[EMAIL PROTECTED] wrote:
Hello
I am writing a literature review on AGI and I am mentioning the
definition of pattern as explained by Ben in his work.
"A pattern is a representation of an object on a simpler scale. For
example, a pattern in a drawing of a mathematical curve could be a
program that can compute the curve from a formula (Looks et al. 2004).
My supervisor told me that "she doesn?t see how this can be simpler than
the actual drawing".
Any other definition I could use in the same context to explain to a
non-technical audience?
thanks
xav
Xav,
[I am copying this to the AGI mailing list because it is more
appropriate there than on Singularity]
A more general definition of pattern would include the idea that there
is a collection of mechanisms that take in a source of information (e.g.
an image consisting of a grid of pixels) and respond in such a way that
each mechanism 'triggers' in some way when a particular arrangement of
signal values appears in the information source.
Note that the triggering of each mechanism is the 'recognition' of a
pattern, and the mechanism in question is a 'recognizer' of a pattern.
(In this way of looking at things, there are many mechanisms, one for
each pattern). The 'particular arrangement of signal values' is the
pattern itself.
Most importantly note that a mechanism does not have to trigger for some
exact, deterministic set of signal values. For example, a mechanism
could respond in a stochastic, noisy way to a whole bunch of different
arrangements of signal values. It is allowed to be slightly
inconsistent, and not always respond in the same way to the same input
(although it would be a particularly bad pattern recognizer if it did
not behave in a reasonably consistent way!). The amount of the
'triggering' reaction does not have to be all-or-nothing, either: the
mechanism can give a graded response.
What the above paragraph means is that the thing that we call a
'pattern' is actually 'whatever makes a mechanism trigger', and we have
to be extremely tolerant of the fact that a wide range of different
signal arrangements will give rise to triggering ... so a pattern is
something much more amorphous and hard to define than simply *one*
arrangement of signals.
Finally, there is one more twist to this definition, which is very
important. Everything said above was about arrangements of signals in
the primary information source ... but we also allow that some
mechanisms are designed to trigger on an arrangement of other
*mechanisms*, not just primary input signals. In other words, this
pattern finding system is hierarchical, and there can be abstract patterns.
This definition of pattern is the most general one that I know of. I
use it in my own work, but I do not know if it has been explicitly
published and named by anyone else.
In this conception, patterns are defined by the mechanisms that trigger,
and further deponent sayeth not what they are, in any more fundamental way.
And one last thing: as far as I can seem this does not easily map onto
the concept of Kolmogorov complexity. At least, the mapping is very
awkward and uninformative, if it exists. If a mechanism triggers on a
possibly stochastic, nondeterminstic set of features, it can hardly be
realised by a feasible algorithm, so talking about a pattern as an
algorithm that can generate the source seems, to me at least, to be
unworkable.
Hope that is useful.
Richard Loosemore
P.S. Nice to see some Welsh in the boilerplate stuff at the bottom of
your message. I used to work at Bangor in the early 90s, so it brought
back fond memories to see "Prifysgol Bangor"! Are you in the Psychology
department?
-------------------------------------------
agi
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