Semantics and Communication for Memory Evolutive Systems
Andrée Ehresmann & Jean-Paul Vanbremeersch
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Source: http://cogprints.org/2075/1/Baden-Baden_92.htm
2. The comparison model in a neural system
Before treating the case of an abstract Memory Evolutive System (MES), let us outline our classification model in the MES modeling a neural system (1991), and explain the underlying ideas in biological terms.
The 'modules' are modeled by the internal centers of Regulation, or Coregulators (CR, cf. 3), Let E be a specific CR (say the 'color' module); its units (which are neurons or 'category-neurons', cf. 1991) are called actors. The actual landscape of E at a time t is formed by all the synaptic paths from a unit of the system which activate some actors at t. Let us suppose a stimulus is presented to the animal at t. It activates first a pattern B of linked units Bi of the system (in the receptors, or eventually in the memory). The pattern is transmitted to E by the synaptic paths which link one of the Bi's to the actors Aj's. These paths are interconnected by the distinguished links of the pattern on one hand, and the operating links between the actors on the other hand. So we get a pattern in the actual landscape which is called the E-trace of B. For a color module, the trace will consist of all the paths along which the color characteristics of the stimulus (wave length, illumination,...) are transmitted to the units of the module, forgetting all other information which are treated by other modules.
In the neural system, we know that the activity of a neuron A is computed from the sum of the activities of all the neurons which activate a synaptic path arriving to A, pondered by the weight of the paths. The activity of an actor induced from the pattern B will be computed in this way taking the sole paths constituting the trace, and we so obtain a pattern A of actors in the module, which is called the pattern E-induced by B, and which represents the constraints forced on the actors by the trace of B.
The pattern A records the activities imposed on the actors, not the paths along which they are transmitted. It follows that 2 patterns B and C may induce the same pattern on E, while they induce different patterns on other CRs. In this case, we say that B and C have the same E-shape.
For instance, a red circle and a red square induce the same pattern in the color module but not in the shape module: they have the same color-shape, but different geometric-shapes. Or if we consider the two patterns of retinal cells activated by two vertical bars not in the same position in the visual field, they activate two different simple cells, but if the bars are near enough, they activate the same complex cell, that means they have the same shape for the orientation module.
If we consider a higher level associative CR (such as a 'conscious CR' in the sense of our 1991 Baden-Baden paper), two patterns will have the same shape for this CR if they have the same shape for the lower CRs it controls. If it so controls many attributes, the two patterns might be recognized as representing the 'same' object despite changes in a few other attributes (in fact, as long as the controlled attributes correspond to a sub-pattern having the same cohesive binding as the whole pattern). For instance, an object is identified whatever be its size or location in the visual field.
3. Implementation in a MES
In preceding papers, we have introduced the notion of a MES to model complex natural systems such as bio-sociological systems or neural systems. The architecture of a MES is a compromise between a parallel distributed processing with a modular organization, and a hierarchical associative network, in which the dynamics is shaped by the dialectics between internal regulatory organs (CRs), each with its own complexity level and time-lag, which leads to the characteristic functioning of a complex system. Contrary. to the complete opacity of a computer levels between them, here the CRs have both partial direct connections and indirect interconnections through the 'fractures' they may generate in other levels.
Let us recall the definition of a MES (cf. Ehresmann-Vanbremeersch 1991, 1992).
The state of the system at a given time is modeled by a category K, formed by its components and the interactions between them (the links modeling transfers of information, energy or constraints).
The system has an organizational hierarchy, with its objects separated into various complexity levels: an object of level k+1 is the cohesive binding (or 'colimit', in the category) of a pattern formed by its own components of the lower level k and some specific links between them.
The dynamics of the system is represented by transition functors between successive state-categories, which model the change of state depending on internal modifications, on the flux of information between the levels and on exchanges or constraints originating from the environment. It is regulated by a family of sub-systems (or modules), the internal Centers of Regulation CRn, each with its own complexity level, its time-scale and its period (or time-lag) represented by a real dn. In the lower levels, the CRs represent specialized modules receiving direct information from the environment; in the higher levels more associative CRs with longer time-lags supervise several other CRs. These CRs operate in parallel by a trial-and-error learning process with cooperative, or eventually conflicting, strategies to modulate the general dynamics of the system.
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