The Neural Representation of Sequences: From Transition Probabilities to Algebraic Patterns and Linguistic Trees
Résumé
A sequence of images, sounds, or words can be stored at several levels of detail, from specific items and their timing to abstract structure. We propose a taxonomy of five distinct cerebral mechanisms for sequence coding: transitions and timing knowledge, chunking, ordinal knowledge, algebraic patterns, and nested tree structures. In each case, we review the available experimental paradigms and list the behavioral and neural signatures of the systems involved. Tree structures require a specific recursive neural code, as yet unidentified by electrophysiology, possibly unique to humans, and which may explain the singularity of human language and cognition. As early as the 1950s, the problem of serial order was identified by Karl Lashley as one of the pressing questions that behavioral and neural sciences should address (Lashley, 1951). The problem can be stated succinctly: how does the brain encode temporal sequences of items, such that this knowledge can be used to retrieve a sequence from memory, recognize it, anticipate on forthcoming items, and generalize this knowledge to novel sequences with a similar structure? Lashley noted that language perception and production, but also bird song or rat spatial navigation behavior, presented special problems for the then-dominant view of associative chains. Humans and other animals do not simply associate each successive item with the next one at a particular delay, but they also grasp abstract multi-item sequential structures. This faculty is most evident in human language: even a single word such as ''inexplicably'' may consist in a nested structure of morphemes [[in-[explic-able]]-ly]. Sixty years of linguistic analysis have confirmed that an accurate representation of language requires the postulation of nested tree structures (Chomsky, 1956). In parallel, behavioral and neurophysiological analyses of much simpler paradigms, involving for instance sequences of tones or gestures, have revealed a rich array of responses that go way beyond the simple associative chain (Restle, 1970; Restle and Brown, 1970). The purpose of the present article is to review those behavioral and neural findings and to provide a minimal taxonomy of brain mechanisms that any accurate model of sequence processing should emulate. We argue that there is evidence for a minimum of five distinct systems capable of representing sequence knowledge at increasing degrees of abstraction (Figure 1): d Transition and timing knowledge: knowledge of the transitions from one item to the next (i.e., the identity and approximate timing of the next item relative to the preceding ones). d Chunking: the grouping of several contiguous items into a single unit that can be manipulated as a whole at the next hierarchical level. d Ordinal knowledge: knowledge of which item comes first, which comes second, and so on, independently of their timing. d Algebraic patterns: abstract schemas that capture the sequential regularities underlying a sequence of items; for instance, the word ''cocolith'' comprises twice the same syllable followed by a different one (AAB pattern). d Nested tree structures generated by symbolic rules: at this level, characteristic of human languages, a sequence can be ''parsed'' according to abstract grammatical rules into a set of groupings, possibly embedded within each other, forming a nested structure of arbitrary depth, and possibly involving the recursive use of the same elements at multiple levels; an example is the parsing of the mathematical equation a + b sin ut as a nested set of parentheses (a+(b (sin (ut)))) or, equivalently, a tree structure:. Transition and Timing Knowledge Many animal species are able to represent the time intervals between sensory or motor events and use these temporal representations in simple computations. An excellent example is provided by a temporal choice task that has been used to probe temporal and probabilistic calculations in mice and humans (Balci et al., 2009; Kheifets and Gallistel, 2012). On each trial, 2 Neuron 88, October 7, 2015 ª2015 Elsevier Inc.