The Placement of the Head that Minimizes Online Memory

Abstract

It is well known that the length of a syntactic dependency determines its online memory cost. Thus, the problem of the placement of a head and its dependents (complements or modifiers) that minimizes online memory is equivalent to the problem of the minimum linear arrangement of a star tree. However, how that length is translated into cognitive cost is not known. This study shows that the online memory cost is minimized when the head is placed at the center, regardless of the function that transforms length into cost, provided only that this function is strictly monotonically increasing. Online memory defines a quasi-convex adaptive landscape with a single central minimum if the number of elements is odd and two central minima if that number is even. We discuss various aspects of the dynamics of word order of subject (S), verb (V) and object (O) from a complex systems perspective and suggest that word orders tend to evolve by swapping adjacent constituents from an initial or early SOV configuration that is attracted towards a central word order by online memory minimization. We also suggest that the stability of SVO is due to at least two factors, the quasi-convex shape of the adaptive landscape in the online memory dimension and online memory adaptations that avoid regression to SOV. Although OVS is also optimal for placing the verb at the center, its low frequency is explained by its long distance to the seminal SOV in the permutation space.

Noisy-context surprisal as a human sentence processing cost model

“…Under this assumption, for which we provide evidence below, dependency locality effects can be seen as a special case of information locality effects. As a theory of production preferences or typology, processing cost as a monotonically increasing function of dependency length suffices to derive the predictions of dependency length minimization (Ferrer i Cancho, 2015).…”

Towards a theory of word order

“…the real implementation of the principle (at present believed to result from decay and interference as reviewed by Liu et al) or the current view of the architecture of memory [8,9]. Our position is grounded on the high predictive power of that principle per se [5].However, the lower generality of the term "dependency length" can be anEmail address: rferrericancho@cs.upc.edu (R. Ferrer-i-Cancho) 1 These were pieces of our PhD thesis [4] that were submitted for publication before its defense. …”

“…the real implementation of the principle (at present believed to result from decay and interference as reviewed by Liu et al) or the current view of the architecture of memory [8,9]. Our position is grounded on the high predictive power of that principle per se [5].…”

“…predictability maximization, and presented a theoretical framework culminating in a conflict between dependency length minimization and predictability maximization [19]. For sociological reasons, these arguments started appearing in print many years later [20,5,21]. For the case of a single head and its dependents, the minimization of dependency lengths yields that the head should be placed at the center of the sequence whereas the principle of predictability maximization (or uncertainty minimization) yields that the head should be placed at one of the ends of the sequence (last if the head is the target of the prediction; first otherwise) [21,20].…”

“…By the turn of the 20th century, we put forward a "Euclidean distance minimization" hypothesis for the distance between syntactically linked words and various word order phenomena [2,3] 1 . Later on, pressure from language researchers forced us to replace it with terms such as "online memory minimization" [5] because our initial formulation was obscure to them. Recently, researchers from all over the world have been granted to use the term "dependency length minimization" by the popes thanks to whom [6] came into light.…”