Eugene Leitl (
Sat, 25 Jan 1997 12:00:56 +0100 (MET)

"Representation and high-speed computation in neural networks", Paul M.
Churchland, in "The foundations of artificial intelligence -- A
sourcebook", Derek Partridge and Yorick Wilks (ed.), Cambridge University
Press (1990), pp. 337-359.

1. Introduction

What I want to sell you is some neuroscience. I want to sell you the idea
that current neuroscience has become directly relevant to the
cognititive/computational issues that have always concerned AI. In what
follows I will outline a highly general scheme for representation and
computation, a scheme inspired in part by the microarchitecture of both
the cerebral and the cerebellar cortex. We shall also explore some of the
interesting properties displayed by computing systems of this general kind.

The basic claim, to be explained as we proceed, is that the brain
represents specific states of affairs by implementing specific positions
in an appropriate state space, and it performs computations on such
representations by means of general coordinate transformations from one
state space to another. (There is no suggestion that this is the only
mode of information-processing in the brain. But its role does seem to be

That one can perform computations by this abstract means will be old news
to some reasons. For them, I hope to occasion surprise with evidence
about the implementation of these procedures in the microanatomy of the
empirical brain. Also intriguing is the natural way in which problems of
sensorimotor coordination can be solved by this approach, since from an
evolutionary point of view, sensorimotor coordination is where cognitive
activity had its raw beginnings. Of further interest is the very great
representational power of such systems, and the truly extraordinary speed
with which even biological implementations of such procedures can perform
computations of great complexity.

The emerging relevance of neuroscience coincides with what may of us
think to be a doldrums in the affairs of traditional ('program writing')
AI, and in the affairs of orthodox cognitive psychology, for which
macroscopic behaviour provides the sole significant constraint on theory.
The diagnosis offered here is that traditional AI needs desperately to
explore, not new areas within 'program space,' but new areas within the
space of possible hardwares. The hardware -- or 'wetware' -- of the
empirical brain represents an existance proof of what can be done with
parallel architectures radically different from those found in
general-purpose serial machines. It behoves AI try to learn from that

The diagnosis of orthodox cognitive psychology is much the same. Whatever
computational activities psychology might ascribe to us, those activities
must not only produce the behaviour we display, the must be implemented
in the wetware we possess. To ignore the nature of that wetware, as the
neurosciences are now revealing it, would be to ignore some of the
strongest available constraints on the development of cognitive theory.

The basic point here is as follows. So long as we assume that the brain,
like a standard serial computer, is truly a general-purpose machine, then
of course the nature of the hardware will carry negligeable information
about the algorithms being executed. For the hardware will be a constant
over the infinite range of 'programs' the brain might be running. But if
the brain is not a general-purpose machine in the technical sense at
issue; if the hardware is highly 'devoted' to relatively narrow areas of
the computational space; then the nature of that hardware assumes an
enormous importance.

Accordingly, I propose to enter this discussion from the hardware end of
things. In what follows I shall outline for you some of the well-known
but still deeply puzzling structural features of the brain's neural
architecture. I shall then outline, as a possible account of the
functional signficance of those structures, the scheme of representation
and computation mentioned above. I shall then outline, as a possible
account of the functional significance of those structures, the scheme of
representation and computation mentioned above. Bear with me, therefore,
while we race through a short rehearsal of the relevant brain microstructure.

2. Laminar cortex, vertical connections, and topographic maps

The outer surface of the brain's great cerebral hemispheres consists of a
thin layer, the classical "grey matter," in which most of their neuronal
cell bodies are located [...]. If one examines the internal structure of
this wrinkled layer, one finds that it subdivides into further layers
[...]. Human cortex has six of these layers. Other creatures display a
different number, but the laminar pattern is still standard.

These further layers are distinguished by the type and concentration of
cells within each sublayer. Moreover, these distinct layers are further
distinguished by their proprietary inputs or outputs. The top several
layers tend to have only inputs of one kind of another, from the sensory
periphery, from other part of the cortex, or from other parts of the
brain. And the bottom layer seems invariably to be an output layer.

Finally, these distinct layers are systematically connected, in the
fashion of nails struck though plywood, by large numbers of
vertically-oriented cells that permit communication between the several
layers. These vertical cells conduct neuronal activity "downwards," from
the superficial input layers above to the output layers below.

If we now leave our microscopic edgewise perspective and look down at the
cortical sheet from the outside, we find that the cortical surface
divides into a patchwork of smaller regions [...]. These areas are
distinguished to some degree by differences in their laminar
cytoarchitecture. An initial taxonomy, into what are called Brodmann's
areas after their discoverer, is based on this criterion.

These areas, or subareas of them, are of further interest because several
of them plainly constitute topographic maps of some aspects of the
sensory or motor periphery, or of some other areas of the brain. For
example, the neighbourhood relations holding between the cells in a given
layer of the visual cortex at the rear of the brain correspond to the
neighbourhood relations holding between the cells in the retina from
which they receive inputs. The bundle of axonal projections from the
retinal cells to the cortical cells preserves the topographic
organization of the retinal cells. The surface of the primary visual
cortex thus constitutes a topographic map of the retinal surface.

It is termed a 'topographic map,' rather than simply a 'map,' because the
distance relations among retinal cells are generally not preserved.
Typically, such maps are metrically deformed, as if they were made of
rubber and then stretched in some fashion.

Many such maps have been identified. The so-called "visual cortex" (areas
17, 18) has already been mentioned. The upper layer of the somatosensory
cortex (area 3) is a topographic map of the body's tactile surface. The
lower layer of the motor cortex (area 4) is a topographic map of the
body's muscle system. The auditory cortex (areas 41, 42) contains a
topographic map of frequence space. And there are many other cortical
areas, less well understood as to exactly what they map, but whose
topographical representation of distant structure is plain.

The general pattern of neural organization is not confined to the surface
of the great cerebral hemispheres. As well, various nuclei of "grey
matter" in the more central regions of the brain -- for example the
superior colliculus, the hippocampus, and the lateral geniculate nucleus
-- displays this same multilayered, topographically organized, vertically
connected structure. Noth everything does (the cerebellum, for example,
is rather different, of which more later), but the patterns described is
one of the major organizational patterns to be found in the brain.

Why this pattern? What is its functional or cognitive significance? What
do these structures do, and how do they do it? We can make contanct with
the representational and computational hypothesis suggested in the
introduction if we first address the independently intriguing problem of
sensorimotor coordination.

[ to be continued, ciao, 'gene ]

[ out of curiosity, does anybody read stuff as above, or do you all just
reflectively hit delete? please write, as my only access to the net is
very expensive, and I do not get much mail ]