Hi,
Yes, copycat simulated a metric in an ad hoc way, because it lacked a
robust way of measuring and utilizing uncertainty...
I am unsure (heh heh) what uncertainty has to do with it. CC got a fixed,
completely known problem. It could only construct valid interpretations, so
there was no doubt that any given one was correct. It had no memory for
previous problems, so it had no principled way of deriving a prior for any
given interpretation or technique (nor did it even have a separate concept of
technique, except as a set of weights on its higher-level concepts such as
"opposite").
Can you describe how you'd (in theory) enhance CC by incorporating measures of
uncertainty?
Without taking a lot of time (maybe I'll elaborate more later), the
point is that humans solve
analogy problems not (usually) by finding specific strong analogies, but
by finding a huge number
of weak analogies and statistically polling the ensemble.... Even when
there is a strong analogy,
it is usually bolstered by a whole lot of weak analogies surrounding it
in "possible analogy space"...
To be at all intelligence, CC needs a memory of MANY previous problems,
so that it can make
many weak probabilistic matches to prior problems, which can guide it
through the large space
of possible transformations of the current problem toward a small set of
potentially appropriate ones
I.e., CC does not use long-term memory to probabilistically guide the
"inference tree pruning"
process, ergo it gets lost in combinatorial explosions and can't find
the right matches or recognize
(via statistical comparison to rightness in prior situations) their
rightness...
The sense in which the "right" analogies are Occam programs is only
statistical: they are "right"
because the patterns they embody simplify a LOT of different
problems.... Their rightness cannot
be identified effectively by a system without long-term memory, and an
effective LTM requires
effective probabilistic inference.
Anyway, the interesting thing in Hofstadter-ian analogy problems is the
identification of
WHAT THE SALIENT ATTRIBUTES ARE ... not the choice of representation
itself.
I must respectfully but implacably disagree. In (a hypothetical) Supercat,
which CC dreamt of being when it grew up, the salient attributes are exactly
the representation, which are invented by the system under the pressures of
the particular problem. (CC itself was aimed this way but did perhaps more
choosing than inventing.) DH's entire point (the FARGument, if you will) with
the whole feline series was that you can't represent and then match --
finding the representation is the hard part, and matching is trivial
thereafter.
Sure ... I think we are just using language in different ways, and it
may be my usage that's
nonstandard.
Hofstadter wrote about knob-creaton and knob-twiddling. I guess we both
agree with him that
the hard part is figuring out what knobs need to be twiddled and
creating them.
If you represent concepts as probabilistic-logical combinations of the
salient attributes, you
will get the same advantages as in your numerical representation plus
more ;-)
If I represent concepts as probabilistic-logical combinations of the salient
attributes, that IS my numerical representation.
But, prob-logic combinations are not necessarily LINEAR combinations
So, to represent them using vectors and matrix multiplication, you need
to use exponentially
huge vectors whose components involve arbitrarily large conjunctions of
elementary terms; and then
you need to use matrices that represent tensorial linearizations of
Boolean functions.
Yuck! ;-)
There are two major problems arising in your numeric vector representation:
-- what are the relevant dimensions. For analogical quadrature to
reduce to vector addition,
you need to make sure the relevant dimensions are PROBABILISTICALLY
INDEPENDENT
in the context in question. But obviously, finding independent
dimensions may be very hard.
Well, I pose it in a different way (namely, what is the appropriate transform
to get from space A to space B) but essentially, that's the hard problem. The
only one-word answer is "Search." But note that a transform is itself a
matrix (2 kinds, at the moment, simple matrix mult and the state-transisiton
matrices that can simulate any system of ODEs). In other words, it's a point
in a space itself, and such spaces are subject to the same
observation/learning/adaptive processes as any other concept.
Yes, but if you need exponentially huge vectors whose components
incorporate large conjunctions
of elementary terms, then your matrices are size
2^(2n)
so this is a really massive and nasty search problem!!!!
i.e.
n data points spawn...
2^n dimensional vectors which spawn...
2^(2n) dimensional vectors (the transformation matrices representing
tensorially linearized logic functions)
.. etc.
Similarly, you're a fan of Moravec's grids in robotics, but modern
robotics uses probabilistic occupancy grids that work better ;-) ...
Huh? Moravec's were the original, Bayesian probability grids. There've been
refinements, but the basic idea, including empirically derived sensor models,
has been quite robust and remains in general use.
I refreshed my memory and you are right, of course. I read Moravec's
robotics stuff long ago
and my LTM apparently is highly imperfect ;-p ...
There are decent arguments that interconnections btw cortical columns
are representing conditional
probabilities in many cases ... if so then focusing on the numeric
vectors of multiple neural activations,
rather than the conditional probabilities they represent, may be
misdirected...
Who said a vector of numbers couldn't be conditional probabilities? Once you
get a step or two up from raw sensor data, the numbers in my vectors can
represent virtually anyting. Even symbols.
What I don't see is how the vector representation resolves any of the
hard issues in AI...
Your whole approach seems to bottom out on a search through an
exponentially large space
of matrices.
But, obviously, reducing AI to search has been done in so many different
ways...
I don't buy the idea that brute force search in this matrix space is
gonna be good enough...
To convince me, you need to explain what clever trick is used to do
pruning in the search space,
in a way that is contrived to prune in the right way to make search work
effectively FOR THE
PARTICULAR SORTS OF PROBLEMS THAT WILL HABITUALLY BE CONFRONTED
BY THE SYSTEM.
???
-- Ben
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