Learning-machines-committee averages over the unitary group of matrices

A committee of learning machines may be conceived of as a group of adaptive systems that adapt independently of each other and whose goal is to solve a common learning problem. Each machine in a committee computes a set of parameter-patterns belonging to a curved space. A natural question is how to combine the learnt patterns in order to obtain a better solution to the learning problem. In the present paper, we treat the case that the parameter space is the Lie group of unitary matrices. In order to combine the learnt patterns, we discuss a possible merging technique based on the differential geometrical structure of the parameter manifold.