The Metric Structure of Weight Space

Authors:
Stefan M. Rüger;Arnfried Ossen
Affiliations:
Fachbereich Informatik, Technische Universität Berlin, Sekr. FR 5-9, D-10 587 Berlin, Germany. E-mail: async@cs.tu-berlin.de, ao@cs.tu-berlin.de;Fachbereich Informatik, Technische Universität Berlin, Sekr. FR 5-9, D-10 587 Berlin, Germany. E-mail: async@cs.tu-berlin.de, ao@cs.tu-berlin.de
Venue:
Neural Processing Letters
Year:
1997

Citing 4
Cited 0

Original Contribution: Uniqueness of the weights for minimal feedforward nets with a given input-output map

Neural Networks
On the geometry of feedforward neural network error surfaces

Neural Computation
Artificial Neural Networks: Approximation and Learning Theory

Artificial Neural Networks: Approximation and Learning Theory
Clustering in Weight Space of Feedforward Nets

ICANN 96 Proceedings of the 1996 International Conference on Artificial Neural Networks

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Abstract

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