Weight space analysis and forecast uncertainty

The usage of location information of weight vectors can help to overcome deficiencies of gradient-based learning for neural networks. We study the non-trivial structure of weight space, i.e. symmetries of feedforward networks in terms of their corresponding groups. We find that these groups naturally act on and partition weight space into disjunct domains. We derive an algorithm to generate representative weight vectors in a fundamental domain. The analysis of the metric structure of the fundamental domain leads to a clustering method that exploits the natural metric of the fundamental domain. It can be implemented efficiently even for large networks. We used it to improve the assessment of forecast uncertainty for an already successful application of neural networks in the area of financial time series.