park@usceast.UUCP (Kihong Park) (03/15/90)
In article <6925@cps3xx.UUCP> leekin@frith.egr.msu.edu () writes: >How does Chaos related to AI disciplines such as Connectionism? There was some recent discussion concerning this topic on comp.ai.neural-nets. Some notes on this issue: It seems that from a physiological standpoint of view, chaotic neural activity patterns might be of great interest. But, apart from that, there is this more general aspect. If one has a system consisting of simple, homogeneous elements arranged according to some connectivity pattern (possibly local), then the time-evolution of the global configuration of the system might very possibly be chaotic. In fact, the so-called class 3 cellular automata(Wolfram) are often of this kind. In many cases, the evolving pattern is so disorganized as to escape polynomial-time prediction algorithms. This empirical observation prompted Wolfram to suggest that they be used as pseudo-number generators. As to its impact in the design of intelligent systems, if one's system is based upon a parallel, distributed substrate on which computations are carried out, then it is to be expected that chaotic behavior will be encountered. In some cases, this might be a useful feature, but in most cases, it will be an unpleasant hinderence if not controlled well. Look at Hopfield nets for example. Fixed points and limit cycles are the "desired" behavior patterns which can encode memories whereas erratic behavior is not so. One final comment may be due: namely, it has to be remembered that in any discrete, deterministic, finite system, the system's behavior will eventually be periodic. But, before the period is reached, the behavior pattern up to then might very well look chaotic. And in case of neural nets where the effective connectivity is variable, one is even less subject to the periodicity constraint. But, again, I think it is the periodic aspect, and less the chaotic aspect which will be most useful in the design of intelligent systems.
ssingh@watserv1.waterloo.edu ($anjay "lock-on" $ingh - Indy Studies) (03/16/90)
In article <3142@usceast.UUCP> park@usceast.UUCP (Kihong Park) writes: > In some cases, this might be a useful feature, but in most >cases, it will be an unpleasant hinderence if not controlled well. There was an article awhile back in Discover called "The Body Chaotic." It mentioned that the EEGs of epileptics during a seizure become far more periodic and regular as whole groups of neurons begin firing in sync across the brain. A normal person's EEG shows little trace of periodicity. It suggests that a nice chaotic "buzz" is the normal state of affairs. BTW, usually wherever there is chaos, fractals are lurking nearby. In the excitement about chaos, fractals seem to have faded into the woodwork. Has anyone seen or done work which tries to tie fractals, chaos, and NNs together into a biologically plausible model? There was talk last year on the cybernetics mailing list about calculating fractal dimensions of Purkinje cells, but I haven't been able to send mail to those persons. Any pointers would be appreciated. -- "No one had the guts... uunnttiill nnooww..." |-$anjay "lock [+] on" $ingh ssingh@watserv1.waterloo.edu N.A.R.C. ]I[-| "No his mind is not for rent, to any God or government."-Rush, Moving Pictures !being!mind!self!cogsci!AI!think!nerve!parallel!cybernetix!chaos!fractal!info!
park@usceast.UUCP (Kihong Park) (03/16/90)
In article <1480@watserv1.waterloo.edu> ssingh@watserv1.waterloo.edu ($anjay "lock-on" $ingh - Indy Studies) writes: >There was an article awhile back in Discover called "The Body Chaotic." >It mentioned that the EEGs of epileptics during a seizure become far >more periodic and regular as whole groups of neurons begin firing in >sync across the brain. A normal person's EEG shows little trace of >periodicity. It suggests that a nice chaotic "buzz" is the normal >state of affairs. This is an interesting valid point. But, remember when one is talking about the dynamics of the brain itself, "periodicity" has to be interpreted in a slightly different way. The brain is a huge chunk of very many interacting modules rather than a one-module entity. Even from a macroscopic viewpoint, physiologists have known for a long time that different parts of the brain have distinguishable functionalities. It is to be expected that within such discernible macro-modules, many more micro-modules will exist. If we assume, just for the sake of argument, that low-level modular structures consist on the order of thousands of neurons, then these "elementary" cohesive units may function abiding by the "periodicity principle". Of course, the time interval within which this regularity manifests itself may very well be rather short. Such modules will interact in a complex fashion whereby one module's short-time behavior will be a function of its surrounding modules. Hence, viewed from "above", the emerging activity pattern(even subglobally), may be very complex. Indeed, it would be exceptional if the global activity pattern of a system composed of very many modules would show apparent regularity. If the information processing done by the system is of a "simple" kind, then global regularity may be the norm. But for complex automata such as the brain, low-level, local regularity coupled with higher-level "irregularity" is to be expected. We know Class 4 cellular automata(Wolfram) are capable of universal computation. Empirical observation says that the time-evolution of these machines shows "regular" local structures, but globally these local regularities may interact in a complicated way. Last argument: from an information-theoretic point-of-view, a system's global behavior being apparently "patternful", i.e., easy to discern simple organization principles, implies that the entropy of the system on the average is low. Very low entropy systems cannot perform complex information processing tasks. Of course, the other extreme is also detrimental. For example, unimodular Hopfield nets are only good at memorizing things in a context-sensitive fashion. Abstracted as CAs, they converge to fixed points or limit cyles, and hence are low-entropy dynamical systems. >BTW, usually wherever there is chaos, fractals are lurking nearby. In the >excitement about chaos, fractals seem to have faded into the woodwork. Has >anyone seen or done work which tries to tie fractals, chaos, and NNs together >into a biologically plausible model? Indeed, chaos and fractals are close-knit subjects. The dynamics of chaotic systems tend to topologically equal cantor sets, a fractal object. But, this may be beside the point when talking about the relation between chaos and neural nets. I have heard that astronomers have identified fractal distributions in the universe. Are fractal distributions or connectivity patterns observable in the brain?
sandyz@ntpdvp1.UUCP (Sandy Zinn) (03/20/90)
> In article <1480@watserv1.waterloo.edu> ssingh@watserv1.waterloo.edu ($anjay "lock-on" $ingh - Indy Studies) writes: > >There was an article awhile back in Discover called "The Body Chaotic." > >It mentioned that the EEGs of epileptics during a seizure become far > >more periodic and regular as whole groups of neurons begin firing in > >sync across the brain. A normal person's EEG shows little trace of > >periodicity. It suggests that a nice chaotic "buzz" is the normal > >state of affairs. > >BTW, usually wherever there is chaos, fractals are lurking nearby. In the > >excitement about chaos, fractals seem to have faded into the woodwork. Has > >anyone seen or done work which tries to tie fractals, chaos, and NNs together > >into a biologically plausible model? > In article <3147@usceast.UUCP>, park@usceast.UUCP (Kihong Park) writes: > Indeed, chaos and fractals are close-knit subjects. > Are fractal distributions or connectivity patterns > observable in the brain? Here's an excerpt from an article written by neurophysiologist Karl Pribram way back in *1959* (!), before fractals were even "invented": The effect of continued intrinsic sector activity will, according to this model, result in a sequence of patterns of information (partitions) of increasing complexity, which in turn allow more and more precise specification of particular elements...more and more information can be conveyed by any given input. As a result, the organism's differentiative behavior remains invariant under a progressively narrower range of systems of *transformations* of the input -- differentiations become more absolute. I'm no mathematician, but this sounds like fractals to me. @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ Sandra Zinn | "The squirming facts (yep these are my ideas | exceed the squamous mind" they only own my kybd) | -- Wallace Stevens
park@usceast.cs.scarolina.edu (Kihong Park) (03/22/90)
In article <350@ntpdvp1.UUCP> sandyz@ntpdvp1.UUCP (Sandy Zinn) writes:
Here's an excerpt from an article written by neurophysiologist Karl Pribram
way back in *1959* (!), before fractals were even "invented":
The effect of continued intrinsic sector activity will, according
to this model, result in a sequence of patterns of information
(partitions) of increasing complexity, which in turn allow more
and more precise specification of particular elements...more and
more information can be conveyed by any given input. As a result,
the organism's differentiative behavior remains invariant under a
progressively narrower range of systems of *transformations* of
the input -- differentiations become more absolute.
I'm no mathematician, but this sounds like fractals to me.
Could you cite the reference where you got the excerpt from, please?
Maybe it's just me, but this single excerpt does not directly indicate to
me a relation to fractals. It would be nice if you could "explain" your
understanding of the paragraph in a few sentences. Thanks.sandyz@ntpdvp1.UUCP (Sandy Zinn) (04/12/90)
(Kihong Park) writes: > Well, my earlier postings indicated the possible relation between chaotic > and regular systems to "complex" information processing systems of which > "intelligent" systems are one genre. Thus, a possible connection of chaos to > "intelligent" systems was suggested at a systems level. Did you post an article with a full explanation of this? I can't quite visualize what you're suggesting, but I'm intrigued. I would appreciate a copy of such an article, or could you take the time to expand this, if you haven't yet? Thanks. @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ Sandra Zinn | "The squirming facts (yep these are my ideas | exceed the squamous mind" they only own my kybd) | -- Wallace Stevens