networks and biology

[Hideyuki Cateau]

Rogene Eichler writes:

>.................
>.................
>You are basing your statement on the ability of a subset of network models
>to explain a very small subset of the behaviors that are observable and
>testable by somewhat similar criteria. Furthermore, it could be argued that
>the criteria you are using for your comparison is qualitative in nature
>because of the testing methods employed to measure human performance in
>some cognitive tasks.
>
>Your work has shown that complex network systems can demonstrate similar
>emergent properties. That statement, supported by the performance measures
>you cited, is very powerful. But you have substituted one black box for
>another- nothing can be said quantitatively about how or where brain function
>occurs.

   I  agree with the first statement of the upper paragraph above. We should 
examine various kinds of neural network model to see the universality of the 
power law, although we have checked it for various parameters of the back 
prop model.  He further says that "...  explain a very small subset of the 
behaviors ...". He is completely correct.  But I am not so serious about the 
point.  At the first sight, the back prop model is too simple a model to be 
regarded as model of the brain.  I never think that the back prop can model 
the whole behavior of our complex brain.  Only one point of similarity 
between the back prop and the brain is surprising to me, and I thought 
it is worth reporting. 

  I know that it is not the first dicovery of the similiarity between neural 
network models and the real brain.   I argued that the novelty of our result 
is that our result is quantitative instead of qualitative.   At this point our
opinions disagree with each other.

He writes:
>...
>the criteria you are using for your comparison is qualitative in nature
>because of the testing methods employed to measure human performance in
>some cognitive tasks.
>...
First of all, I do not think that measuring the human cognitive tasks 
are always qualitative.  I am a physisist. So,  when I was not familiar 
with works of psychologists,  I certainly thought that most psychological 
experiments would be only qualitative.  I believed that they had in general 
low reproducibility, compared with physical experiments.   But I changed my 
idea after I read many psychological papers and I myself performed a psycho-
logical experiment of the power law in question.  The power law was very 
stable.  The value of the exponent varies depending on  persons or other 
factors, but the value always fell within the range between 1 and 2.  
This is a definite quantitative fact.   The exponent for back prop was two 
up to errors, as I wrote in the original mail.  This is nothing but a 
quatitative accordance.  If the exponent for back prop had been observed to 
be 10, for example, we would have concluded that the behaviors of the brain 
and back prop  qualitatively coincided, but the accordance were not 
quantitative.

   I agree that our result have not opened a black box, which he mentioned 
in his last paragraph.   It would be a very long way to the point when we 
open the black box when we finally see the secret of the brain.  What we 
could do now is to hit the black box and carefully hear the sound it emits, 
to tumble it down and observe the reaction etc.
We, in some sense, hit the black box by the psychological experiment and 
got the power law as reaction of it.   On the other hand we verified that 
it was the same reaction when we hit the back prop.  It is encouraging 
to the neural networkers who believe that the study of the neural network 
model is useful for the study of the brain.

H.Cateau