We describe symmetries of feedforward networks in terms of their corresponding groups, which naturally act on and partition weight space. This leads to an algorithm that generates representative weight vectors in a specific fundamental domain. The closure of this domain turns out to be a manifold with singular points. We derive a canonical metric for the manifold that can be implemented efficiently even for large networks. One application would be the clustering of resulting weight vectors of an experiment in order to identify inadequate models or learning methods.