From Computational Theory to Psychology and Neurophysiology -- a case study from vision

SUMMARY: The CNS needs to be understood at four nearly independent levels of description: (1) that at which the nature of a computation is expressed; (2) that at which the algorithms that implement a computation are characterlsed; (3) that at which an algorithm is committed to particular mechanisms; and (4) that at which the mechanisms are realised in hardware. In general, the nature of a computation is determined by the problem to be solved, the mechanisms that are used depend upon the available hardware, and the particular algorithms chosen depend on the problem and on the available mechanisms. Examples are given of theories at each level from current research in vision, and a brief review of the immediate prospects for the field is given. Working papers are informal papers intended for internal use. Introduction Modern neurophysiology has learned much about the operation of the individual neuron, but deceivingly little about the meaning of the circuits they compose. The reason for this can be attributed, at least in part, to a failure to recognise what it means to understand a complex information-processing system. Complex systems cannot be understood as a simple extrapolation of the properties of their elementary components.. One does not formulate a description of thermodynamic al effects using a large set of wave equations, one for each of the particles involved. One describes such effects at their own level, and tries to show that in principle, the microscopic and. macroscopic descriptions are consistent with one another. The core of the problem is that a system as complex as a nervous system or a developing embryo must be analyzed and understood at several different levels. For a system that solves an information processing problem, we may distinguish four important levels of description. At the lowest, there is basic component and circuit analysis-how do transistors, neurons, diodes and synapses work? The second level is the study of particular mechanisms; adders, multipliers, and memories accessed by address or by content. The third level is that of the algorithm, and the top level contains the theory of the overall. computation. For example, take the case of Fourier analysis. The computational theory of the Fourier transform is well understood, and is expressed independently of the particular way in which it is computed. One level down, there are several algorithms for implementing a Fourier transform-the Fast Fourier transform (Cooley & Tukey 1965) which is a …