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
Abstract
The authors progress in the theory of Memory Evolutive Systems (based on Category theory), already presented in former Baden-Baden Conferences (1988, 89, 90, 91). In this model for natural open self-organizing systems, such as biological, sociological or neural systems, the dynamics is modulated by the competitive interactions between the global system and a family of internal more or less specialized Centers of Regulation (CR) with a differential access to a central hierarchical Memory. Each CR operates at its own complexity level and time-scale, but their strategies are competitive, whence a 'dialectics between heterogeneous CRs which is at the root of higher order cognition, up to consciousness (cf. Baden-Baden 1991).
The problem tackled in the present paper is the emergence of Semantics through the detection of specific invariances by the CRs that leads to classify objects according to their main attributes, and form new formal units representing their invariance classes. The idea is that each CR classifies two objects B and B' as having 'the same shape' if they activate the same pattern of its actors though along different paths. This categorization is memorized as concepts in a higher sub-module of the Memory formed by the projective limits of such patterns. The concepts so defined play an essential part in the evaluation, selection and memorization of appropriate strategies, as well as in internal or external communications.
Introduction
The actions of an animal, on which its fitness depends, require that it might form an adequate enough representation of its environment. In preceding papers (1987, 1989, 1991), we have shown how memorization of past experiences develops and leads to the formation of higher order units in the memory (representing Hebb (1949) assemblies of neurons, or Edelman (1989) neural groups). However, storage of items is not sufficient for action. Efficious learning relies on the recognition of constancies through changing circumstances, that is on a kind of classification of the memorized items according to their main attributes, so that the animal may react in a specific manner not only to a particular situation, but also to all similar situations. For instance, a toad will jump after a fly or after any flying object of the approximate size.
lt is necessary to distinguish a hierarchy of categorization problems:
1. Two objects being given at the same time (either external or retrieved from the memory), to compare them with respect to a particular attribute, for instance their color, or their orientation.
2. To recognize an object despite changes in some of its attributes, for instance 'grandmother with her glasses on or off'.
3. At a higher level, to characterize the class of objects having a common attribute by a unique unit, its 'concept', for instance the color 'red'.
4. To be able to communicate concepts, in particular for man thanks to the development of a language.
Remark that the difference between comparing items (1) and characterizing a class of partially similar items (3) is the same as that proposed by Leibniz between 'clear ideas' and 'distinct ideas'.
We are going to study these problems, first giving the ideas in a neural system, then transposing to a general Memory Evolutive System .
1, Perceptual constancies
The first problem to be considered is the comparison of two objects with respect to a specific attribute.
The vision of animals admits a large class of invariances: they can recognize the form of an object despite change in size, orientation, position in the visual field, movement,..., or color despite change in the spectral context of the illumination. Neurophysiological data may explain some of these perceptual constancies. For instance, Hubel and Wiesel have shown that the visual cortex of mammals contains columns of 'simple cells' which detect bars of a given orientation and of a special position in their field, but also 'complex cells' which detect bars of a given orientation whatever be their position in the field (up to some bounds), or their motion. Some mathematical theories have been developed for the generation of scale and rotation invariances in automatic pattern recognition, such as logarithmic scaling, Fourier-Mellin transforms (cf. Reitboeck 1984); but they depend on vision characteristics. Here we will propose a more general framework.
The modular theory of brain function (cf. e.g., Fodor 1981) postulates the existence of distinct 'modules' to treat specific features, such as a 'geometric' module for form, a 'color' module... The modules treat objects and discriminate two objects according to a specific attribute, without considering their resemblance or differences for other attributes.
For instance a square will be differentiated from a circle by the shape module, while if they have both the same color, the color module will not distinguish between them. But this process does not imply the module operates a real categorization of the perceptual world: the module may compare two objects and recognize if they are similar for its attribute, but this comparison does not entail a characterization of the classes of similar objects. The color module recognizes that this square and this circle have the same color, but it does not give a characterization of a 'red object'.
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