Finding Hierarchical Structure in Binary Sequences: Evidence from Lindenmayer Grammar Learning

Abstract

In this article, we explore the extraction of recursive nested structure in the processing of binary sequences. Our aim was to determine whether humans learn the higher‐order regularities of a highly simplified input where only sequential‐order information marks the hierarchical structure. To this end, we implemented a sequence generated by the Fibonacci grammar in a serial reaction time task. This deterministic grammar generates aperiodic but self‐similar sequences. The combination of these two properties allowed us to evaluate hierarchical learning while controlling for the use of low‐level strategies like detecting recurring patterns. The deterministic aspect of the grammar allowed us to predict precisely which points in the sequence should be subject to anticipation. Results showed that participants’ pattern of anticipation could not be accounted for by “flat” statistical learning processes and was consistent with them anticipating upcoming points based on hierarchical assumptions. We also found that participants were sensitive to the structure constituency, suggesting that they organized the signal into embedded constituents. We hypothesized that the participants built this structure by merging recursively deterministic transitions.

Uncovering hierarchical structure through statistical dependency

“…[18] interpreted this result as suggesting that participants were sensitive to the structural status of the Fib k-points. However, [17] pointed out that the surface regularities of Skip differ from Fib as soon as the second order conditional probability is considered. In Skip, k-points have a second order conditional probability of p(1|01) = .36 while in Fib it is equal to p(1|01) = .62.…”

“…The effect can therefore also be explained by 'flat' statistical processing. [17] studied the extraction of hierarchical structure in the Fib grammar using a similar experimental setup as [18,21], except that the stimuli were presented in the center of the screen. In their proposal, k-points are not assigned any particular status, as hierarchical structure extraction is assumed to take place through the recursive merge of deterministic transitions.…”

“…Recent research [17,18] suggests that a parameter independent of complexity to which the cognitive system may also be sensitive to is signal self-similarity. These studies have explored hierarchical structure extraction by presenting to participants aperiodic self-similar sequences that were generated by the Fibonacci grammar.…”

“…So far, only [17,18] reported results that suggest hierarchical structure extraction from the Fib grammar. However, the theoretical viewpoints adopted by each of these studies differ substantially.…”

“…We will refer to this hypothesis as the "k-points hypothesis". [17] adopted a computational approach that attributes less weight to the formal aspects of the Fib grammar. Their idea is that the parser would progressively create a multi-level hierarchical representation by the recursive application of transitional probabilities.…”