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The information aspects of a neural complex viewed in terms of memory capacity also penetrate the coordinated organization of firing patterns in recurrently connected cellular units. That is, the memory traces refer to systematic sequential firing of articular sets of neurons and the variety in memory space depicts the vagaries in traces pertinent to different sequences of different sets of neurons. In the universe of the neural complex, any cellular unit may, in general, participate in many such traces defined by the temporal relations among the participating neurons (as observed by Little [33]). The traces are embedded in a given cellular set via selective modulations of the synaptic weighting among the participant neurons in accordance with the fashion of arrangement (of the neurons) in sets in the firing patterns. Not only the temporal traces but also the spatial proliferation of state-transitions are the embodiments of memory considerations in the neural system. As observed by MacGregor [109], “from the very onset, anatomical connections and associated temporal firing patterns are two distinct but intrinsically coupled manifestations of a unitary phenomenon.”

Do the memory traces overlap? MacGregor [109] answers this question by considering the cross-talk mediated by inappropriately activated synapsis through synaptic adjustments. That is, two distinct traces may call for the same single synapse between two cells that participate in both traces, but each asks for a distinct value to be assigned to the synapse; or it is likely in multiple embedded nets that a given neural cell may project to some subset of cells because of its position in one trace and to another subset of cells as a result of its position in a second trace. Implicitly, this is the same as Gardner and Derrida's approach [102,103] of learning an explicit target function or extraction of a rule formalized in terms of replica symmetry consideration discussed in Chapter 4.

The multiple traces embedded in a random fashion can be regarded as being completely independent of each other, and the cross-talk can be regarded as a disruptive aspect of memory borne by a recurrently connected network. The stochastical theory of cross-talk has been comprehensively addressed by MacGregor who associates the concepts of beds and realizations in describing the memory traces; that is, the firing of specific sequences of sets of neurons which represent the items of information consists of physiological variations (or realizations) of primarily anatomical sites which are dubbed as beds. Thus, the population of excitatory and inhibitory neurons taken as an ordered sequence of sets constitutes the bed of a trace, and a realization is an observable physiological manifestation of an underlying bed. It consists of an ordered sequence of subsets of active neurons some of which are members of the corresponding sets of the bed and which fire over a given time interval in the temporal correspondence that exists among the cells of the bed.

Using the above notion in describing the neural complex, MacGregor and Gerstein [110] elucidated mathematical expressions to show how the memory capacity of recurrently connected nets depends on their characteristic anatomical and physiological parameters; and considerations of overlaps of traces, disruptive cross-talks, and random background activities were judiciously algorithmized in determining the storage capacities of information (via traces) pertinent to large interconnected networks.

The aforesaid existing body of information-theoretics as applied to the neural complex, however, does not per se determine the pragmatic and semantic utility of neural information with regard to self-organizing (cybernetic) control-goals. This is due to the fact that the techniques pursued by the statistical theory of information do not match the analysis of control problems. Classical statistical theory of information describes only the processes involved in the transmission and storage of information, but it is not comprehensible to treat information vis-a-vis control strategies or the extent of contraction of the parameter subspace as a result of previous training.


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