Learning linguistic rules

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As Noam Chomsky has explained, knowledge of language is clearly more than simply assessing the probabilities of transitions between words. At the very least, we need to consider abstract rules involving categories of words (nouns, adjectives, verbs). Even transition probabilities between these categories are not enough: all languages have a tree-like structure of embedded constituents, and are governed by recursive syntactic rules that result in dependencies of variable and arbitrary distance.

According to Chomsky, the complexity of these rules and the "poverty" of the stimuli a child hears require us to postulate the existence of a universal grammar, a set of linguistic principles prior to all learning. However, a recent article attacks this point of view by showing that, on the basis of listening to a few dozen sentences, a hierarchical Bayesian learning algorithm manages to select, from among millions of rules, those of the universal grammar (Perfors, Tenenbaum & Regier, 2011). It would therefore not be necessary to assume that these rules are innate.

Empirical testing of this idea remains almost entirely unexplored, as only a handful of empirical studies have investigated the ability of very young children to learn grammar. At seventeen months, children can spot the alternation of function words (such as the article " le ") and common nouns (such as " chien "). By the age of one, they can extract the grammatical structure of a syllable sequence, and generalize it to new sequences. Above all, the seminal experiment by Marcus and colleagues shows that, as early as seven months, babies are sensitive to abstract structures or " algebraic " in the repetition of a series of syllables (Marcus, Vijayan, Bandi Rao & Vishton, 1999). Extended to adults (Pena, Bonatti, Nespor & Mehler, 2002), this research suggests that, in the human brain, two very different mechanisms are at work during sequence learning: (1) a statistical learning mechanism, sensitive to transition probabilities, and (2) an abstract, all-or-nothing rule learning mechanism, which extracts algebraic rules (ABB, AxC, etc.). From the second year of life, the second mechanism would enable the child to discover abstract rules on non-adjacent items (Gomez & Maye, 2005).

A recent article tackles the particular challenge of learning numbers and counting (Piantadosi, Tenenbaum & Goodman, 2012). Indeed, while very young children easily learn to recite the numbers " one two three four... ", they don't necessarily know what they mean (Wynn, 1990). For several months, they learn, one by one, the meaning of each of the numbers one, two, three and so on. It's not until they're around three and a half years old that they suddenly make a remarkable conceptual leap: they understand that each number name corresponds to a specific quantity. Piantadosi and colleagues managed to account for these observations by Bayesian learning within a space of lambda-calculus formulas, a " language of thought " endowed with primitives and composition laws. The proposed algorithm succeeds in discovering the recursive rules governing a domain such as numbers.

Conclusion

Although the baby statistician hypothesis remains speculative, it is proving extremely productive, both empirically and theoretically. A series of recent experiments has turned our knowledge on its head, demonstrating the extent and subtlety of the inferences that a child under a year old is capable of making. It cannot be ruled out that a child's brain harbors a rapid inference mechanism right from the start. Bayesian models of learning are only partly innate. Admittedly, they presuppose the existence of a complex machinery of probabilistic inference and a very vast space of hypotheses (which, in the human species, unlike perhaps all other animal species, includes recursive functions). But they also rely on hierarchical selection, which massively eliminates inappropriate hypotheses and rapidly converges towards abstract categories or rules. In this sense, these models simply clarify the maxim put forward by Jean-Pierre Changeux in L'homme neuronal (1983) : to learn is to eliminate .