[Comp-neuro] KCC addendum

[Carson Chow]

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