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).