Chunking dynamics: heteroclinics in mind

Abstract

Recent results of imaging technologies and non-linear dynamics make possible to relate the structure and dynamics of functional brain networks to different mental tasks and to build theoretical models for the description and prediction of cognitive activity. Such models are non-linear dynamical descriptions of the interaction of the core components—brain modes—participating in a specific mental function. The dynamical images of different mental processes depend on their temporal features. The dynamics of many cognitive functions are transient. They are often observed as a chain of sequentially changing metastable states. A stable heteroclinic channel (SHC) consisting of a chain of saddles—metastable states—connected by unstable separatrices is a mathematical image for robust transients. In this paper we focus on hierarchical chunking dynamics that can represent several forms of transient cognitive activity. Chunking is a dynamical phenomenon that nature uses to perform information processing of long sequences by dividing them in shorter information items. Chunking, for example, makes more efficient the use of short-term memory by breaking up long strings of information (like in language where one can see the separation of a novel on chapters, paragraphs, sentences, and finally words). Chunking is important in many processes of perception, learning, and cognition in humans and animals. Based on anatomical information about the hierarchical organization of functional brain networks, we propose a cognitive network architecture that hierarchically chunks and super-chunks switching sequences of metastable states produced by winnerless competitive heteroclinic dynamics.

Dynamical bridge between brain and mind

“…Such a set of equations can also incorporate the evolution of cognitive resources, for example, attention, working memory, language, and their hierarchical organization [58,60,61]. The interaction of different modalities, such as emotion and cognition, which is important for the understanding of normal and pathological mental dynamics, can be described by the same type of equations [62,63].…”

Non-reward neural mechanisms in the orbitofrontal cortex

“…A stable heteroclinic channel is defined by a sequence of successive metastable ('saddle') states. Under the proper conditions, all the tra jectories in the neighborhood of these saddle points remain in the channel, ensuring robustness and reproducibility of the dynamical tra jectory through the state space (Rabinovich et al 2008, Rabinovich et al 2014). This approach might be considered in future as a somewhat different implementation of the system described here.…”

“…Although the system described here was modelled with networks that have realistic dynamics as they move into and out of stable attractor states (Treves 1993, Battaglia and Treves 1998, Panzeri et al 2001, Deco et al 2005, Deco and Rolls 2006, Rolls 2016a another approach to such modelling is a network that when the system does not have sufficient time to fall into a stable attractor state, nevertheless may visit a succession of states in a stable tra jectory (Rabinovich, Huerta andLaurent 2008, Rabinovich, Varona, Tristan andAfraimovich 2014). A possible way to understand the operation of such a system is that of a stable heteroclinic channel.…”

Sensitive Finite-State Computations Using a Distributed Network With a Noisy Network Attractor

“…Connecting heteroclinic orbits are trajectories that are contained in the unstable manifold of one equilibrium and the stable manifold of another. Heteroclinic networks composed of a network of such trajectories have been proposed by a number of authors as a way that neural systems can encode information and perform computations [2], [6], [27], [29], [30], [34].…”

“…Nonetheless there are models of computational systems that are sensitive to arbitrary low-amplitude inputs. These include models with heteroclinic connections between: equilibria [29], [30], periodic orbits [2], [6], [27] or chaotic saddles/Milnor attractors [37]. Our model develops these ideas to construct explicit realizations of Turing Machines (TMs) using a system first described in [4].…”