Virtually from its origins, with Alan Turing and W.S. McCulloch's formulations, the use of the computational paradigm (CP) as a conceptual and theoretical framework to help to explain Neurophysiology and Cognition has aroused controversy. Some of the objections raised, relating to its constitutive and formal limitations, still prevail. We believe that others stem from the assumption that its objectives are different from those of a methodological approach to the problem of neural modeling.

In this work we start from the hypothesis that it is useful to look at the neuronal circuits assuming that they are the neurophysiological support of a calculus, whose full description requires considering, at least, three levels of organization: circuits and mechanisms, neurophysiological symbols and knowledge and emerging behavior. We also stress the figure of the external observer and the need to distinguish between two description domains in each level: the level's own domain and the domain of the external observer. Finally, we describe a procedure for using the computational paradigm qualitatively in order to try to do "reverse neurophysiology", drawing on two abstraction processes that link the calculus at signal level with cognition. We end by considering the real limitations (constitutive) and apparent (wrong objectives) of the CP and its integrating and non-exclusive nature.

On how the computational paradigm can help us to model and interpret the neural function

First, the meaning of the logical level representations in Cerebral Dynamics and a summary of the formal neural nets Analysis and Synthesis algorithms, are presented. Co-operative concepts are introduced (quantity of function, lesion and residual function) such that function is associated with macroscopic state's dynamics obtained from probabilistic measures on microstates. To gain some insight on how processes are in real neurons a digital simulation of the residual function calculus is included. The lesion's effects strongly depend on the net's structure (local function, connectivity and measure program). So we conclude that a key point in co-operativity is to find the neurophysiological counterpart of global functions that can be segmented. For simple cases (e.g., counters) the rule is immediate. For more complex neural processes, the logical is not enough for significant results, so that a computational paradigm at a semantic level is suggested as a much improved approach.

A logical model of co-operative processes in cerebral dynamics

It is our personal belief that we need a more reflexive attitude reconsidering where the problems are, what are the proper questions, what formal tools we need and how to use these tools to solve the questions in the way to attain a more thorough understanding of neural computation in the brain. In this paper we comment on some points that could be of interest in the biological perspective of neural computation. First some methodological remarks as well a theoretical frame of reference is metioned. Then, some of the anatomical and physiological basis are reported and finally, a frame for cooperative computation is introduced. Here neural nets are considered as "source of inspiration" to formulate inference networks, where in addition to analogical and logical calculus, a more general concurrent computation is permited. In this way, classical connectionisme (with the pass of numerical values) and symbolic computation (with the pass of messages and instructions) are integrated, and we can focus on the study of organizational principles more genuine of the neural tissue.

Always Trying to Write an Equation for the Brain

The significance of the McCulloch‐Pitts formal neural net theory is still nowadays frequently misunderstood at present, and their basic units are wrongly considered as factual models for neurons. As a consequence, the whole original theory and its later addenda are unreasonably criticized for their simplicity. But, as it was proved then and since, the theory is after the modular neurophysiological counterpart of logical machines, so that it actually provides biologically plausible models for automata, Turing Machines etc and not viceversa. In its true context, no theory has surpassed its proposals. In McCulloch and Pitts Memoriam and for the sake of future theoretical research, we stress this important historical point, including also some recent results on the neurophysiological counterparts of modular arbitrary probabilistic automata.

On the biological formal counterparts of logical machines

Virtually from its origins, with Turing and McCulloch's formulations, the use of the computational paradigm as a conceptual and theoretical framework to explain neurophysiology and cognition has aroused controversy. Some of the objections raised, relating to its constitutive and formal limitations, still prevail. We believe that others stem from the assumption that its objectives are different from those of a methodological approximation to the problem of knowing.

In this work we start from the hypothesis that it is useful to look at the neuronal circuits assuming that they are the neurophysiological support of a calculus, whose full description requires considering three nested levels of organization, one of circuits, other of neurophysiological symbols and another of knowledge, and two description domains, the intrinsic to each level and that of the external observer.

On the use of the computational paradigm in neurophysiology and cognitive science

The paper presents the fundamentals of the theory of neural nets with loops based on functional matrices, which are a generalization of the state transition matrices for a net. Problems of analysis and synthesis; given a net, find its functional matrix and vice versa, are treated for probabilistic and deterministic nets. Questions about universal nets, oscillations, and stability are studied for deterministic nets. Reduction of probabilistic nets with loops is considered. It is shown that any probabilistic net with loops can be duplicated by a deterministic net with loops plus a probabilistic loop-free encoder. The motivation for the work is a search for formulation of the general theory of neural nets that could be tied to the theory of triadic intensional relations, as suggested by Warren S. McCulloch.

R. Moreno-Díaz

Papers

Deterministic and probabilistic neural nets with loops