Building Function Approximators on top of Haar Scattering Networks

The field of artificial neural networks has exploded during the 1980s due to its universal approximation capabilities, as can be seen in [1], but the lack of understanding of the underlying statistical and geometric features extracted from the analyzed signal discouraged significantly its usage among scientists and researchers, as can be seen in [2-3]. Since then, most of its usage has been relegated to applications where such understanding can be neglected, such as computer vision, nonlinear statespace estimators and other tasks related to control where exact algorithmic approaches are unknown or too difficult to implement, according to [3]. More recently, aiming to enlightening these black-boxes, several approaches have been under heavy development, such as variables contributions in the feed forward structure [4], visualization using saliency maps [5], generation of skeletal structures [6], fuzzy rule based evaluation of all permutations [3], extraction of functional relations using sensitivity analysis of input data [7], as many others. In a parallel way, other researchers have been successfully developing new kinds of feed-forward neural architectures that behave much more like a transparent box, where the extracted features can be directly evaluated and understood. Convolutional Neural Networks are a great example of such achievements, as can be seen in [8-10]. Despite its several layers, they can be employed on different types of tasks, including text classification, natural language processing, computer vision and so on, with a good understanding of what is happening behind the curtains. Manuscript received January 15, 2018. This work was supported in part by the FIPE (Institute of Economic Research Foundation) by means of a postdoctoral scholarship.