Provided by Cognitive Sciences ePrint Archive
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iiiiuιeiiieinαuon oɪ
sycnoιogιcaι spaces.
Wlodzislaw Duch
Department of Computer Methods, Nicholas Copernicus University, Grudziadzka 5, 87-100 Toruii,
Poland; Email: duch@phys.uni.torun.pl
Abstract— Psychological spaces give natural framework for con-
struction of mental representations. Neural model of psychological
spaces provides a link between neuroscience and psychology. Cate-
gorization performed in high-dimensional spaces by dynamical asso-
ciative memory models is approximated with low-dimensional feedfor-
ward neural models calculating probability density functions in psy-
chological spaces. Applications to the human categorization experi-
ments are discussed.
I. Introduction.
Although great progress has been made in recent years in
understanding how the brain generates behavior reconcilia-
tion of language used in psychology and language used in
neuroscience still remains one of the most important prob-
lems. Roger Shepard in a paper “Toward a universal law of
generalization for psychological science” [1] wrote: “What
is required is not more data or more refined data but a dif-
ferent conception of the problem”, pointing out that psycho-
logical laws should be formulated in appropriate psycholog-
ical spaces (P-spaces) [2]. Unified theory of mind in cog-
nitive science that Allen Newell hoped for is still missing
[3]. Clearly a set of new concepts, a mapping between neu-
rophysiological and psychological events, is needed. How
should the higher order cognitive processes, such as catego-
rization, be reduced, at least in principle, to neurodynamics?
How are the mental representations in the long-term mem-
ory formed? In this paper a model offering plausible solu-
tions to these questions is described.
Categorization, or creation of concepts, is one of the most
important cognitive processes. Itis also one of the most dif-
ficult processes to understand if one tries to see it from the
point of view of both psychology and neuroscience. Cur-
rent research on category learning and concept formation
frequently ignores constraints coming from neural plausi-
bility of postulated mechanisms. Connectionist models are
at best loosely inspired by the idea that neural processes are
at the basis of cognition. An explanation given by a formal
theory, even if it fits psychological data, may allow for pre-
dictions, but it may not give us more understanding of hu-
man cognition than a few-parameter fits allowing for pre-
diction of sun eclipses gave the ancient astronomers.
Psychologists frequently use a language of psychologi-
cal or feature spaces to describe results of categorization ex-
periments. Shepard showed [1] the existence of universal
scaling laws in psychological spaces. Therefore it should be
very interesting to construct models of mental events taking
place in P-spaces and to show how such models could be re-
alized by neural dynamics. One of the mysteries in brain
research is how are the mental representations acquired?
Learning at the beginning involves many groups of neurons
but after proficiency is gained brain’s activity becomes lo-
calized. One solution to these problems is offered below.
II. Mind and neurodynamics.
There is growing theoretical and experimental evidence
that the original idea of local reverberations in groups of
cortical neurons coding the internal representations of cat-
egories, put forth by the psychologist Donald Hebb already
in 1949, is correct [4]. Local circuits seem to be involved in
perception and in memory processes. Analysis of integra-
tion of information from the visual receptive fields in terms
of modules composed of dense local cortical circuitry [5] al-
lows for explanation of a broad range of experimental data
on orientation, direction selectivity and supersaturation. It
would be most surprising if the brain mechanisms operating
at the perceptual level were not used at higher levels of in-
formation processing. Neocortex has highly modular orga-
nization, with neurons arranged in six layers and grouped in
macrocolumns that in turn contain microcolumns of about
110 neuron each. Successful models of memory, such as the
tracelink model of Murre [6], make good use of this modular
structure, postulating that each episodic memory is coded
in a number of memory traces that are simultaneously ac-
tivated and their activity dominates the global dynamics of
the brain, reinstating similar neural state as was created dur-
ing the actual episode.
How is then mind related to neurodynamics? In physics
macroscopic properties results from microinteractions, in
psychology behavior should also result from neurodynam-
ics. In practice direct attempts at connecting neural dynam-
ics with higher cognition seem to be hopelessly difficult.
Macroscopic physics is possible because space-time, either
Euclidean in classical physics, or described by differential
geometry in relativistic physics, is a good arena for physi-
cal events. It seems fruitful to use P-spaces as an arena for
mental events. A sketch of such theory was given recently
[7].
A reasonable hypothesis relating psychological concepts
to brain activity seems to be the following: the activity
of microcolumns shows quasidiscrete attractor dynamics.
Several stable patterns of excitations may form, each cod-
ing a specific concept. Via axon collaterals of pyramidal
cells, extending at distances of several millimeters, each mi-
crocolumn excites other microcolumns coding related con-
cepts. These excitations should depend on the particular
form of local dynamics. From the mathematical point of
view the structure of local excitations is determined by at-
tractors in the dynamics of neural cell assemblies. A col-
lection of mode-locking spiking neurons provides a good