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A new field of research is rapidly expanding at the crossroad betweenstatistical physics, information theory and combinatorial optimization. Inparticular, the use of cutting edge statistical physics concepts and methodsallow one to solve very large constraint satisfaction problems like randomsatisfiability, coloring, or error correction. Several aspects of thesedevelopments should be relevant for the understanding of functional complexityin neural networks. On the one hand the message passing procedures which areused in these new algorithms are based on local exchange of information, andsucceed in solving some of the hardest computational problems. On the otherhand some crucial inference problems in neurobiology, like those generated inmulti-electrode recordings, naturally translate into hard constraintsatisfaction problems. This paper gives a non-technical introduction to thisfield, emphasizing the main ideas at work in message passing strategies andtheir possible relevance to neural networks modeling. It also introduces a newmessage passing algorithm for inferring interactions between variables fromcorrelation data, which could be useful in the analysis of multi-electroderecording data.

Constraint satisfaction problems and neural networks: a statistical physics perspective