Modularity, evolution, and the binding problem: a view from stability theory

Any biological object, and specifically the brain, is the result of evolution. Evolution proceeds by accumulation and combination of stable intermediate states-as is well known, survival of the fittest really means survival of the stable. Simple examples abound: for instance, human emotional response involves both a fast archaic loop bypassing the cortex, and a slower cortical loop; motion control architecture in vertebrates is believed to involve combinations of simple motor primitives. However, in themselves, accumulations and combinations of stable elements have no reason to be stable. Hence the hypothesis that evolution will favor a particular form of stability, which automatically guarantees stability in combination. Such a form of stability, which we refer to as 'contraction,' can be characterized mathematically. Thus, contraction theory may help guide functional modeling of the central nervous system, and conversely it provides a systematic method to build arbitrarily complex robots out of simpler elements. Furthermore, contraction theory may shed light on the problem of perceptual unity (binding problem) by providing simple models and conditions for the overall convergence of a large number of specialized processing elements connected through networks of feedback loops.