In press: M. Arbib (Ed.), The Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press.

Abstract

this article we discuss the problem of learning in modular and hierarchical systems. Modular and hierarchical systems allow complex learning problems to be solved by dividing the problem into a set of sub-problems, each of which may be simpler to solve than the original problem. Within the context of supervised learning---our focus in this article---modular architectures arise when we assume that the data can be well described by a collection of functions, each of which is defined over a relatively local region of the input space. A modular architecture can model such data by allocating di#erent modules to di#erent regions of the space. Hierarchical architectures arise when we assume that the data are well described by a multi-resolution model---a model in which regions are divided recursively into sub-region