On the convergence of validity interval analysis

Validity interval analysis (VIA) is a generic tool for analyzing the input-output behavior of feedforward neural networks. VIA is a rule extraction technique that relies on a rule refinement algorithm. The rules are of the form R_i→R₀ i.e. "if the input of the neural network is in the region R_i, then its output is in the region R₀," where regions are axis parallel hypercubes. VIA conjectures, then refines and checks rules for inconsistency. This process can be computationally expensive, and the rule refinement phase becomes critical. Hence, the importance of knowing the complexity of these rule refinement algorithms. In this paper, we show that the rule refinement part of VIA always converges in one run for single-weight-layer networks, and has an exponential average rate of convergence for multilayer networks. We also discuss some variations of the standard VIA formulae