learning: to honor or not to honor? Child development, 61 (5), 1474-90 PMID: 2245739

Byers-Heinlein, K., & Werker, J. (2009). Monolingual, bilingual, trilingual: infants' language experience influences the development of a word-learning heuristic Developmental Science, 12 (5), 815-823 DOI: 10.1111/j.1467-7687.2009.00902.x

Jaswal VK, & Hansen MB (2006). Learning words: children disregard some pragmatic information that conflicts with mutual exclusivity. Developmental science, 9 (2), 158-65 PMID: 16472316

Grassmann, S., & Tomasello, M. (2010). Young children follow pointing over words in interpreting acts of reference Developmental Science, 13 (1), 252-263 DOI: 10.1111/j.1467-7687.2009.00871.x

Healey, E. and Scarabela, B. (2009). Are children willing to accept two labels for one object? Proceedings of the Child Language Seminar. University of Reading.

Inferential Models of Bilingualism

de Boer (2000)'s models showed that shared representations in a communicative system could be achieved given certain principles. Steels & Belpaeme (2005) extended this framework to the domain of colour, which is a bit more intuitive to understand: A speaker and a hearer are placed in an environment full of coloured tiles. A speaker chooses a colour and names it (with the name only the speaker knows), e.g. 'blurby'. The hearer hears the colour name, and tries to match it with a colour tile it can see. It then points to the colour tile it thinks the speaker meant, and the speaker points to the colour tile it actually meant. The hearer then adjusts its internal representations to fit what it has learned. This involves creating a new 'node' placed in a colour map at the location of the colour tile, labelled 'blurby'. From now on, the hearer can recognise any colour close to this as a 'blurby' colour. Over many exchanges like this, individuals come to share the same names for the same colour tiles.

However, no studies have looked at the additional problems produced by bilingualism. What happens when there are two languages being used? Not only can there be two labels for each type of colour tile, but the boundaries between lables can be different (for example, Welsh is one of the many languges that only has one word for the range of colours extending from green to blue).

In fact, no models even allow the possibility of having two labels for the same percept (labels are selected by calculating distances of label foci in a perceptual space). Additionally, most models implicitly assume a mutual exclusivity bias - if agents experience a new label, they assume it refers to a division of the perceptual space that they don't posses and adjust their perceptual space accordingly. However, agents could not necessarily assume this if they were learning two languages.

The solution is not as simple as creating two separate colour maps for each language, since all children have the potential to become bilingual there is no clear default. Also, being bilingual may affect the way you decide which object is being referred to. Studies into the Mutual Exclusivity bias have found that bilinguals are more likely to accept two labels for a single object, especially when they can tell the labels come from different languages (Au & Glusman, 1990; Healey & Scarabela, 2009; Byers-Heinlein & Werker, 2009).

Andrew Smith has investigated the problem of indeterminacy with computational models (Smith, 2005,2005b). The model is based on Steels' (1996) model of perceptually grounded meaning creation. Agents learn labels from each other which refer to perceptions of a simulated environment. Because agents do not have access to each other's internal representations, they need some way of overcoming indeterminacy when faced with a label they do not understand. Smith (2005) suggests that this can be achieved by relying on individual-level representation constraints (perceptual biases) or inferential tactics. One of these inferential tactics is Mutual Exclusivity. Smith models mutual exclusivity by having the agents exclude from consideration all objects for which it already understands a word when perceiving a new word.

The challenge, in light of more recent findings concerning bilinguals, is to define a model which favours mutual exclusivity within languages, but violates it between languages. It's not obvious how this could be achieved, nor how to test it. From previous studies, it's clear that stable 'bilingualism' is unlikely to emerge in such models, so perhaps two systems need to be developed in segregation and then integrated at a test stage.

First, however, there is the problem of detecting which language a word belongs to, or realising that more than one language is being spoken at all. Smith's agents perceive the world through a number of perceptual channels. Although some sort of entropy model could distinguish between two sets of words, it's unclear why this would be useful except for deciding which language was being spoken. In other words, it would only aid the fitting of the model without really explaining how it works.

One way of aiding the learning of labels in bilingual contexts would be to increase the number of perceptual channels to encode the communication context. For instance, an analogue perception of the signal to model language membership cues from prosody (although this still has the same problem as the entropy solution above). Alternatively, some channels could encode a perception of the speaker themselves. Each agent would have perceivable features, analogous to facial features perhaps, which could be used to distinguish which agent was speaking.

The channels could also be extended to include the encoding of a pragmatic cue, enabling a modeling of the experiments in Au & Glusman (1990) and Healey & Skarabela (2009).

Perhaps, however, these models already achieve such phenomena. The models begin with an inherently bilingual society - each agent begins with a minimal, random vocabulary and conceptual divisions. One question is what factors lead to a single, shared system. Is it an inevitable outcome in a cultural system with limits on resources and exposure to stimuli? Or does a shared system emerge because of biases implicit in the model which disfavour bilingualism? There appears to be a gap in the literature anyway, possibly even a PhD-shaped one.

Au TK, & Glusman M (1990). The principle of mutual exclusivity in word learning: to honor or not to honor? Child development, 61 (5), 1474-90 PMID: 2245739
Byers-Heinlein K, & Werker JF (2009). Monolingual, bilingual, trilingual: infants' language experience influences the development of a word-learning heuristic. Developmental science, 12 (5), 815-23 PMID: 19702772
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Dubloons, loonies and moonies

Recently, I've been thinking about the Mutual Exclusivity bias - the tendency children and adults have to assume one meaning has only one associated word (in other words, to avoid homonomy). This bias seems to work against bilinguals, who have two words for many things. I'll get round to discussing this at some other point. In the meantime, here's an extract from an interesting article by Neil Wick on the tendency for new words for new meanings to converge on a single, conventional form. Wick charts the course of nicknames for the newly introduced $2 coin in Canada. It's worth noting that money is not a normal object - its meaning remains constant in all contexts. However, it's quite a good story:

"Speculation on a name began as soon as the new Canadian coin was announced in the February, 1995, federal budget. On March 3, The Globe and Mail reported that “the ink was barely dry on Paul Martin’s new budget before lock-up wags were bantering around a new name for the $2 coin” and doubloon was mentioned among other suggestions (“We like Ike” 1995). Both The Globe and The Star printed numerous letters hotly debating myriad possible names. One thing seemed beyond debate—writers felt strongly that a name would emerge. The Toronto Star confidently predicted on October 7, 1995, “It will acquire its own nickname” (Aaron, 1995). The Word Play columnist at The Globe implicitly acknowledged a lexical gap on February 24, 1996: “Writers of letters to The Globe and Mail have been diligent about filling this void” (Clements, 1996). One reporter even suggested that the coin needed a name. On February 16, 1996, a Star business reporter stated “All it needs is a nickname— and there is no shortage of suggestions” (Hemeon, 1996). The Mint would have no part in settling the debate. A Globe story on March 23, quoted a Mint spokesperson: “We’re not in the habit of giving names to any of our coins. For us a 10-cent piece is a 10-cent piece.” Characterizing such coin names as too unprofessional to be used by Mint workers, he declared, “The public will have to sort out [what to call the coin] on its own” (Grange, 1996). In spite of the heated debates which still continued after the coin’s launch, a consensus was already forming a month before the launch, as evidenced by responses to The Star’s request for readers to phone in their name suggestions (Stefaniuk, 1996a). Among 57 names and variations submitted by readers, four stood out. Teddy had 11 votes, Toonie/Twoonie/Twooney had 10, and two variants were tied for third place with 9 votes each: Doubloon/Doubloonie and Moonie (Stefaniuk, 1996b). Aaron (1996b) lamented on March 9, that “the horrible term ‘twoonie’ seems to have an edge in public acceptance.” On February 19, 1996, the official launch date for the new coin, Freeman (1996) wrote in The Globe that the new coin “has already picked up a string of unofficial names such as toonie, doubloon, bearbuck, blooney, Doosie and Loonie II.” Meanwhile, a March 14 Star article about panhandlers’ experiences with the new coin (DeMara, 1996) used the word toonie 10 times without remark, prompting an angry letter accusing The Star of “trying to shove the word ‘toonie’ down our throats” (Moshinsky, 1996). “Over here, it’s poly (polar bear – see?) or polies; always was, always will be, The Star’s decree notwithstanding,” the reader wrote. This reader may have overestimated the influence of the paper on public consensus. In fact, if the name depended on a Star decree, dubloon or dubloonie probably would have won out. This was the name used most by The Star in early stories, it was preferred by the Coins columnist (Aaron, 1995) who found toonie to be a “horrible term” (1996a) as already noted, and it was even the personal choice of the chief lexicographer of the new Gage Canadian dictionary (Grange, 1996). Toronto Star art critic Christopher Hume on March 21, 1996, recognized that the lack of a stable name put the two-dollar coin in a different category than that of the one-dollar coin introduced nine years earlier: “By contrast, the loonie has become part of the culture. The word has entered the vocabulary” (Hume, 1996). He called the two-dollar coin “still, annoyingly, nameless” yet he matter-of-factly called it a toonie twice in that same column. By the end of August, Aaron was describing the coin as “affectionately called the ‘toonie’” (Aaron, 1996a), and by September, The Star acknowledged that “its colloquial name ‘toonie’ is part of the vernacular” (Vincent, 1996). In March of the following year, Kesterton (1997) wrote in The Globe that “Fairly quickly and dismissively, Canadians have come to call the $2 coin the ‘toonie,’ despite the many clever terms that were suggested by word mavens …”. Clearly, cleverness alone was not enough. The winning candidate was efficiently short—less than three syllables as with the other coins’ names, incorporated an allusion to the word two, rhymed with loonie, and recalled the familiar collocation looney tunes. Importantly, it started to build momentum in public acceptance early in the process and once established in a few speakers’ lexicons, there was little chance that those speakers would accept alternatives barring major pressure from another stronger group of speakers."