Combining Multilayer Networks to Combine Learning

This paper explores methods to combine networks, implementations of network combination on multicomputers, and applications of network combination. We divide the network combination process into two steps. First, a matching algorithm rearranges the networks so that corresponding weights in the networks being combined play corresponding roles in the networks' functions. Then a proportioning algorithm chooses a convex combination of the matched networks. The combination network is a weight-by-weight convex combination of the matched networks. This paper begins by examining combinations of pairs of networks. Matching and proportioning algorithms are developed, analyzed, implemented, and tested. Next, algorithms are developed to combine several networks. Then the combination process is poked and prodded to explore its nature, its utility, and its limits.