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Heterarchy of Neural Computing


E.A. Yankovskaya

This article discusses the concept of «Heterarchy» as a conceptual model of a complex system. This model can be used as a general framework for describing the structure and behavior of cognitive systems of different types. The Etymology of the term «heterarchy» refers to the Greek terminology, this term is a compound which consists of two stems: «heteros» («the other, «foreign») and archein («power», «management» and «origin»). The word «heterarchy» literally means "something which is under control of another". According to this meaning the concept «heterarchy» helps to describe the alternative type of organization but not a kind of desorganization. Thus, this concept is contingent and to the concept of «hierarchy». The term «hierarchy» came into scientific discourse from the conception of the neurophysiologist William McCulloch. who was one of the founders of cognitive science and cybernetics. Also McCulloch was one of the founders of connectionism, thus the term «heterarchy» was associated with development of connectionism in the field of cognitive researchers and modeling of intelligence. The heterarchical model describing the structure of nervous system and cognitive processes was suggested as an alternative to hierarchical models. Such models associated with the traditional epistemology and model-symbolic approach. They are used for explaining of sustainable behavior, involuntary and successful actions. There are some basic principles of hierarchical models. The principles of hierarchical models are: duality, linearity, homogeneity and static. Concerning the field of cognitive researches there some implementations of these principals in the models of cognitive systems. Duality is realized as separation of algorithms of cognitive activities and their carrier (separation of «hard» and «soft» according to the computer metaphor of mind). Linearity is realized as the transitivity of these algorithms. Homogeneity is realized as the reducing the cognitive algorithms to the simple rules of one type. And static is realized as a lack of initial review of the rules of system's behavior. Intelligent system based on these principles inevitably faces the frame problem. The core of the frame problem is the question how do we account for our apparent ability to make decisions on the basis only of what is relevant to an ongoing situation without having explicitly to consider all that is not relevant to the current context? Obviously, it is impossible to formalize the action in a particular context because it means that cognitive agent should formalize the whole world. Thus the understanding of intelligent systems and of cognitive behvior requires another approach an other principal of modeling. Connectionism as a partial alternative to the model-symbolic approach tries imitate the real properties of nervous system. Activities of nervous can not be completely formalized with using of hierarchical models. And connectionism offers heterarchical principals of model of cognitive systems. The main principals of heterarchy are non-duality, recursivity, heterogeneity, dynamism. The non-duality means that it's impossible to separate cognitive functions and properties and their carrier. The recursivity is realized as the non-transitive recursive interdependence of various levels of cognitive system. The heterogeneity is realized as interaction of different levels in the one complex system. The dynamism initiates gradual changes some components of the cognitive system and some algorithms ruling system's actions. Despite the opposition of heterarchy and hierarchy they are not absolute alternatives. They are rather contingent or complementary categories. Heterarchy can be defined as «entangled hierarchy». It means that different interacting levels are united in common complex system which is heterarchy. All these levels are necessary for sustainability of whole system although they cannot play equal roles in all situations. From this point of view the classical hierarchy is one type of structure within the complex system. Comparing with hierarchy heterarchy is more redundant. It's difficult to construct and to rule heterarchical system because it doesn't use an unified set of algorithms. Besides some actions of such system are unpredictable. But heterarchical structure of cognitive systems initiates effectiveness of their actions.

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