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A Fly on the Wall of Mean Field Theory

October 17, 2011

Recently I attended a great workshop in Marseilles, France on mean field methods in neural modeling (click here if you don’t know what that means). It was wonderfully organized by Nicolas Brunel (University of Paris 5) and Olivier Faugeras (INRIA Sophia Antipolis), and I went as a fly to a feast of mathematicians. Though everyone there was warm and welcoming, I did feel like a member of a different (and lower) species due to my limited mathematical background. I met many amazing people, but not one of them was an experimentalist or an engineer. In one sense, that was good because I’m more of a lone fly – the type that doesn’t like to hang out with the swarm. I had one main goal: to find out if these folks really have something that an experimentalist and engineer can use. In the end, I’m still not sure. Perhaps I missed the forest for the trees.

In case you’re wondering which one I am, experimentalist or engineer, I’m both. This post explains a little, but I also spent two years working in an electrophysiology lab under the guidance of the incredibly generous Chris Wilson. My real talent is translating knowledge across fields, as opposed to a technical prowess in any specific domain. I viewed myself as a cross-pollinating fly on the wall rather than a scavenger. At the workshop, the mathematicians were clearly seeking the golden equation that will advance the field of mathematics. In my world, I’m really seeking the golden experiment that will advance the field of neuroscience. In Marseilles I saw many a slide of experimental data. In every such case, however, it seemed that the data was the prelude and the model was the finale. No cycle. No symbiosis. No reinjection of theory back into reality. Of course, these were mathematicians talking to mathematicians. This was not an SfN meeting, so no big surprise there.

That lack of biology was one disappointment with the workshop. Another was my sense that the majority of the mathematicians really had no worries about whether their models had any real parallels with finite physiology. The program description literally stated an interest in an approach that is “amenable to experimental testing” and that clarifies the relationship between spiking networks and neural field models. Years ago I flirted with the use of mean field modeling for studying truly biological neuroscience, but I couldn’t see the connection and was compelled to move on. I decided to try again, so I spent 8+ hours crossing the Atlantic Ocean and full of anticipation of seeing where the mean field rubber hits the road. I’m a modeler too, and I know that every model (including my own) is wrong by default. I simply wanted a better understanding of what is “wrong” with mean field modeling. Not many people were concerned with this at the workshop though. There were some, like the fascinating Carson Chow (NIH) who has published on finite-size effects, and the passionate Aaditya Rangan (New York University) who posed the question of the importance of subpopulation correlations in the context of mean field modeling. Unfortunately for me, these interests seemed to languish on the fringe.

Do I sound negative? I began this post by saying the workshop was “great”. Well, it was, but mainly because of the caliber and character of the passionate people that I met. I came back to the States with two important impressions from that workshop: (1) Mean field modeling has been kept alive mainly by a brilliant group of mathematicians. (2) The public bridge between mean field theory and the reality of biology is far, far away from the beaten path. In a way, I feel I’ve discovered some remote, isolated tribe with a challenging language but a wonderful openness. To mix my metaphors, I hope I can buzz around these people enough to pollinate more connections to my own world.


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