Ehresmann connections and feedforward neural networks

In this paper, we describe how Ehresmann connections can be used to study certain properties of feedforward neural networks. Essentially, we calculate a Lie group approximation to the structure of the inverse image set above a certain point in the output space and this structure can then be locally transported to the inverse image above a, neighbouring point in the output space by means of an Ehresmann connection. This enables us to find a continuous approximation to the underlying topological structure of the data from discrete data pairs (input/output pairs). (C) 1999 Elsevier Science Ltd. All rights reserved.