A Multiscale Scheme for Approximating the Quantron´s Discriminating Function

Finding an accurate approximation of a discriminating function in order to evaluate its extrema is a common problem in the field of machine learning. A new type of neural network, the Quantron, generates a complicated wave function whose global maximum value is crucial for classifying patterns. To obtain an analytical approximation of this maximum, we present a multiscale scheme based on compactly supported inverted parabolas. Motivated by the Quantron´s architecture as well as Laplace´s method, this scheme stems from the multiresolution analysis (MRA) developed in the theory of wavelets. This approximation method will be performed, first, one scale at a time and, second, as a global approach. Convergence will be proved and results analyzed.