A novel approach to investigate recursion and iteration in visual hierarchical processing

Abstract

We describe a new method to explore recursive cognition in the visual domain. We define recursion as the ability to represent multiple hierarchical levels using the same rule, entailing the ability to generate new levels beyond those previously encountered. With this definition recursion can be distinguished from general hierarchical embedding. To investigate this recursion/hierarchy distinction in the visual domain, we developed two novel methods: The Visual Recursion Task (VRT), in which an inferred rule is used to represent new hierarchical levels, and the Embedded Iteration Task (EIT), in which additional elements are added to an existing hierarchical level. We found that adult humans can represent recursion in the visuo-spatial domain, and that this ability is distinct from both general intelligence and the ability to represent iterative processes embedded within hierarchical structures. Compared with embedded iteration, visual recursion correlated positively with other recursive planning tasks (Tower of Hanoi), but not with specific visuo-spatial resources (spatial short-term memory and working memory). We conclude that humans are able to use recursive representations to process complex visuo-spatial hierarchies and that our visual recursion task taps into specific cognitive resources. This method opens exciting opportunities to explore the relationship between visual recursion and language.Keywords Recursion . Iteration . Cognition . Vision . Fractals . RepresentationThe capacity to understand and generate complex hierarchies is one of the most fascinating features of human cognition. In many domains, including language, music, problem-solving, action-sequencing, and spatial navigation, humans organize basic elements into higher-order groupings and structures (Badre, 2008;Chomsky, 1957;Hauser, Chomsky, & Fitch, 2002; Nardini, Jones, Bedford, & Braddick, 2008;Unterrainer & Owen, 2006;Wohlschlager, Gattis, & Bekkering, 2003). This ability to encode the relationship between basic elements (words, people, etc.) and the broader structures in which these are embedded (sentences, corporations, etc.), affords flexibility to human behavior. For example, in action sequencing, and unlike pure serial associative behavior, hierarchical representations allow the omission or modification of certain steps, without impairing the overall goal.Here, we define hierarchies as non-cyclical tree-like organizations, where higher levels incorporate multiple lower levels in structural representations (Fitch & Martins, 2014), i.e., in which elements are embedded within other elements. This embedding can refer to the grouping of constituents within a higher order set, such as the grouping of individuals within a family (family = {ind1; ind2; ind3}), or it can refer to the establishment of asymmetrical dominance-subordination relationships between constituents, such as in social hierarchies (ind1 dominant over ind2, ind2 dominant over ind3, etc.).Electronic supplementary material The online version of this article

Recursion in action: An fMRI study on the generation of new hierarchical levels in motor sequences

“…Our approach involved the comparison of brain activity during active generation of motor sequences following two different rules – “Recursion” and “Iteration”–which can be used to generate or transform hierarchies (Hulst, ; Martins, ; Martins, Martins, & Fitch, ). A third rule–“Repetition”–controlled for simple action repetition and working memory without any transformation rule.…”

“…and "Iteration"-which can be used to generate or transform hierarchies (Hulst, 2010;Martins, 2012;Martins, Martins, & Fitch, 2015).…”

Shared neural and cognitive mechanisms in action and language: The multiscale information transfer framework

“…Hierarchical structure does not only allow producers to deal with memory and interference constraints, but also to recombine lower‐level items in a flexible manner while maintaining fluency (Christiansen & Chater, ). As a result, individual steps can be modified or omitted, which would not be possible if sequences were driven by purely sequential association links (Diedrichsen & Kornysheva, ; MacDonald, ; Martins et al, ). For example, in getting dressed, clothes may be put on in different (although by no means fully random) orders.…”

How domain-specific is merge?

“…In the Visual Recursion Task (VRT) (Martins, 2015b), participants are shown three successive iterations of a fractal. After the three images appear, two images are shown simultaneously and participants must select the image that best corresponds to the correct continuation of the rule established by the first three images.…”

“…"animals") at the start of a VRT trial and named examples of this category for the duration of the trial; and 2) an Arithmetic Recursion condition ('math') -tapping into recursive concatenationin which participants received a base value (N) at the start of a VRT trial and counted down backwards by three (N i =N i-1 -3) for the duration of the trial. To compare any specific effects of dual-task interference on the VRT performance, in a second experiment, a new group of participants (N=48) completed a control task, he Embedded Iteration Task (EIT), a non-recursive iterative rule-based visual task (Martins, 2015b), with the same procedure and dual-task interference conditions as Experiment 1.…”