Self-organization of two interacting winner-take-all systems

Winner-take-all (WTA) networks are ubiquitous in computational models of the brain. A WTA system determines its largest input. If the input space is the product of multiple factors, search in the product space can be expensive, in which case it is computationally attractive to work on the marginal factors. In this paper we study the organization of two interacting WTA systems, one for each factor. We give analytical results on the fixed points of this system, and illustrate a few issues on the relative speed of convergence of the two factors.