[Comp-neuro] "realistic models"

james bower bower at uthscsa.edu
Mon Aug 18 19:41:43 CEST 2008

Bard and everyone else:

On Aug 17, 2008, at 8:30 AM, G. Bard Ermentrout wrote:

> Carson Chow, a former colleague,  has an interesting summary of this  
> doscussion on
> sciencehouse.blogspot.com

Yes, a well written summary of several of the points -- and the  
introduction of an idea that, in fact, does lie somewhere near the  
foundation of this debate.   The question as to whether the brain can  
be represented by a structure (whatever it is) less complex than the  
brain itself -- formally, this moves us into complexity theory and a  
Kolmogorovian (sic)  framework for thinking about levels of  
complexity.  I actually like the characterization "Kolmogorov  
Complexity Complete" (KCC).   And yes, I do suspect that the brain is  
KCC - and more formally, that the brain approaches in its complexity  
the complexity of the problem(s) it evolved to solve.

Which brings us to a specific aspect of Kolmogorov complexity which is  
directly relevant to neuroscience, and that is the relationship  
between the complexity of the solution to a problem and the intrinsic  
complexity of the problem itself.  In his book "Vision", Marr proposed  
(in what he referred to actually as a 'bottom up' approach to  
understanding the nervous system), that one must first understand the  
nature of the computational problem being solved, and then consider  
the set of algorythms that could solve the problem and then and only  
then, look at the particular instance of that set implemented in the  
brain (under the assumption that the brain was not KCC).   Complexity  
theory provides a formal framework (oh that again) for considering the  
relationship between the inherent complexity of a particular problem,  
and the complexity of the solution to that problem -- I believe (and  
someone will surely correct me if I am wrong), there is a fundamental  
principle that the complexity of the problem sets a kind of floor for  
the complexity of the solutions to the problem.   That is, you can  
find more complex solutions to a problem -- but you can't find a  
solution with less complexity than the problem itself, if you did,  
then you could recast the original problem in a less complex form.   
Accordingly, if the brain is KCC, then, by definition, solutions to  
real brain problems involving 4 input 'neurons', 10 in the hidden  
layer, and 3 output 'neurons' must be underestimating the real nature  
of the problem the brain solves.  Or in other words, if the solution  
to the problem is less complex than the brain, then one has  
misunderstood the problem.

In this context, Todd Troyer's post today makes the rather important  
point, that probably our greatest deficiency in studying the brain is  
that our understanding of the complexities of natural behavior  
significantly lags even our understanding of the structure of neurons.  
And yes, neuroethology is the branch of neuroscience that has made the  
effort to try to link behavior (and even natural behavior) to the  
brain.  Linking to a previous post, most (although not all)  
neuroethologists study "simpler" systems.  Furthermore, the roots of  
neuroethology are european, and place much more emphasis on innate  
patterns of behavior, than did american behaviorists, who did think  
that with the right combination of m and m's, animals could  
significantly stretch what they associated with what.

Anyway, neurobiologists are very adept at designing behavioral  
experiments in which the complexites of real behavior are  
"controlled".  In doing so, they run the risk of turning the nervous  
systems of monkeys (for example)  into "oriented bar detectors" rather  
than real functioning nervous systems.   Of course, monkeys do  
everything in their power to use their full brains to second guess  
experimentalists - and therefore an important feature of the process  
of training monkeys is to defeat their efforts (as one of my monkey  
studying friends has said) to find a complex solution to  what is  
really a simple problem you want them to solve.  ie. one has to  
convince the monkey's brain that you really only want it to do  
something dumb - because, of course, the monkey's brain is not  
inclined to believe that it is supposed to do dumb things, especially  
when it is extremely thirsty.  Anyway, I assume that most of you would  
agree that our lack of understanding (or even efforts to understand)  
complex natural behavior is a rather significant problem.  If you  
don't really know what the thing does (ie. you don't study the  
circumstances for which it was engineered), that should at least  
complicate the process of understanding the engineering.

But anyway, returning to Bard's post and something a bit more  
concrete, lets discuss dendrites, which are the brain objects most  
brutalized by abstract modeling.

In one view (offered by Bard below - although not necessarily  
completely reflecting his point of view I am sure), practical  
considerations of building stuff in real stuff (carbon), means that  
if, for whatever reasons, a neuron needs to receive 150,000 excitatory  
synaptic inputs (like the Cerebellar Purkinje cell), it has no choice  
but to have a large dendrite -- and one uses currents in those  
dendrites to effectively negate its existence by making the spatial  
position of a particular input on the dendrite irrelevant with respect  
to the soma.  Ironically enough, to my knowledge the first  
demonstration of this effective form of spatial independence in a  
complex realistic model was generated by our own work (De Schutter,  
E., and Bower, J.M. (1994)  Responses of cerebellar Purkinje cells  
are  independent of the dendritic location of granule cell synaptic  
inputs.  Proc. Natl. Acad. Sci. (US). 91: 4736-4740).  If this was all  
that was going on, it is likely that there is some (non-stuff  
constrained) mathematical description that could capture the essence  
of the cell with less complexity.  In fact, several examples for the  
Purkinje cell have already been generated.

However, there is another consequence of dendrites occupying physical  
space that almost certainly is important to neuronal function, and  
that is the opportunity it allows for local interactions to produce  
differences in local responses due to the particular patterns of local  
inputs.  Here I am not talking about the relatively simple  "soma- 
centric" form of pattern recognition, that underlies a great deal of  
current thinking about how neurons work (including sadly cerebellar  
Purkinje cell: Steuber, V, Mittmann, W, Hoebeek, F.E., De Zeeuw, C.I.,  
Hausser, M., De Schutter, E.  Cerebellar LTD and pattern recognition  
in Purkinje cells, Neuron54: 121-136, 2007), but instead about the  
kind of local response complexities that can result from slight  
differences in timing between different inputs (as was demonstrated in  
the earliest models by Rall).  Unfortunately, we know next to nothing  
about the actual (natural) complexities of input patterns on neurons  
in mammalian brains.  Is there a reduced model of a neuron that can  
still deal with all the possible combinations of effects produced by  
variations in local patterns of inputs, that has less than the  
complexity of the neuron -- I doubt it - although I also suspect that  
some of the interest in cortical oscillations is driven by the desire  
to constrain the possible spatial temporal patterns of inputs to  
single cells (which of course, oscillations don't).  Anyway, if one  
considers in addition, that inputs to dendrites are not only  
excititory, but inhibitory, and the interactions between excitation  
and inhibition can be very complex, not only post-synaptically, but  
also because the circuitry dictating the timing for each is often  
different,  And then at the level of spines and channels (and  
molecules), their are timing dependent interacts operating over  
multiple time scales (including those governing the plastic changes we  
all like to attribute to the physical manifestation of "learning") and  
for sure these interactions are primarily local, and then throw in the  
fact that it appears that different regions of the dendrite have  
different types of channels (as well as different kinds of inhibition,  
etc), all of which can be modulated by chemicals (modulators) that  
also often have different distributions in dendrites, it sure looks  
like evolution has "used" the physical space it has no choice but to  
deal with, to pack in a rather spectacular amount of complexity.

Finally, to return to the grand, one of the arguments used (completely  
inappropriately) by the creationists against evolutionists, is that  
the second law of thermodynamics precludes the generation of complex  
structures without some form of intelligent intervention (for your  
amusement if you are interested in this debate:        http://video.google.com/videoplay?docid=4007930854195650071&ei=V6qpSOvtIYiE4QLNx7zRAg&q=James+bower+creationism&hl=en) 
.  Of course, this is a fundamental misunderstanding of the second  
law, which is stated and considered in the context of a closed system  
(an example of the use of assumptions in physics to reduce complexity  
and thus facilitate understanding - but perhaps miss the point).  The  
second law could just as well be formulated to consider the case in  
which there is a continual source of energy (the sun), influencing  
chemistry -- under those conditions, the chemistry becomes more and  
more complicated -- producing what we call "life" (in  my case only  
for convenience).  Even with the sun shining, selection is a very  
tough master -- and efficiency matters -- everywhere it has been  
measured (frogs, etc), selection by females pushes males to their  
physical "phelpian" limits (swim Michael swim).  This, I think is what  
has pushed the brain to KCCness, along with one female related factor.

In fact, space in the brain is not a giveaway - there are neurons with  
almost no dendrites, and also neurons with extensive dendrites.  In  
KCC terms, the brain would, for certain, limit its size by any means  
necessary.  Why?

A number of years ago - I was at one of the early Neural Network  
meetings, and was eating lunch with a bunch of NN practisioners - the  
question at hand was, given that large brains (read 'intellegance") is  
so adaptive, why aren't our brains twice as large?  My response (and  
you already know sometimes I say things I shouldn't), was -- well --  
perhaps you should ask your wife, but perhaps the fact that most of  
you are still single suggests that big brains might not be as adaptive  
as you think.

Ah well, another misjudged effort at humor.

Best to all,


> - Years ago Carson and I would go to neuro lectures (which I  
> generally find far more accessible than math colloquia - and I am a  
> professional mathematician! - which speaks on the issue that I think  
> it is far easier form a mathematician  to gain an appreciation for  
> biology than vice versa, but I digress) and there were a number on  
> the complex channels found in dendrites which from an evolutionary  
> point of view, must be quite costly. However, in almost all the  
> cases, the final point of the speaker was that this was to  
> compensate fro being out at the end of the dendrite, so that we used  
> to say that nature is trying to make all neurons point neurons.  
> Computationally, we can put as many inputs as we want into a point -  
> but anatomy and physiology prevent this in real cells, hence the  
> complex structure.
> - This leads to a second point - the neural turing test. (There have  
> been contests related to this). I recently heard Eugene Izhikevich  
> give a talk and he showed a picture of a recording froma cortical  
> pyramidal cell receiving a complex stimulus pattern (whatever that  
> means, Jim) and his 2 variable 4 parameter model - the sub and super  
> threshold behavior was almost indistinguishable and this model was  
> fit for the FI curve only. I realize that the pyramidal cell  
> stimulus was quite simplistic, but one could presumably do the same  
> stim mixed with other stimuli in the dendrites. maybe there are  
> complex dendritic calculations going on - but the bottom line is  
> what is the output of the cell - that is all that matters. So any  
> model that does this in a reasonable way will, to me, be a realistic  
> model since the cell on the other side of the wall cannot  
> distinguish it. I would guess that Jim Bower would claim there is no  
> such model that does this except the most delatiled model with all  
> the channels and structure. However, I am less pessimistic about  
> this for the following reason:
> -Yannis Kevrikides has deveolped some very useful numerical tools  
> that exploit a common freature in many complex physical and  
> biological systems (here, I am a strong reductionist and believe  
> with every fiber of my body that biology is describable by physical  
> pronciples - I lost all shreds of mysticism in Nov 1969 - although I  
> continued to exploit others making money casting horoscopes - a  
> mathematical exercise, in fact)
> basically, most systems, even complex ones, behave in such a manner  
> as to drastically reduce dimensionality. They are strongly  
> contracting or dissipative and as a consequence, are captured by far  
> fewer degrees of freedom. Kevrikides methods allow one to compute in  
> these lower degrees without knowing the underlying reduced  
> equations. Nevertheless, they are there. Mathematicians and  
> physicists have used these ideas for years and call it averaging,  
> mean field reduction, etc and of course experimentalists do use  
> these ideas as well and call it PCA in which they show that only a  
> few modes capture the majority of the variance. Thus, the Turing  
> test neuron is not pie in the sky and I believe that there are  
> reduced models that will do what the "realistic" model does with as  
> much precision as you would like.
> Regards
> Bard Ermentrout
> _______________________________________________
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> Comp-neuro at neuroinf.org
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Dr. James M. Bower Ph.D.

Professor of Computational Neuroscience

Research Imaging Center
University of Texas Health Science Center -
-  San Antonio
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San Antonio Texas  78284-6240

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