Thursday, 11 February 2010

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.

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