Modeling Neural Representations

As the final part of the semantics of neurons, and as a prelude to the second part, the neurosemantics of language, this chapter seeks mathematical formulations for the mechanisms that enable the construction of representations in the brain. It is not a general review of the rich variety of mathematical solutions proposed so far for simulating neural circuits, currently available on the market. It is the introduction to the mathematical framework adopted in all the neurosemantic models that will be described in the second part. One of the main challenges any endeavor of mathematical formalization of neural activities must face, is their impressive abundance. The number of neurons involved in almost all cognitive functions is so large that it is impossible to give an overall sense of their activity by means of individual descriptions. Mathematics only offers the great advantage of synthesis, the possibility of capturing in a concise formulation the principles ruling the behavior of millions of interacting elements. Mathematical formulations can be implemented in a software, and the simulated results can be analyzed in detail. In the cortex, neurons are characterized not only by their large number, but also by properties such as local cooperative and competitive interactions, which fit well within an established mathematical framework, that of self-organization. The adopted neural architecture derives from this general framework. In the interpretation of the activities of many neurons in the same cortical area, resulting from a simulation, a well established neurocomputational concept will be used, that of population coding, discussed in the last section of this chapter.