[Comp-neuro] KCC addendum
Carson Chow
ccchow at pitt.edu
Wed Aug 20 17:22:05 CEST 2008
Hi again,
Actually, I was only half correct in my previous posting that you could
not prove something was Kolmogorov Complexity Complete (KCC). While it
is true that you couldn't prove something is KCC you could prove the
negative (i.e. that something is not KCC) by simply providing a program
that is shorter than the original string. So I think Bard's suggestion
of a Neural Turing test would be a possible way to test this at the
neuron level We could have a challenge where people try to reproduce
Jim's Purkinje cell model with a simpler model. The test would be that
it would have to produce the exact same output to whatever input
conditions are given. My guess is that for a finite set of data, this
can be done but as you provide more input data you'll have to constantly
refine the simple model. It may be hard to prove if this process will
converge to something simpler than the original model. Also, it could
be possible that neurons are KCC but the entire brain is not. A simple
example is a group of correlated elements interacting. The total could
have less complexity (i.e. entropy) than the sum of the parts.
best,
Carson
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