[Comp-neuro] Mosaic of Detailed and Abstract (was Attractors, variability and noise)

[Mario Negrello]

Chris wrote:
> I'm quite disappointed at the 'detailed' vs 'abstract' debate --
> both are relevant *depending on the explanatory target*.
> *Unified* explanations will come by being able to move between
> these levels of description smoothly (notably this has not yet
> been achieved by physics either).
Fair poit. But I think the question is whether the 'explanatory  
targets' of 'abstract' can be made to 'smoothly' interface with the  
'detailed' in a whole picture. Can we beat the physicists in moving  
between levels of description?

For instance, there are many theorems one can prove about synchrony  
with the kuramoto model of coupled oscilators, loved for its  
simplicity. Those conclusions are contained in the language of the  
model. I am aware of no story as to how a compartmental model is like  
the kuramoto model, and which of the conclusions of kuramoto can be  
applied to compartmental. But i can imagine someone searching for the  
correspondence between the two, so as to justify the conclusions of  
the kuramoto model (or vice versa). It is not too hard to come up with  
such a story. The drawback is that in this case, we are modelling  
models.

A concrete example modelling models is Judith Dayhof's model of  
networks of synchronous spiking neurons, in which she found that  
synchronous communicating populations act like sigmoids. Lovely  
conclusion for everybody out there using sigmoidal units, of course.  
But, and this is a big one, the sigmoids are amalgamating in firing  
rates, what in the origin are individual spikes. So, in principle,  
from a certain perspective one sees the sigmoids, but much more may be  
concealed behind averaging. Hypothetically, there could be properties  
in the individual spikes that would falsify the conclusion (such as  
long paths). And i don't even mention the assumptions that are  
necessary to make stitching of models work.

If to build an abstract model is to create a piece of a scientific  
puzzle, it is not clear to me that it is possible to position the  
piece in a bigger puzzle. The pieces from other puzzles may not fit,  
be contraditory, or be incomensurable, such as in physics as you  
pointed out. I haven't read the mosaic article you referenced below,  
but the analogy stumbles on the form of the pieces of the mosaic, and  
whether new pieces can be easily integrated. That shape of those  
pieces has much to do with the language of the theory that begets the  
model. Correspondances between models is not necessary by a long shot.

Every every computational model, like any method of empirical  
assessment, produces results in according to what it sees, in the  
language it speaks, while neglecting what it does not. Putting models  
together is similar, one has to come up with translations, and as it  
goes, translations invoke ad-libs on the part of the translator. This  
creative freedom is what complicates the affairs when one builds  
hierarchical models of models. Smooth transitions in hierarchical  
compositions of models are subjective stitches which show.

For me, the debate was 'abstract' vs. 'detailed' only in this sense:  
conclusions of one are not necessarily compatible with the other. And  
to make them so, is often to tell a story. A mathematically tenable  
story, to be sure, but still a story.


[1]	J. Dayhoff. Computational Properties of Networks of Synchronous  
Groups of Spiking Neurons. Neural Computation, 19(9):2433, 2007.



> The centrality of mechanisms, hierarchies of such, decomposition
> and synthesis of complex systems has become a clear
> focus of recent philosophy of science (Craver 2004;
> Bechtel & Richardson, 1993; all of which is far more relevant to
> biology than Kuhn).  This emphasis eliminates the polarized
> debate currently taking place on this list.
Maybe. But polarizing debates highlights contrasts.

Cheers, M.

> Eliasmith, C. and C. H. Anderson (2003). Neural Engineering:  
> Computation, representation and dynamics in neurobiological systems.
> MIT Press.
>
> Singh, R. and C. Eliasmith (2006). Higher-dimensional neurons  
> explain the tuning and dynamics of working memory cells. Journal of  
> Neuroscience. 26: 3667-3678.
>
> Litt, Eliasmith, & Thagard, (in press) Neural affective decision
> theory: Choices, brains, and emotions, Cognitive Systems Research  
> Available online 14 April 2008. doi:10.1016/j.cogsys.2007
> (http://www.sciencedirect.com/science/article/B6W6C-4S8TBBS-1/2/259722b8d5c60fb9906a76437cde38fb 
> )
>
> Bechtel, W. and Richardson, R. C. (1993). Discovering complexity:  
> Decomposition and localization as strategies in scientific research.  
> Princeton: Princeton University Press.
>
> Craver (2007) Explaining the brain: mechanisms and the mosaic unity  
> of neuroscience. Oxford University Press.
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