A Computational Model of Children's Semantic Memory

delay. We used 7 texts. We tested the ability of the semantic
representations to estimate the amount of knowledge
recalled. This amount is classically estimated by means of a
propositional analysis: first, the text as well as the
participant production are coded as propositions. Then, the
number of text propositions that occur in the production is
calculated. This measure is a good estimate of the
knowledge recalled. Using our semantic memory model,
this is accounted for by the cosine between the vector
representing the text and the vector representing the
participant production.

Table 4 displays all correlations between these two
measures. They range from .45 to .92, which means that the
LSA cosine applied to our children's semantic space is a
good estimate of the knowledge recalled.

Table 4: Correlations between LSA cosines and number
of propositions recalled for different texts.

In an experiment with adults, Foltz et al. (1996) have shown
that LSA measures can be used to predict comprehension.
Besides validating our model of semantic memory, this
experiment shows that an appropriate semantic space can be
used to assess text comprehension in a much faster way than
propositional analysis, which is a very tedious task.

Conclusion

A model of the development of children's semantic
memory

Our model is not only a computational model of children's
semantic memory, but of its development. Other
computational models of human memory have been
developed but some of them are based on inputs that do not
correspond to what humans are exposed to. They are good
models of the memory itself, but not of the way it is
mentally constructed. In order to be cognitively plausible,
models of the construction of semantic memory need to be
approximately based on the kind of input to humans.

LSA is such model. Its performance is similar to those of
human people. It needs an input of a few million words,
which is comparable to what humans are exposed to
(Landauer & Dumais, 1997). On the contrary, PMI-IR
(Turney, 2001) is a good model of semantic similarities,
even better than LSA in modeling human judgement of
synonymy, but it is based on an input of thousands of
millions of words, since it relies on all the texts published
on the web. This is of course cognitively unplausible. HAL
(Burgess, 1998) is another model of human memory. It is
quite similar to LSA except that it does not rely on a
dimension reduction step. It is currently based on a corpus
of 300 million words, which is closer to the human inputs
than PMI-IR, although this could be considered quite
overestimated.

Further investigations

Our semantic space provides a means for researchers
studying children's cognitive processes to design and
simulate computational models on top of these basic
representations. In particular, computational models of text
comprehension could be tested using the basic semantic
similarities that the space provides. It would also be possible
to investigate the development of semantic memory by
looking at the evolution of various semantic similarities
according to the size of the corpus in detail. In particular,
Landauer & Dumais (1997) claim that we learn the meaning
of a word through the exposition to texts that do not contain
it. Our semantic space gives the opportunity to test this
assertion by checking the kind of paragraphs that cause an
increase of similarity through incremental exposure to the
corpus.

Improvements

Our semantic space could be improved in many ways. Its
composition (50% stories, 25% production, 12.5% reading
textbooks, 12.5% encyclopedia) is very rough and work has
to be done to better know the amount and nature of texts
that children are exposed to. Several studies led us to think
that lemmatization could significantly improve the results,
especially for the French language that has so many forms
for some verbs. We did perform the previous experiments
on a lemmatized version of the corpus (using the Brill
tagger on the French files developed by ATILF, and the
Flemm lemmatizer written by Fiametta Namer). Results
were worse than with the non-lemmatized version. In order
to know more about this surprising result, we distinguished
between verbs and nouns. We found that the overall
decrease is mainly due to a decrease for the nouns. One
reason could be that the singular and plural forms of a noun
are not arguments of the same predicates. For instance, the
word vague (wave) is generally used in its plural form in the
context of the sea, but more frequently in the singular form
in its metaphorical meaning (a wave of success). Therefore,
if both forms are grouped into the same one, this affects the
co-occurrence relations and modifies the semantic
representations.

Another way of improvement would have to deal with
syntax. LSA does not take any syntactic information into
account: all paragraphs are just bags of words. A slight
improvement would consist in considering a more precise
unit of context than a whole paragraph. A sliding context
window (like in the HAL model for instance) would take
into account the local context of each word. This might
improve the semantic representations, while being
cognitively more plausible. We are working in that
direction.

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