Time Scale Hierarchies in the Functional Organization of Complex Behaviors

Traditional approaches to cognitive modelling generally portray cognitive events in terms of ‘discrete’ states (point attractor dynamics) rather than in terms of processes, thereby neglecting the time structure of cognition. In contrast, more recent approaches explicitly address this temporal dimension, but typically provide no entry points into cognitive categorization of events and experiences. With the aim to incorporate both these aspects, we propose a framework for functional architectures. Our approach is grounded in the notion that arbitrary complex (human) behaviour is decomposable into functional modes (elementary units), which we conceptualize as low-dimensional dynamical objects (structured flows on manifolds). The ensemble of modes at an agent’s disposal constitutes his/her functional repertoire. The modes may be subjected to additional dynamics (termed operational signals), in particular, instantaneous inputs, and a mechanism that sequentially selects a mode so that it temporarily dominates the functional dynamics. The inputs and selection mechanisms act on faster and slower time scales then that inherent to the modes, respectively. The dynamics across the three time scales are coupled via feedback, rendering the entire architecture autonomous. We illustrate the functional architecture in the context of serial behaviour, namely cursive handwriting. Subsequently, we investigate the possibility of recovering the contributions of functional modes and operational signals from the output, which appears to be possible only when examining the output phase flow (i.e., not from trajectories in phase space or time). Author Summary: In most established approaches to cognitive modelling, cognitive events are treated as ‘discrete’ states, thus passing by the continuous nature of cognitive processes. In contrast, some novel approaches explicitly acknowledge cognition’s temporal structure but provides no entry points into cognitive categorization of events and experiences. We attempt to incorporate both aspects in a new framework, which departs from the established idea that complex (human) behaviour is made up of elementary functional ‘building blocks’, referred to as modes. We model these as mathematical objects that are inherently dynamic (i.e., account for change over time). A mechanism sequentially selects the modes required and binds them together to compose complex behaviours. These modes may be subjected to brief inputs. The ensemble of these three ingredients, which influence one another and operate on different time scales, constitutes a functional architecture. We illustrate the architecture via cursive handwriting simulations, and investigate the possibility of recovering the contributions of the architecture from the written word. This appears possible only when focussing on the dynamic modes.